Content check — Elementary Algebra, Chapter 1: Foundations

Every problem in the chapter beside the book’s answer, a chapter at a time as you scroll.

Chapter 1: Foundations

981 problems · 16 figures

Try It 1.1 §1.1 source ↗

For the number 27,493,615, find the place value of each digit:

ⓐ 2 ⓑ 1 ⓒ 4 ⓓ 7 ⓔ 5

Answer

ⓐ ten millions ⓑ tens ⓒ hundred thousands ⓓ millions ⓔ ones

Try It 1.2 §1.1 source ↗

For the number 519,711,641,328, find the place value of each digit:

ⓐ 9 ⓑ 4 ⓒ 2 ⓓ 6 ⓔ 7

Answer

ⓐ billions ⓑ ten thousands ⓒ tens ⓓ hundred thousands ⓔ hundred millions

Try It 1.3 §1.1 source ↗

Name the number

9,

258,

137,

904,

061

using words.

Answer

nine trillion, two hundred fifty-eight billion, one hundred thirty-seven million, nine hundred four thousand, sixty-one

Try It 1.4 §1.1 source ↗

Name the number

17,

864,

325,

619,

004

using words.

Answer

seventeen trillion, eight hundred sixty-four billion, three hundred twenty-five million, six hundred nineteen thousand, four

Try It 1.5 §1.1 source ↗

Write the number two billion, four hundred sixty-six million, seven hundred fourteen thousand, fifty-one as a whole number using digits.

Answer

2,466,714,051

Try It 1.6 §1.1 source ↗

Write the number eleven billion, nine hundred twenty-one million, eight hundred thirty thousand, one hundred six as a whole number using digits.

Answer

11,921,830,106

Try It 1.7 §1.1 source ↗

Round to the nearest hundred:

17,852 .

Answer

17,900

Try It 1.8 §1.1 source ↗

Round to the nearest hundred:

468,751 .

Answer

468,800

Try It 1.9 §1.1 source ↗

Round 206,981 to the nearest: ⓐ hundred ⓑ thousand ⓒ ten thousand.

Answer

ⓐ 207,000 ⓑ 207,000 ⓒ 210,000

Try It 1.10 §1.1 source ↗

Round 784,951 to the nearest: ⓐ hundred ⓑ thousand ⓒ ten thousand.

Answer

ⓐ 785,000 ⓑ 785,000 ⓒ 780,000

Try It 1.11 §1.1 source ↗

Determine whether 4,962 is divisible by 2, by 3, by 5, by 6, and by 10.

Answer

by 2, 3, and 6

Try It 1.12 §1.1 source ↗

Determine whether 3,765 is divisible by 2, by 3, by 5, by 6, and by 10.

Answer

by 3 and 5

Try It 1.13 §1.1 source ↗

Find the prime factorization of 80.

Answer

2 \cdot 2 \cdot 2 \cdot 2 \cdot 5

Try It 1.14 §1.1 source ↗

Find the prime factorization of 60.

Answer

2 \cdot 2 \cdot 3 \cdot 5

Try It 1.15 §1.1 source ↗

Find the prime factorization of 126.

Answer

2 \cdot 3 \cdot 3 \cdot 7

Try It 1.16 §1.1 source ↗

Find the prime factorization of 294.

Answer

2 \cdot 3 \cdot 7 \cdot 7

Try It 1.17 §1.1 source ↗

Find the least common multiple by listing multiples: 9 and 12.

Answer

Try It 1.18 §1.1 source ↗

Find the least common multiple by listing multiples: 18 and 24.

Answer

Try It 1.19 §1.1 source ↗

Find the LCM using the prime factors method: 9 and 12.

Answer

Try It 1.20 §1.1 source ↗

Find the LCM using the prime factors method: 18 and 24.

Answer

Try It 1.21 §1.1 source ↗

Find the LCM using the prime factors method: 21 and 28.

Answer

Try It 1.22 §1.1 source ↗

Find the LCM using the prime factors method: 24 and 32.

Answer

1.1-1 §1.1 source ↗

Use Place Value with Whole Numbers

In the following exercises, find the place value of each digit in the given numbers.

51,493 ⓐ 1, ⓑ 4, ⓒ 9, ⓓ 5, ⓔ 3

Answer

ⓐ thousands ⓑ hundreds ⓒ tens ⓓ ten thousands ⓔ ones

1.1-3 §1.1 source ↗

Use Place Value with Whole Numbers

In the following exercises, find the place value of each digit in the given numbers.

164,285 ⓐ 5, ⓑ 6, ⓒ 1, ⓓ 8, ⓔ 2

Answer

ⓐ ones ⓑ ten thousands ⓒ hundred thousands ⓓ tens ⓔ hundreds

1.1-5 §1.1 source ↗

Use Place Value with Whole Numbers

In the following exercises, find the place value of each digit in the given numbers.

93,285,170 ⓐ 9 ⓑ 8 ⓒ 7 ⓓ 5 ⓔ 3

Answer

ⓐ ten millions ⓑ ten thousands ⓒ tens ⓓ thousands ⓔ millions

1.1-7 §1.1 source ↗

Use Place Value with Whole Numbers

In the following exercises, find the place value of each digit in the given numbers.

7,284,915,860,132 ⓐ 7 ⓑ 4 ⓒ 5 ⓓ 3 ⓔ 0

Answer

ⓐ trillions ⓑ billions ⓒ millions ⓓ tens ⓔ thousands

1.1-9 §1.1 source ↗

In the following exercises, name each number using words.

1,078

Answer

one thousand, seventy-eight

1.1-11 §1.1 source ↗

In the following exercises, name each number using words.

364,510

Answer

three hundred sixty-four thousand, five hundred ten

1.1-13 §1.1 source ↗

In the following exercises, name each number using words.

5,846,103

Answer

five million, eight hundred forty-six thousand, one hundred three

1.1-15 §1.1 source ↗

In the following exercises, name each number using words.

37,889,005

Answer

thirty-seven million, eight hundred eighty-nine thousand, five

1.1-17 §1.1 source ↗

In the following exercises, write each number as a whole number using digits.

four hundred twelve

Answer

412

1.1-19 §1.1 source ↗

In the following exercises, write each number as a whole number using digits.

thirty-five thousand, nine hundred seventy-five

Answer

35,975

1.1-21 §1.1 source ↗

In the following exercises, write each number as a whole number using digits.

eleven million, forty-four thousand, one hundred sixty-seven

Answer

11,044,167

1.1-23 §1.1 source ↗

In the following exercises, write each number as a whole number using digits.

three billion, two hundred twenty-six million, five hundred twelve thousand, seventeen

Answer

3,226,512,017

1.1-25 §1.1 source ↗

In the following, round to the indicated place value.

Round to the nearest ten.

ⓐ 386 ⓑ 2,931

Answer

ⓐ 390 ⓑ 2,930

1.1-27 §1.1 source ↗

In the following, round to the indicated place value.

Round to the nearest hundred.

ⓐ 13,748 ⓑ 391,794

Answer

ⓐ 13,700 ⓑ 391,800

1.1-29 §1.1 source ↗

In the following, round to the indicated place value.

Round to the nearest ten.

ⓐ 1,492 ⓑ 1,497

Answer

ⓐ 1,490 ⓑ 1,500

1.1-31 §1.1 source ↗

In the following, round to the indicated place value.

Round to the nearest hundred.

ⓐ 63,994 ⓑ 63,940

Answer

ⓐ 64,000 ⓑ 63,900

1.1-33 §1.1 source ↗

In the following exercises, round each number to the nearest ⓐ hundred, ⓑ thousand, ⓒ ten thousand.

392,546

Answer

ⓐ 392,500 ⓑ 393,000 ⓒ 390,000

1.1-35 §1.1 source ↗

In the following exercises, round each number to the nearest ⓐ hundred, ⓑ thousand, ⓒ ten thousand.

2,586,991

Answer

ⓐ 2,587,000 ⓑ 2,587,000 ⓒ 2,590,000

1.1-37 §1.1 source ↗

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10.

Answer

divisible by 2, 3, and 6

1.1-39 §1.1 source ↗

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10.

Answer

divisible by 3 and 5

1.1-41 §1.1 source ↗

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10.

900

Answer

divisible by 2, 3, 5, 6, and 10

1.1-43 §1.1 source ↗

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10.

986

Answer

divisible by 2

1.1-45 §1.1 source ↗

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10.

350

Answer

divisible by 2, 5, and 10

1.1-47 §1.1 source ↗

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10.

22,335

Answer

divisible by 3 and 5

1.1-49 §1.1 source ↗

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

Answer

2 \cdot 43

1.1-51 §1.1 source ↗

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

132

Answer

2 \cdot 2 \cdot 3 \cdot 11

1.1-53 §1.1 source ↗

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

693

Answer

3 \cdot 3 \cdot 7 \cdot 11

1.1-55 §1.1 source ↗

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

432

Answer

2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3

1.1-57 §1.1 source ↗

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

2,160

Answer

2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5

1.1-59 §1.1 source ↗

In the following exercises, find the least common multiple of the each pair of numbers using the multiples method.

8, 12

Answer

1.1-61 §1.1 source ↗

In the following exercises, find the least common multiple of the each pair of numbers using the multiples method.

12, 16

Answer

1.1-63 §1.1 source ↗

In the following exercises, find the least common multiple of the each pair of numbers using the multiples method.

20, 30

Answer

1.1-65 §1.1 source ↗

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

8, 12

Answer

1.1-67 §1.1 source ↗

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

28, 40

Answer

280

1.1-69 §1.1 source ↗

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

55, 88

Answer

440

1.1-71 §1.1 source ↗

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

Writing a Check Jorge bought a car for $24,493. He paid for the car with a check. Write the purchase price in words.

Answer

twenty-four thousand, four hundred ninety-three dollars

1.1-73 §1.1 source ↗

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

Buying a Car Jorge bought a car for $24,493. Round the price to the nearest ⓐ ten ⓑ hundred ⓒ thousand; and ⓓ ten-thousand.

Answer

ⓐ $24,490 ⓑ $24,500 ⓒ $24,000 ⓓ $20,000

1.1-75 §1.1 source ↗

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

Population The population of China was 1,339,724,852 on November 1, 2010. Round the population to the nearest ⓐ billion ⓑ hundred-million; and ⓒ million.

Answer

ⓐ 1,000,000,000 ⓑ 1,300,000,000 ⓒ 1,340,000,000

1.1-77 §1.1 source ↗

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

Grocery Shopping Hot dogs are sold in packages of 10, but hot dog buns come in packs of eight. What is the smallest number that makes the hot dogs and buns come out even?

Answer

1.1-79 §1.1 source ↗

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

Give an everyday example where it helps to round numbers.

Answer

Answers may vary.

1.1-81 §1.1 source ↗

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

What is the difference between prime numbers and composite numbers?

Answer

Answers may vary.

Try It 1.23 §1.2 source ↗

Translate from algebra into English:

ⓐ $14 \leq 27$ ⓑ $19 - 2 \neq 8$ ⓒ $12 > 4 \div 2$ ⓓ $x - 7 < 1$

Answer

ⓐ 14 is less than or equal to 27 ⓑ 19 minus 2 is not equal to 8 ⓒ 12 is greater than 4 divided by 2 ⓓ x minus 7 is less than 1

Try It 1.24 §1.2 source ↗

Translate from algebra into English:

ⓐ $19 \geq 15$ ⓑ $7 = 12 - 5$ ⓒ $15 \div 3 < 8$ ⓓ $y + 3 > 6$

Answer

ⓐ 19 is greater than or equal to 15 ⓑ 7 is equal to 12 minus 5 ⓒ 15 divided by 3 is less than 8 ⓓ y plus 3 is greater than 6

Try It 1.25 §1.2 source ↗

Determine if each is an expression or an equation: ⓐ

3 (x - 7) = 27

ⓑ

5 (4 y - 2) - 7

Answer

ⓐ equation ⓑ expression

Try It 1.26 §1.2 source ↗

Determine if each is an expression or an equation: ⓐ

y^{3} \div 14

ⓑ

4 x - 6 = 22

Answer

ⓐ expression ⓑ equation

Try It 1.27 §1.2 source ↗

Simplify: ⓐ

5^{3}

ⓑ

1^{7} .

Answer

ⓐ 125 ⓑ 1

Try It 1.28 §1.2 source ↗

Simplify: ⓐ

7^{2}

ⓑ

0^{5} .

Answer

ⓐ 49 ⓑ 0

Try It 1.29 §1.2 source ↗

Simplify: ⓐ

12 - 5 \cdot 2

ⓑ

(12 - 5) \cdot 2 .

Answer

ⓐ 2 ⓑ 14

Try It 1.30 §1.2 source ↗

Simplify: ⓐ

8 + 3 \cdot 9

ⓑ

(8 + 3) \cdot 9 .

Answer

ⓐ 35 ⓑ 99

Try It 1.31 §1.2 source ↗

Simplify:

30 \div 5 +

10 (3 - 2) .

Answer

Try It 1.32 §1.2 source ↗

Simplify:

70 \div 10 +

4 (6 - 2) .

Answer

Try It 1.33 §1.2 source ↗

Simplify:

9 +

5^{3} -

[4 (9 + 3)] .

Answer

Try It 1.34 §1.2 source ↗

Simplify:

7^{2} -

2 [4 (5 + 1)] .

Answer

Try It 1.35 §1.2 source ↗

Evaluate

8 x - 3,

when ⓐ

x = 2

and ⓑ

x = 1 .

Answer

ⓐ 13 ⓑ 5

Try It 1.36 §1.2 source ↗

Evaluate

4 y - 4,

when ⓐ

y = 3

and ⓑ

y = 5 .

Answer

ⓐ 8 ⓑ 16

Try It 1.37 §1.2 source ↗

Evaluate

x = 3,

when ⓐ

x^{2}

ⓑ

4^{x} .

Answer

ⓐ

9

ⓑ

64

Try It 1.38 §1.2 source ↗

Evaluate

x = 6,

when ⓐ

x^{3}

ⓑ

2^{x} .

Answer

ⓐ

216

ⓑ

64

Try It 1.39 §1.2 source ↗

Evaluate

3 x^{2} + 4 x + 1

when

x = 3 .

Answer

Try It 1.40 §1.2 source ↗

Evaluate

6 x^{2} - 4 x - 7

when

x = 2 .

Answer

Try It 1.41 §1.2 source ↗

Identify the coefficient of each term: ⓐ

17 x

ⓑ

41 b^{2}

Answer

ⓐ 17 ⓑ 41 ⓒ 1

Try It 1.42 §1.2 source ↗

Identify the coefficient of each term: ⓐ 9p ⓑ

13 a^{3}

ⓒ

y^{3} .

Answer

ⓐ 9 ⓑ 13 ⓒ 1

Try It 1.43 §1.2 source ↗

Identify the like terms:

9,

2 x^{3},

y^{2},

8 x^{3},

15,

9 y,

11 y^{2} .

Answer

9 and 15,

y^{2}

and

11 y^{2},

2 x^{3}

and

8 x^{3}

Try It 1.44 §1.2 source ↗

Identify the like terms:

4 x^{3},

8 x^{2},

19,

3 x^{2},

24,

6 x^{3} .

Answer

19 and 24,

8 x^{2}

and

3 x^{2},

4 x^{3}

and

6 x^{3}

Try It 1.45 §1.2 source ↗

Identify the terms in the expression

4 x^{2} + 5 x + 17 .

Answer

4 x^{2}, 5 x, 17

Try It 1.46 §1.2 source ↗

Identify the terms in the expression

5 x + 2 y .

Answer

5x, 2y

Try It 1.47 §1.2 source ↗

Simplify:

3 x^{2} +

7 x +

9 +

7 x^{2} +

9 x +

8 .

Answer

10 x^{2} + 16 x + 17

Try It 1.48 §1.2 source ↗

Simplify:

4 y^{2} +

5 y +

2 +

8 y^{2} +

4 y +

5 .

Answer

12 y^{2} + 9 y + 7

Try It 1.49 §1.2 source ↗

Translate the English phrase into an algebraic expression: ⓐ the difference of

14 x^{2}

and 13 ⓑ the quotient of 12x and 2.

Answer

ⓐ

14 x^{2} - 13

ⓑ

12 x \div 2

Try It 1.50 §1.2 source ↗

Translate the English phrase into an algebraic expression: ⓐ the sum of

17 y^{2}

and

19

ⓑ the product of

7

and

y .

Answer

ⓐ

17 y^{2} + 19

ⓑ 7y

Try It 1.51 §1.2 source ↗

Translate the English phrase into an algebraic expression: ⓐ Eleven more than

x

ⓑ Fourteen less than

11 a .

Answer

ⓐ

x + 11

ⓑ

11 a - 14

Try It 1.52 §1.2 source ↗

Translate the English phrase into an algebraic expression: ⓐ 13 more than z ⓑ 18 less than 8x.

Answer

ⓐ

z + 13

ⓑ

8 x - 18

Try It 1.53 §1.2 source ↗

Translate the English phrase into an algebraic expression: ⓐ four times the sum of p and q ⓑ the sum of four times p and q.

Answer

ⓐ

4 (p + q)

ⓑ

4 p + q

Try It 1.54 §1.2 source ↗

Translate the English phrase into an algebraic expression: ⓐ the difference of two times x and 8, ⓑ two times the difference of x and 8.

Answer

ⓐ

2 x - 8

ⓑ

2 (x - 8)

Try It 1.55 §1.2 source ↗

The length of a rectangle is 7 less than the width. Let w represent the width of the rectangle. Write an expression for the length of the rectangle.

Answer

w - 7

Try It 1.56 §1.2 source ↗

The width of a rectangle is 6 less than the length. Let l represent the length of the rectangle. Write an expression for the width of the rectangle.

Answer

l - 6

Try It 1.57 §1.2 source ↗

Geoffrey has dimes and quarters in his pocket. The number of dimes is eight less than four times the number of quarters. Let q represent the number of quarters. Write an expression for the number of dimes.

Answer

4 q - 8

Try It 1.58 §1.2 source ↗

Lauren has dimes and nickels in her purse. The number of dimes is three more than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.

Answer

7 n + 3

1.2-83 §1.2 source ↗

Use Variables and Algebraic Symbols

In the following exercises, translate from algebra to English.

$16 - 9$

Answer

16 minus 9, the difference of sixteen and nine

1.2-85 §1.2 source ↗

Use Variables and Algebraic Symbols

In the following exercises, translate from algebra to English.

$28 \div 4$

Answer

28 divided by 4, the quotient of twenty-eight and four

1.2-87 §1.2 source ↗

Use Variables and Algebraic Symbols

In the following exercises, translate from algebra to English.

$(2) (7)$

Answer

2 times 7, the product of two and seven

1.2-89 §1.2 source ↗

Use Variables and Algebraic Symbols

In the following exercises, translate from algebra to English.

$14 < 21$

Answer

fourteen is less than twenty-one

1.2-91 §1.2 source ↗

Use Variables and Algebraic Symbols

In the following exercises, translate from algebra to English.

$36 \geq 19$

Answer

thirty-six is greater than or equal to nineteen

1.2-93 §1.2 source ↗

Use Variables and Algebraic Symbols

In the following exercises, translate from algebra to English.

$y - 1 > 6$

Answer

y minus 1 is greater than 6, the difference of y and one is greater than six

1.2-95 §1.2 source ↗

Use Variables and Algebraic Symbols

In the following exercises, translate from algebra to English.

$2 \leq 18 \div 6$

Answer

2 is less than or equal to 18 divided by 6; 2 is less than or equal to the quotient of eighteen and six

1.2-97 §1.2 source ↗

In the following exercises, determine if each is an expression or an equation.

$9 \cdot 6 = 54$

Answer

equation

1.2-99 §1.2 source ↗

In the following exercises, determine if each is an expression or an equation.

$5 \cdot 4 + 3$

Answer

expression

1.2-101 §1.2 source ↗

In the following exercises, determine if each is an expression or an equation.

$x + 9$

Answer

expression

1.2-103 §1.2 source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

$5^{3}$

Answer

125

1.2-105 §1.2 source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

$2^{8}$

Answer

256

1.2-107 §1.2 source ↗

In the following exercises, simplify using the order of operations.

ⓐ $3 + 8 \cdot 5$ ⓑ $(3 + 8) \cdot 5$

Answer

ⓐ 43 ⓑ 55

1.2-109 §1.2 source ↗

In the following exercises, simplify using the order of operations.

$2^{3} - 12 \div (9 - 5)$

Answer

1.2-111 §1.2 source ↗

In the following exercises, simplify using the order of operations.

$3 \cdot 8 + 5 \cdot 2$

Answer

1.2-113 §1.2 source ↗

In the following exercises, simplify using the order of operations.

$2 + 8 (6 + 1)$

Answer

1.2-115 §1.2 source ↗

In the following exercises, simplify using the order of operations.

$4 \cdot 12 / 8$

Answer

1.2-117 §1.2 source ↗

In the following exercises, simplify using the order of operations.

$(6 + 10) \div (2 + 2)$

Answer

1.2-119 §1.2 source ↗

In the following exercises, simplify using the order of operations.

$20 \div 4 + 6 \cdot 5$

Answer

1.2-121 §1.2 source ↗

In the following exercises, simplify using the order of operations.

$3^{2} + 7^{2}$

Answer

1.2-123 §1.2 source ↗

In the following exercises, simplify using the order of operations.

$3 (1 + 9 \cdot 6) - 4^{2}$

Answer

149

1.2-125 §1.2 source ↗

In the following exercises, simplify using the order of operations.

$2 [1 + 3 (10 - 2)]$

Answer

1.2-127 §1.2 source ↗

Evaluate an Expression

In the following exercises, evaluate the following expressions.

$7 x + 8$ when $x = 2$

Answer

1.2-129 §1.2 source ↗

Evaluate an Expression

In the following exercises, evaluate the following expressions.

$x^{2}$ when $x = 12$

Answer

144

1.2-131 §1.2 source ↗

Evaluate an Expression

In the following exercises, evaluate the following expressions.

$x^{5}$ when $x = 2$

Answer

1.2-133 §1.2 source ↗

Evaluate an Expression

In the following exercises, evaluate the following expressions.

$x^{2} + 3 x - 7$ when $x = 4$

Answer

1.2-135 §1.2 source ↗

Evaluate an Expression

In the following exercises, evaluate the following expressions.

${(x - y)}^{2}$ when
$x = 10, y = 7$

Answer

1.2-137 §1.2 source ↗

Evaluate an Expression

In the following exercises, evaluate the following expressions.

$a^{2} + b^{2}$ when $a = 3, b = 8$

Answer

1.2-139 §1.2 source ↗

Evaluate an Expression

In the following exercises, evaluate the following expressions.

$2 l + 2 w$ when
$l = 15, w = 12$

Answer

1.2-141 §1.2 source ↗

Simplify Expressions by Combining Like Terms

In the following exercises, identify the coefficient of each term.

Answer

1.2-143 §1.2 source ↗

Simplify Expressions by Combining Like Terms

In the following exercises, identify the coefficient of each term.

$5 r^{2}$

Answer

1.2-145 §1.2 source ↗

In the following exercises, identify the like terms.

$x^{3},$ $8 x,$ $14,$ $8 y,$ $5,$ $8 x^{3}$

Answer

x^{3} and 8 x^{3},

14 and 5

1.2-147 §1.2 source ↗

In the following exercises, identify the like terms.

$9 a,$ $a^{2},$ $16,$ $16 b^{2},$ $4,$ $9 b^{2}$

Answer

16 and 4,

16 b^{2} and 9 b^{2}

1.2-149 §1.2 source ↗

In the following exercises, identify the terms in each expression.

$15 x^{2} + 6 x + 2$

Answer

15 x^{2}, 6 x, 2

1.2-151 §1.2 source ↗

In the following exercises, identify the terms in each expression.

$10 y^{3} + y + 2$

Answer

10 y^{3}, y, 2

1.2-153 §1.2 source ↗

In the following exercises, simplify the following expressions by combining like terms.

$10 x + 3 x$

Answer

13x

1.2-155 §1.2 source ↗

In the following exercises, simplify the following expressions by combining like terms.

$4 c + 2 c + c$

Answer

1.2-157 §1.2 source ↗

In the following exercises, simplify the following expressions by combining like terms.

$7 u + 2 + 3 u + 1$

Answer

10 u + 3

1.2-159 §1.2 source ↗

In the following exercises, simplify the following expressions by combining like terms.

$10 a +$ $7 +$ $5 a -$ $2 +$ $7 a -$ $4$

Answer

22 a + 1

1.2-161 §1.2 source ↗

In the following exercises, simplify the following expressions by combining like terms.

$3 x^{2} +$ $12 x +$ $11 +$ $14 x^{2} +$ $8 x +$ $5$

Answer

17 x^{2} + 20 x + 16

1.2-163 §1.2 source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the phrases into algebraic expressions.

the difference of 14 and 9

Answer

14 - 9

1.2-165 §1.2 source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the phrases into algebraic expressions.

the product of 9 and 7

Answer

9 \cdot 7

1.2-167 §1.2 source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the phrases into algebraic expressions.

the quotient of 36 and 9

Answer

36 \div 9

1.2-169 §1.2 source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the phrases into algebraic expressions.

the sum of 8x and 3x

Answer

8 x + 3 x

1.2-171 §1.2 source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the phrases into algebraic expressions.

the quotient of y and 3

Answer

\frac{y}{3}

1.2-173 §1.2 source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the phrases into algebraic expressions.

eight times the difference of y and nine

Answer

8 (y - 9)

1.2-175 §1.2 source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the phrases into algebraic expressions.

Eric has rock and classical CDs in his car. The number of rock CDs is 3 more than the number of classical CDs. Let c represent the number of classical CDs. Write an expression for the number of rock CDs.

Answer

c + 3

1.2-177 §1.2 source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the phrases into algebraic expressions.

Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let $n$ represent the number of nickels. Write an expression for the number of pennies.

Answer

2 n - 7

1.2-179 §1.2 source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the phrases into algebraic expressions.

Car insurance Justin’s car insurance has a $750 deductible per incident. This means that he pays $750 and his insurance company will pay all costs beyond $750. If Justin files a claim for $2,100.

ⓐ how much will he pay?

ⓑ how much will his insurance company pay?

Answer

ⓐ $750 ⓑ $1,350

1.2-181 §1.2 source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the phrases into algebraic expressions.

Explain the difference between an expression and an equation.

Answer

Answers may vary

1.2-183 §1.2 source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the phrases into algebraic expressions.

Explain how you identify the like terms in the expression $8 a^{2} +$ $4 a +$ $9 -$ $a^{2} -$ $1 .$

Answer

Answers may vary

Try It 1.59 §1.3 source ↗

Order each of the following pairs of numbers, using

<

> :

ⓐ

15___7

ⓑ

−2___5

ⓒ

−3___−7

ⓓ

5___−17 .

Answer

ⓐ > ⓑ < ⓒ > ⓓ >

Try It 1.60 §1.3 source ↗

Order each of the following pairs of numbers, using

<

> :

ⓐ

8___13

ⓑ

3___−4

ⓒ

−5___−2

ⓓ

9___−21 .

Answer

ⓐ < ⓑ > ⓒ < ⓓ >

Try It 1.61 §1.3 source ↗

Find: ⓐ the opposite of 4 ⓑ the opposite of

−3

ⓒ

− (−1) .

Answer

ⓐ

−4

ⓑ 3 ⓒ 1

Try It 1.62 §1.3 source ↗

Find: ⓐ the opposite of 8 ⓑ the opposite of

−5

ⓒ

− (−5) .

Answer

ⓐ

−8

ⓑ 5 ⓒ 5

Try It 1.63 §1.3 source ↗

Evaluate

− n,

when ⓐ

n = 4

ⓑ

n = −4 .

Answer

ⓐ

−4

ⓑ 4

Try It 1.64 §1.3 source ↗

Evaluate

− m,

when ⓐ

m = 11

ⓑ

m = −11 .

Answer

ⓐ

−11

ⓑ 11

Try It 1.65 §1.3 source ↗

Simplify: ⓐ

| 4 |

ⓑ

| −28 |

ⓒ

| 0 | .

Answer

ⓐ 4 ⓑ 28 ⓒ 0

Try It 1.66 §1.3 source ↗

Simplify: ⓐ

| −13 |

ⓑ

| 47 |

ⓒ

| 0 | .

Answer

ⓐ 13 ⓑ 47 ⓒ 0

Try It 1.67 §1.3 source ↗

Fill in <, >, or

=

for each of the following pairs of numbers: ⓐ

| −9 |___-

| −9 |

ⓑ

2___- | −2 |

ⓒ

−8___| −8 |

ⓓ

− (−9)___-

| −9 | .

Answer

ⓐ > ⓑ > ⓒ < ⓓ >

Try It 1.68 §1.3 source ↗

Fill in <, >, or

=

for each of the following pairs of numbers: ⓐ

7___- | −7 |

ⓑ

− (−10)___-

| −10 |

ⓒ

| −4 |___-

| −4 |

ⓓ

−1___| −1 | .

Answer

ⓐ > ⓑ > ⓒ > ⓓ <

Try It 1.69 §1.3 source ↗

Simplify:

19 -

| 11 -

4 (3 - 1) | .

Answer

Try It 1.70 §1.3 source ↗

Simplify:

9 -

| 8 -

4 (7 - 5) | .

Answer

Try It 1.71 §1.3 source ↗

Evaluate: ⓐ

| x | when x =

−17

ⓑ

| − y | when y =

−39

ⓒ

− | m | when m =

22

ⓓ

− | p | when p =

−11 .

Answer

ⓐ

17

ⓑ

39

ⓒ

−22

ⓓ

−11

Try It 1.72 §1.3 source ↗

Evaluate: ⓐ

| y | when y =

−23

ⓑ

| − y | when y =

−21

ⓒ

− | n | when n =

37

ⓓ

− | q | when q =

−49 .

Answer

ⓐ

23

ⓑ

21

ⓒ

−37

ⓓ

−49

Try It 1.73 §1.3 source ↗

Add: ⓐ

2 + 4

ⓑ

−2 + (−4) .

Answer

ⓐ 6 ⓑ

−6

Try It 1.74 §1.3 source ↗

Add: ⓐ

2 + 5

ⓑ

−2 + (−5) .

Answer

ⓐ 7 ⓑ

−7

Try It 1.75 §1.3 source ↗

Add: ⓐ

−2 + 4

ⓑ

2 + (−4) .

Answer

ⓐ 2 ⓑ

−2

Try It 1.76 §1.3 source ↗

Add: ⓐ

−2 + 5

ⓑ

2 + (−5) .

Answer

ⓐ 3 ⓑ

−3

Try It 1.77 §1.3 source ↗

Simplify: ⓐ

−31 + (−19)

ⓑ

15 + (−32) .

Answer

ⓐ

−50

ⓑ

−17

Try It 1.78 §1.3 source ↗

Simplify: ⓐ

−42 + (−28)

ⓑ

25 + (−61) .

Answer

ⓐ

−70

ⓑ

−36

Try It 1.79 §1.3 source ↗

Simplify:

−2 + 5 (−4 + 7) .

Answer

Try It 1.80 §1.3 source ↗

Simplify:

−4 + 2 (−3 + 5) .

Answer

Try It 1.81 §1.3 source ↗

Subtract: ⓐ

6 - 4

ⓑ

−6 - (−4) .

Answer

ⓐ 2 ⓑ

−2

Try It 1.82 §1.3 source ↗

Subtract: ⓐ

7 - 4

ⓑ

−7 - (−4) .

Answer

ⓐ 3 ⓑ

−3

Try It 1.83 §1.3 source ↗

Subtract: ⓐ

−6 - 4

ⓑ

6 - (−4) .

Answer

ⓐ

−10

ⓑ 10

Try It 1.84 §1.3 source ↗

Subtract: ⓐ

−7 - 4

ⓑ

7 - (−4) .

Answer

ⓐ

−11

ⓑ 11

Try It 1.85 §1.3 source ↗

Simplify: ⓐ

21 - 13

and

21 + (−13)

ⓑ

−11 - 7

and

−11 + (−7) .

Answer

ⓐ 8 ⓑ −18

Try It 1.86 §1.3 source ↗

Simplify: ⓐ

15 - 7

and

15 + (−7)

ⓑ

−14 - 8

and

−14 + (−8) .

Answer

ⓐ

8

ⓑ

−22

Try It 1.87 §1.3 source ↗

Simplify: ⓐ

6 - (−13)

and

6 + 13

ⓑ

−5 - (−1)

and

−5 + 1 .

Answer

ⓐ

19

ⓑ

−4

Try It 1.88 §1.3 source ↗

Simplify: ⓐ

4 - (−19)

and

4 + 19

ⓑ

−4 - (−7)

and

−4 + 7 .

Answer

ⓐ 23 ⓑ 3

Try It 1.89 §1.3 source ↗

Simplify:

8 - (−3 - 1) - 9

Answer

Try It 1.90 §1.3 source ↗

Simplify:

12 -

(−9 - 6) -

14

Answer

1.3-185 §1.3 source ↗

Use Negatives and Opposites of Integers

In the following exercises, order each of the following pairs of numbers, using < or >.

ⓐ $9___4$
ⓑ $−3___6$
ⓒ $−8___−2$
ⓓ $1___−10$

Answer

ⓐ > ⓑ < ⓒ < ⓓ >

1.3-187 §1.3 source ↗

In the following exercises, find the opposite of each number.

ⓐ 2 ⓑ $−6$

Answer

ⓐ

−2

ⓑ 6

1.3-189 §1.3 source ↗

In the following exercises, simplify.

$− (−4)$

Answer

1.3-191 §1.3 source ↗

In the following exercises, simplify.

$− (−15)$

Answer

1.3-193 §1.3 source ↗

In the following exercises, evaluate.

$− c$ whenⓐ $c = 12$ ⓑ $c = −12$

Answer

ⓐ

−12

ⓑ 12

1.3-195 §1.3 source ↗

Simplify Expressions with Absolute Value

In the following exercises, simplify.

ⓐ $| −32 |$ ⓑ $| 0 |$ ⓒ $| 16 |$

Answer

ⓐ 32 ⓑ 0 ⓒ 16

1.3-197 §1.3 source ↗

In the following exercises, fill in <, >, or $=$ for each of the following pairs of numbers.

ⓐ $−6___| −6 |$ ⓑ $− | −3 |___−3$

Answer

ⓐ < ⓑ

=

1.3-199 §1.3 source ↗

In the following exercises, simplify.

$− (−5) and − | −5 |$

Answer

5, −5

1.3-201 §1.3 source ↗

In the following exercises, simplify.

$8 | −7 |$

Answer

1.3-203 §1.3 source ↗

In the following exercises, simplify.

$| 15 -$ $7 | -$ $| 14 -$ $6 |$

Answer

1.3-205 §1.3 source ↗

In the following exercises, simplify.

$18 - | 2 (8 - 3) |$

Answer

1.3-207 §1.3 source ↗

In the following exercises, evaluate.

ⓐ $− | p | when p =$ $19$
ⓑ $− | q | when q =$ $−33$

Answer

ⓐ

−19

ⓑ

−33

1.3-209 §1.3 source ↗

Add Integers

In the following exercises, simplify each expression.

$−21 + (−59)$

Answer

−80

1.3-211 §1.3 source ↗

Add Integers

In the following exercises, simplify each expression.

$48 + (−16)$

Answer

1.3-213 §1.3 source ↗

Add Integers

In the following exercises, simplify each expression.

$−14 + (−12) + 4$

Answer

−22

1.3-215 §1.3 source ↗

Add Integers

In the following exercises, simplify each expression.

$135 +$ $(−110) +$ $83$

Answer

108

1.3-217 §1.3 source ↗

Add Integers

In the following exercises, simplify each expression.

$19 + 2 (−3 + 8)$

Answer

1.3-219 §1.3 source ↗

Subtract Integers

In the following exercises, simplify.

$8 - 2$

Answer

1.3-221 §1.3 source ↗

Subtract Integers

In the following exercises, simplify.

$−5 - 4$

Answer

−9

1.3-223 §1.3 source ↗

Subtract Integers

In the following exercises, simplify.

$8 - (−4)$

Answer

1.3-225 §1.3 source ↗

Subtract Integers

In the following exercises, simplify.

ⓐ $44 - 28$ ⓑ $44 + (−28)$

Answer

ⓐ 16 ⓑ 16

1.3-227 §1.3 source ↗

Subtract Integers

In the following exercises, simplify.

ⓐ $27 - (−18)$ ⓑ $27 + 18$

Answer

ⓐ 45 ⓑ 45

1.3-229 §1.3 source ↗

In the following exercises, simplify each expression.

$15 - (−12)$

Answer

1.3-231 §1.3 source ↗

In the following exercises, simplify each expression.

$48 - 87$

Answer

−39

1.3-233 §1.3 source ↗

In the following exercises, simplify each expression.

$−17 - 42$

Answer

−59

1.3-235 §1.3 source ↗

In the following exercises, simplify each expression.

$−103 - (−52)$

Answer

−51

1.3-237 §1.3 source ↗

In the following exercises, simplify each expression.

$−45 - (–54)$

Answer

1.3-239 §1.3 source ↗

In the following exercises, simplify each expression.

$8 - 3 - 7$

Answer

−2

1.3-241 §1.3 source ↗

In the following exercises, simplify each expression.

$−5 - 4 + 7$

Answer

−2

1.3-243 §1.3 source ↗

In the following exercises, simplify each expression.

$−14 - (−27) + 9$

Answer

1.3-245 §1.3 source ↗

In the following exercises, simplify each expression.

$(2 - 7) - (3 - 8)$

Answer

1.3-247 §1.3 source ↗

In the following exercises, simplify each expression.

$− (6 - 8) -$ $(2 - 4)$

Answer

1.3-249 §1.3 source ↗

In the following exercises, simplify each expression.

$25 -$ $[10 - (3 - 12)]$

Answer

1.3-251 §1.3 source ↗

In the following exercises, simplify each expression.

$6 \cdot 3 - 4 \cdot 3 - 7 \cdot 2$

Answer

−8

1.3-253 §1.3 source ↗

In the following exercises, simplify each expression.

$5^{2} - 6^{2}$

Answer

−11

1.3-255 §1.3 source ↗

In the following exercises, simplify each expression.

Elevation The highest elevation in the United States is Mount McKinley, Alaska, at 20,320 feet above sea level. The lowest elevation is Death Valley, California, at 282 feet below sea level.

Use integers to write the elevation of:

ⓐ Mount McKinley. ⓑ Death Valley.

Answer

ⓐ 20,320 feet ⓑ −282 feet

1.3-257 §1.3 source ↗

In the following exercises, simplify each expression.

State budgets In June, 2011, the state of Pennsylvania estimated it would have a budget surplus of $540 million. That same month, Texas estimated it would have a budget deficit of $27 billion.

Use integers to write the budget of:

ⓐ Pennsylvania.
ⓑ Texas.

Answer

ⓐ $540 million ⓑ

− $27

billion

1.3-259 §1.3 source ↗

In the following exercises, simplify each expression.

Stock Market The week of September 15, 2008 was one of the most volatile weeks ever for the US stock market. The closing numbers of the Dow Jones Industrial Average each day were:

Monday	$−504$
Tuesday	$+ 142$
Wednesday	$−449$
Thursday	$+ 410$
Friday	$+ 369$

What was the overall change for the week? Was it positive or negative?

Answer

32, negative

1.3-261 §1.3 source ↗

In the following exercises, simplify each expression.

Give an example of a negative number from your life experience.

Answer

Answers may vary

1.3-263 §1.3 source ↗

In the following exercises, simplify each expression.

Explain why the sum of $−8$ and 2 is negative, but the sum of 8 and $−2$ is positive.

Answer

Answers may vary

Try It 1.91 §1.4 source ↗

Multiply: ⓐ

−6 \cdot 8

ⓑ

−4 (−7)

ⓒ

9 (−7)

ⓓ

5 \cdot 12 .

Answer

ⓐ

−48

ⓑ 28 ⓒ

−63

ⓓ 60

Try It 1.92 §1.4 source ↗

Multiply: ⓐ

−8 \cdot 7

ⓑ

−6 (−9)

ⓒ

7 (−4)

ⓓ

3 \cdot 13 .

Answer

ⓐ

−56

ⓑ 54 ⓒ

−28

ⓓ 39

Try It 1.93 §1.4 source ↗

Multiply: ⓐ

−1 \cdot 9

ⓑ

−1 \cdot (−17) .

Answer

ⓐ

−9

ⓑ 17

Try It 1.94 §1.4 source ↗

Multiply: ⓐ

−1 \cdot 8

ⓑ

−1 \cdot (−16) .

Answer

ⓐ

−8

ⓑ 16

Try It 1.95 §1.4 source ↗

Divide: ⓐ

−42 \div 6

ⓑ

−117 \div (−3) .

Answer

ⓐ

−7

ⓑ 39

Try It 1.96 §1.4 source ↗

Divide: ⓐ

−63 \div 7

ⓑ

−115 \div (−5) .

Answer

ⓐ

−9

ⓑ 23

Try It 1.97 §1.4 source ↗

Simplify:

8 (−3) +

5 (−7) -

4 .

Answer

−63

Try It 1.98 §1.4 source ↗

Simplify:

9 (−3) +

7 (−8) -

1 .

Answer

−84

Try It 1.99 §1.4 source ↗

Simplify: ⓐ

{(−3)}^{4}

ⓑ

− 3^{4} .

Answer

ⓐ 81 ⓑ

−81

Try It 1.100 §1.4 source ↗

Simplify: ⓐ

{(−7)}^{2}

ⓑ

− 7^{2} .

Answer

ⓐ 49 ⓑ

−49

Try It 1.101 §1.4 source ↗

Simplify:

17 - 4 (8 - 11) .

Answer

Try It 1.102 §1.4 source ↗

Simplify:

16 - 6 (7 - 13) .

Answer

Try It 1.103 §1.4 source ↗

Simplify:

12 (−9) \div {(−3)}^{3} .

Answer

Try It 1.104 §1.4 source ↗

Simplify:

18 (−4) \div {(−2)}^{3} .

Answer

Try It 1.105 §1.4 source ↗

Simplify:

−27 \div 3 +

(−5) (−6) .

Answer

Try It 1.106 §1.4 source ↗

Simplify:

−32 \div 4 +

(−2) (−7) .

Answer

Try It 1.107 §1.4 source ↗

When

n = −8,

evaluate ⓐ

n + 2

ⓑ

− n + 2 .

Answer

ⓐ

−6

ⓑ 10

Try It 1.108 §1.4 source ↗

When

y = −9,

evaluate ⓐ

y + 8

ⓑ

− y + 8 .

Answer

ⓐ

−1

ⓑ 17

Try It 1.109 §1.4 source ↗

Evaluate

{(x + y)}^{2}

when

x = −15

and

y = 29 .

Answer

196

Try It 1.110 §1.4 source ↗

Evaluate

{(x + y)}^{3}

when

x = −8

and

y = 10 .

Answer

Try It 1.111 §1.4 source ↗

Evaluate:

17 - k

when ⓐ

k = 19

and ⓑ

k = −19 .

Answer

ⓐ

−2

ⓑ 36

Try It 1.112 §1.4 source ↗

Evaluate:

−5 - b

when ⓐ

b = 14

and ⓑ

b = −14 .

Answer

ⓐ

−19

ⓑ 9

Try It 1.113 §1.4 source ↗

Evaluate:

3 x^{2} - 2 x + 6

when

x = −3 .

Answer

Try It 1.114 §1.4 source ↗

Evaluate:

4 x^{2} - x - 5

when

x = −2 .

Answer

Try It 1.115 §1.4 source ↗

Translate and simplify the sum of 9 and

−16,

increased by 4.

Answer

(9 + (−16)) +

4;

-

3

Try It 1.116 §1.4 source ↗

Translate and simplify the sum of

−8

and

−12,

increased by 7.

Answer

(−8 + (−12)) +

7;

-

13

Try It 1.117 §1.4 source ↗

Translate and simplify ⓐ the difference of 14 and

−23

ⓑ subtract 21 from

−17 .

Answer

ⓐ

14 - (−23); 37

ⓑ

−17 - 21; - 38

Try It 1.118 §1.4 source ↗

Translate and simplify ⓐ the difference of 11 and

−19

ⓑ subtract 18 from

−11 .

Answer

ⓐ

11 - (−19); 30

ⓑ

−11 - 18; - 29

Try It 1.119 §1.4 source ↗

Translate to an algebraic expression and simplify if possible: the product of

−5

and 12.

Answer

−5 (12); - 60

Try It 1.120 §1.4 source ↗

Translate to an algebraic expression and simplify if possible: the product of 8 and

−13 .

Answer

8 (−13); - 104

Try It 1.121 §1.4 source ↗

Translate to an algebraic expression and simplify if possible: the quotient of

−63

and

−9 .

Answer

−63 \div (−9); 7

Try It 1.122 §1.4 source ↗

Translate to an algebraic expression and simplify if possible: the quotient of

−72

and

−9 .

Answer

−72 \div (−9); 8

Try It 1.123 §1.4 source ↗

In the morning, the temperature in Anchorage, Alaska was 15 degrees. By mid-afternoon the temperature had dropped to 30 degrees below zero. What was the difference in the morning and afternoon temperatures?

Answer

The difference in temperatures was 45 degrees.

Try It 1.124 §1.4 source ↗

The temperature in Denver was

−6

degrees at lunchtime. By sunset the temperature had dropped to

−15

degrees. What was the difference in the lunchtime and sunset temperatures?

Answer

The difference in temperatures was 9 degrees.

Try It 1.125 §1.4 source ↗

The Bears played poorly and had seven penalties in the game. Each penalty resulted in a loss of 15 yards. What is the number of yards lost due to penalties?

Answer

The Bears lost 105 yards.

Try It 1.126 §1.4 source ↗

Bill uses the ATM on campus because it is convenient. However, each time he uses it he is charged a $2 fee. Last month he used the ATM eight times. How much was his total fee for using the ATM?

Answer

A $16 fee was deducted from his checking account.

1.4-265 §1.4 source ↗

Multiply Integers

In the following exercises, multiply.

$−4 \cdot 8$

Answer

−32

1.4-267 §1.4 source ↗

Multiply Integers

In the following exercises, multiply.

$9 (−7)$

Answer

−63

1.4-269 §1.4 source ↗

Multiply Integers

In the following exercises, multiply.

$- 1 \cdot 6$

Answer

−6

1.4-271 §1.4 source ↗

Multiply Integers

In the following exercises, multiply.

$−1 (−14)$

Answer

1.4-273 §1.4 source ↗

Divide Integers

In the following exercises, divide.

$−24 \div 6$

Answer

−4

1.4-275 §1.4 source ↗

Divide Integers

In the following exercises, divide.

$−52 \div (−4)$

Answer

1.4-277 §1.4 source ↗

Divide Integers

In the following exercises, divide.

$−180 \div 15$

Answer

−12

1.4-279 §1.4 source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$5 (−6) +$ $7 (−2) -$ $3$

Answer

−47

1.4-281 §1.4 source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

${(−2)}^{6}$

Answer

1.4-283 §1.4 source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$− 4^{2}$

Answer

−16

1.4-285 §1.4 source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$−3 (−5) (6)$

Answer

1.4-287 §1.4 source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$(8 - 11) (9 - 12)$

Answer

1.4-289 §1.4 source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$26 - 3 (2 - 7)$

Answer

1.4-291 §1.4 source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$65 \div (−5) +$ $(−28) \div (−7)$

Answer

−9

1.4-293 §1.4 source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$9 -$ $2 [3 - 8 (−2)]$

Answer

−29

1.4-295 §1.4 source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

${(−3)}^{2} -$ $24 \div (8 - 2)$

Answer

1.4-297 §1.4 source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$y + (−14)$ when ⓐ $y = −33$ ⓑ $y = 30$

Answer

ⓐ

−47

ⓑ 16

1.4-299 §1.4 source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

ⓐ $a + 3$ when $a = −7$

ⓑ $− a + 3$ when $a = −7$

Answer

ⓐ

−4

ⓑ 10

1.4-301 §1.4 source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$m + n$ when
$m = −15, n = 7$

Answer

−8

1.4-303 §1.4 source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$r + s$ when $r = −9, s = −7$

Answer

−16

1.4-305 §1.4 source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

${(x + y)}^{2}$ when
$x = −3, y = 14$

Answer

121

1.4-307 §1.4 source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$−2 x + 17$ when

ⓐ $x = 8$

ⓑ $x = −8$

Answer

ⓐ 1

ⓑ 33

1.4-309 §1.4 source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$10 - 3 m$ when
ⓐ $m = 5$
ⓑ $m = −5$

Answer

ⓐ

−5

ⓑ 25

1.4-311 §1.4 source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$2 w^{2} - 3 w + 7$ when
$w = −2$

Answer

1.4-313 §1.4 source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$9 a - 2 b - 8$ when
$a = −6 and b = −3$

Answer

−56

1.4-315 §1.4 source ↗

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

the sum of 3 and $−15,$ increased by 7

Answer

(3 + (−15)) +

7;

-

5

1.4-317 §1.4 source ↗

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

the difference of 10 and $−18$

Answer

10 - (−18); 28

1.4-319 §1.4 source ↗

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

the difference of $−5$ and $−30$

Answer

−5 - (−30); 25

1.4-321 §1.4 source ↗

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

the product of $−3 and 15$

Answer

−3 \cdot 15; - 45

1.4-323 §1.4 source ↗

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

the quotient of $−60$ and $−20$

Answer

−60 \div (−20); 3

1.4-325 §1.4 source ↗

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

the quotient of $−6$ and the sum of a and b

Answer

\frac{−6}{a + b}

1.4-327 §1.4 source ↗

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

the product of $−10$ and the difference of $p and q$

Answer

−10 (p - q)

1.4-329 §1.4 source ↗

Use Integers in Applications

In the following exercises, solve.

Temperature On January $15,$ the high temperature in Anaheim, California, was $84 ° .$ That same day, the high temperature in Embarrass, Minnesota was $−12 ° .$ What was the difference between the temperature in Anaheim and the temperature in Embarrass?

Answer

96 °

1.4-331 §1.4 source ↗

Use Integers in Applications

In the following exercises, solve.

Football On the first down, the Chargers had the ball on their 25-yard line. They lost 6 yards on the first-down play, gained 10 yards on the second-down play, and lost 8 yards on the third-down play. What was the yard line at the end of the third-down play?

Answer

1.4-333 §1.4 source ↗

Use Integers in Applications

In the following exercises, solve.

Checking Account Mayra has $124 in her checking account. She writes a check for $152. What is the new balance in her checking account?

Answer

− $28

1.4-335 §1.4 source ↗

Use Integers in Applications

In the following exercises, solve.

Checking Account Diontre has a balance of $− $38$ in his checking account. He deposits $225 to the account. What is the new balance?

Answer

$187

1.4-337 §1.4 source ↗

Use Integers in Applications

In the following exercises, solve.

Stock market Javier owns 300 shares of stock in one company. On Tuesday, the stock price dropped $12 per share. What was the total effect on Javier’s portfolio?

Answer

− $3600

1.4-339 §1.4 source ↗

Use Integers in Applications

In the following exercises, solve.

In your own words, state the rules for multiplying integers.

Answer

Answers may vary

1.4-341 §1.4 source ↗

Use Integers in Applications

In the following exercises, solve.

Why is $− 2^{4} \neq {(−2)}^{4} ?$

Answer

Answers may vary

Try It 1.127 §1.5 source ↗

Find three fractions equivalent to

\frac{3}{5} .

Answer

\frac{6}{10},

\frac{9}{15},

\frac{12}{20};

answers may vary

Try It 1.128 §1.5 source ↗

Find three fractions equivalent to

\frac{4}{5} .

Answer

\frac{8}{10},

\frac{12}{15},

\frac{16}{20};

answers may vary

Try It 1.129 §1.5 source ↗

Simplify:

- \frac{42}{54} .

Answer

- \frac{7}{9}

Try It 1.130 §1.5 source ↗

Simplify:

- \frac{45}{81} .

Answer

- \frac{5}{9}

Try It 1.131 §1.5 source ↗

Simplify:

- \frac{69}{120} .

Answer

- \frac{23}{40}

Try It 1.132 §1.5 source ↗

Simplify:

- \frac{120}{192} .

Answer

- \frac{5}{8}

Try It 1.133 §1.5 source ↗

Simplify:

\frac{7 x}{7 y} .

Answer

\frac{x}{y}

Try It 1.134 §1.5 source ↗

Simplify:

\frac{3 a}{3 b} .

Answer

\frac{a}{b}

Try It 1.135 §1.5 source ↗

Multiply:

- \frac{10}{28} \cdot \frac{8}{15} .

Answer

- \frac{4}{21}

Try It 1.136 §1.5 source ↗

Multiply:

- \frac{9}{20} \cdot \frac{5}{12} .

Answer

- \frac{3}{16}

Try It 1.137 §1.5 source ↗

Multiply:

\frac{11}{3} (−9 a) .

Answer

−33 a

Try It 1.138 §1.5 source ↗

Multiply:

\frac{13}{7} (−14 b) .

Answer

−26 b

Try It 1.139 §1.5 source ↗

Divide:

- \frac{3}{5} \div \frac{p}{7} .

Answer

- \frac{21}{5 p}

Try It 1.140 §1.5 source ↗

Divide:

- \frac{5}{8} \div \frac{q}{3} .

Answer

- \frac{15}{8 q}

Try It 1.141 §1.5 source ↗

Find the quotient:

-

\frac{7}{27} \div (- \frac{35}{36}) .

Answer

\frac{4}{15}

Try It 1.142 §1.5 source ↗

Find the quotient:

-

\frac{5}{14} \div (- \frac{15}{28}) .

Answer

\frac{2}{3}

Try It 1.143 §1.5 source ↗

Simplify:

\frac{\frac{2}{3}}{\frac{5}{6}} .

Answer

\frac{4}{5}

Try It 1.144 §1.5 source ↗

Simplify:

\frac{\frac{3}{7}}{\frac{6}{11}} .

Answer

\frac{11}{14}

Try It 1.145 §1.5 source ↗

Simplify:

\frac{\frac{a}{8}}{\frac{a b}{6}} .

Answer

\frac{3}{4 b}

Try It 1.146 §1.5 source ↗

Simplify:

\frac{\frac{p}{2}}{\frac{p q}{8}} .

Answer

\frac{4}{q}

Try It 1.147 §1.5 source ↗

Simplify:

\frac{6 - 3 (5)}{3^{2} + 3} .

Answer

- \frac{3}{4}

Try It 1.148 §1.5 source ↗

Simplify:

\frac{4 - 4 (6)}{3^{2} + 3} .

Answer

- \frac{5}{3}

Try It 1.149 §1.5 source ↗

Simplify:

\frac{8 (−2) + 4 (−3)}{−5 (2) + 3} .

Answer

Try It 1.150 §1.5 source ↗

Simplify:

\frac{7 (−1) + 9 (−3)}{−5 (3) - 2} .

Answer

Try It 1.151 §1.5 source ↗

Translate the English phrase into an algebraic expression: the quotient of the difference of a and b, and cd.

Answer

\frac{a - b}{c d}

Try It 1.152 §1.5 source ↗

Translate the English phrase into an algebraic expression: the quotient of the sum of

p

and

q,

and

r

Answer

\frac{p + q}{r}

1.5-343 §1.5 source ↗

Find Equivalent Fractions

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

$\frac{3}{8}$

Answer

\frac{6}{16},

\frac{9}{24},

\frac{12}{32}

answers may vary

1.5-345 §1.5 source ↗

Find Equivalent Fractions

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

$\frac{5}{9}$

Answer

\frac{10}{18},

\frac{15}{27},

\frac{20}{36}

answers may vary

1.5-347 §1.5 source ↗

Simplify Fractions

In the following exercises, simplify.

$- \frac{40}{88}$

Answer

- \frac{5}{11}

1.5-349 §1.5 source ↗

Simplify Fractions

In the following exercises, simplify.

$- \frac{108}{63}$

Answer

- \frac{12}{7}

1.5-351 §1.5 source ↗

Simplify Fractions

In the following exercises, simplify.

$\frac{120}{252}$

Answer

\frac{10}{21}

1.5-353 §1.5 source ↗

Simplify Fractions

In the following exercises, simplify.

$- \frac{3 x}{12 y}$

Answer

- \frac{x}{4 y}

1.5-355 §1.5 source ↗

Simplify Fractions

In the following exercises, simplify.

$\frac{14 x^{2}}{21 y}$

Answer

\frac{2 x^{2}}{3 y}

1.5-357 §1.5 source ↗

Multiply Fractions

In the following exercises, multiply.

$\frac{3}{4} \cdot \frac{9}{10}$

Answer

\frac{27}{40}

1.5-359 §1.5 source ↗

Multiply Fractions

In the following exercises, multiply.

$- \frac{2}{3} (- \frac{3}{8})$

Answer

\frac{1}{4}

1.5-361 §1.5 source ↗

Multiply Fractions

In the following exercises, multiply.

$- \frac{5}{9} \cdot \frac{3}{10}$

Answer

- \frac{1}{6}

1.5-363 §1.5 source ↗

Multiply Fractions

In the following exercises, multiply.

$(- \frac{14}{15}) (\frac{9}{20})$

Answer

- \frac{21}{50}

1.5-365 §1.5 source ↗

Multiply Fractions

In the following exercises, multiply.

$(- \frac{63}{84}) (- \frac{44}{90})$

Answer

\frac{11}{30}

1.5-367 §1.5 source ↗

Multiply Fractions

In the following exercises, multiply.

$4 \cdot \frac{5}{11}$

Answer

\frac{20}{11}

1.5-369 §1.5 source ↗

Multiply Fractions

In the following exercises, multiply.

$\frac{3}{7} \cdot 21 n$

Answer

1.5-371 §1.5 source ↗

Multiply Fractions

In the following exercises, multiply.

$−8 (\frac{17}{4})$

Answer

−34

1.5-373 §1.5 source ↗

Divide Fractions

In the following exercises, divide.

$\frac{3}{4} \div \frac{2}{3}$

Answer

\frac{9}{8}

1.5-375 §1.5 source ↗

Divide Fractions

In the following exercises, divide.

$- \frac{7}{9} \div (- \frac{7}{4})$

Answer

\frac{4}{9}

1.5-377 §1.5 source ↗

Divide Fractions

In the following exercises, divide.

$\frac{3}{4} \div \frac{x}{11}$

Answer

\frac{33}{4 x}

1.5-379 §1.5 source ↗

Divide Fractions

In the following exercises, divide.

$\frac{5}{18} \div (- \frac{15}{24})$

Answer

- \frac{4}{9}

1.5-381 §1.5 source ↗

Divide Fractions

In the following exercises, divide.

$\frac{8 u}{15} \div \frac{12 v}{25}$

Answer

\frac{10 u}{9 v}

1.5-383 §1.5 source ↗

Divide Fractions

In the following exercises, divide.

$−5 \div \frac{1}{2}$

Answer

−10

1.5-385 §1.5 source ↗

Divide Fractions

In the following exercises, divide.

$\frac{3}{4} \div (−12)$

Answer

- \frac{1}{16}

1.5-387 §1.5 source ↗

In the following exercises, simplify.

$\frac{- \frac{8}{21}}{\frac{12}{35}}$

Answer

- \frac{10}{9}

1.5-389 §1.5 source ↗

In the following exercises, simplify.

$\frac{- \frac{4}{5}}{2}$

Answer

- \frac{2}{5}

1.5-391 §1.5 source ↗

In the following exercises, simplify.

$\frac{\frac{m}{3}}{\frac{n}{2}}$

Answer

\frac{2 m}{3 n}

1.5-393 §1.5 source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{22 + 3}{10}$

Answer

\frac{5}{2}

1.5-395 §1.5 source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{48}{24 - 15}$

Answer

\frac{16}{3}

1.5-397 §1.5 source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{−6 + 6}{8 + 4}$

Answer

1.5-399 §1.5 source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{4 \cdot 3}{6 \cdot 6}$

Answer

\frac{1}{3}

1.5-401 §1.5 source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{4^{2} - 1}{25}$

Answer

\frac{3}{5}

1.5-403 §1.5 source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{8 \cdot 3 + 2 \cdot 9}{14 + 3}$

Answer

2 \frac{8}{17}

1.5-405 §1.5 source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{5 \cdot 6 - 3 \cdot 4}{4 \cdot 5 - 2 \cdot 3}$

Answer

\frac{9}{7}

1.5-407 §1.5 source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{5^{2} - 3^{2}}{3 - 5}$

Answer

−8

1.5-409 §1.5 source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{7 \cdot 4 - 2 (8 - 5)}{9 \cdot 3 - 3 \cdot 5}$

Answer

\frac{11}{6}

1.5-411 §1.5 source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{9 (8 - 2) - 3 (15 - 7)}{6 (7 - 1) - 3 (17 - 9)}$

Answer

\frac{5}{2}

1.5-413 §1.5 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

the quotient of r and the sum of s and 10

Answer

\frac{r}{s + 10}

1.5-415 §1.5 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

the quotient of the difference of $x and y, and - 3$

Answer

\frac{x - y}{−3}

1.5-417 §1.5 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

Baking. A recipe for chocolate chip cookies calls for $\frac{3}{4}$ cup brown sugar. Imelda wants to double the recipe. ⓐ How much brown sugar will Imelda need? Show your calculation. ⓑ Measuring cups usually come in sets of $\frac{1}{4},$ $\frac{1}{3},$ $\frac{1}{2},$ $and 1$ cup. Draw a diagram to show two different ways that Imelda could measure the brown sugar needed to double the cookie recipe.

Answer

ⓐ

(2) (\frac{3}{4}); \frac{3}{2}

cups ⓑ answers will vary

1.5-419 §1.5 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

Portions Don purchased a bulk package of candy that weighs $5$ pounds. He wants to sell the candy in little bags that hold $\frac{1}{4}$ pound. How many little bags of candy can he fill from the bulk package?

Answer

20 bags

1.5-421 §1.5 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

Rafael wanted to order half a medium pizza at a restaurant. The waiter told him that a medium pizza could be cut into 6 or 8 slices. Would he prefer 3 out of 6 slices or 4 out of 8 slices? Rafael replied that since he wasn’t very hungry, he would prefer 3 out of 6 slices. Explain what is wrong with Rafael’s reasoning.

Answer

Answers may vary

1.5-423 §1.5 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

Explain how you find the reciprocal of a fraction.

Answer

Answers may vary

Try It 1.153 §1.6 source ↗

Find the sum:

\frac{x}{4} + \frac{3}{4} .

Answer

\frac{x + 3}{4}

Try It 1.154 §1.6 source ↗

Find the sum:

\frac{y}{8} + \frac{5}{8} .

Answer

\frac{y + 5}{8}

Try It 1.155 §1.6 source ↗

Find the difference:

- \frac{19}{28} - \frac{7}{28} .

Answer

- \frac{13}{14}

Try It 1.156 §1.6 source ↗

Find the difference:

- \frac{27}{32} - \frac{1}{32} .

Answer

- \frac{7}{8}

Try It 1.157 §1.6 source ↗

Find the difference:

- \frac{9}{x} - \frac{7}{x} .

Answer

- \frac{16}{x}

Try It 1.158 §1.6 source ↗

Find the difference:

- \frac{17}{a} - \frac{5}{a} .

Answer

- \frac{22}{a}

Try It 1.159 §1.6 source ↗

Simplify:

-

\frac{2}{9} +

(- \frac{4}{9}) -

\frac{7}{9} .

Answer

−1

Try It 1.160 §1.6 source ↗

Simplify:

\frac{5}{9} +

(- \frac{4}{9}) -

\frac{7}{9} .

Answer

- \frac{2}{3}

Try It 1.161 §1.6 source ↗

Add:

\frac{7}{12} + \frac{11}{15} .

Answer

\frac{79}{60}

Try It 1.162 §1.6 source ↗

Add:

\frac{13}{15} + \frac{17}{20} .

Answer

\frac{103}{60}

Try It 1.163 §1.6 source ↗

Subtract:

\frac{13}{24} - \frac{17}{32} .

Answer

\frac{1}{96}

Try It 1.164 §1.6 source ↗

Subtract:

\frac{21}{32} - \frac{9}{28} .

Answer

\frac{75}{224}

Try It 1.165 §1.6 source ↗

Add:

\frac{y}{6} + \frac{7}{9} .

Answer

\frac{3 y + 14}{18}

Try It 1.166 §1.6 source ↗

Add:

\frac{x}{6} + \frac{7}{15} .

Answer

\frac{5 x + 14}{30}

Try It 1.167 §1.6 source ↗

Simplify: ⓐ

\frac{3 a}{4} - \frac{8}{9}

ⓑ

\frac{3 a}{4} \cdot \frac{8}{9} .

Answer

ⓐ

\frac{27 a - 32}{36}

ⓑ

\frac{2 a}{3}

Try It 1.168 §1.6 source ↗

Simplify: ⓐ

\frac{4 k}{5} - \frac{1}{6}

ⓑ

\frac{4 k}{5} \cdot \frac{1}{6} .

Answer

ⓐ

\frac{24 k - 5}{30}

ⓑ

\frac{2 k}{15}

Try It 1.169 §1.6 source ↗

Simplify:

\frac{{(\frac{1}{3})}^{2}}{2^{3} + 2} .

Answer

\frac{1}{90}

Try It 1.170 §1.6 source ↗

Simplify:

\frac{1 + 4^{2}}{{(\frac{1}{4})}^{2}} .

Answer

272

Try It 1.171 §1.6 source ↗

Simplify:

\frac{\frac{1}{3} + \frac{1}{2}}{\frac{3}{4} - \frac{1}{3}} .

Answer

Try It 1.172 §1.6 source ↗

Simplify:

\frac{\frac{2}{3} - \frac{1}{2}}{\frac{1}{4} + \frac{1}{3}} .

Answer

\frac{2}{7}

Try It 1.173 §1.6 source ↗

Evaluate

x + \frac{3}{4}

when ⓐ

x = - \frac{7}{4}

ⓑ

x = - \frac{5}{4} .

Answer

ⓐ

−1

ⓑ

- \frac{1}{2}

Try It 1.174 §1.6 source ↗

Evaluate

y + \frac{1}{2}

when ⓐ

y = \frac{2}{3}

ⓑ

y = - \frac{3}{4} .

Answer

ⓐ

\frac{7}{6}

ⓑ

- \frac{1}{4}

Try It 1.175 §1.6 source ↗

Evaluate

- \frac{1}{2} - y

when

y = - \frac{1}{4} .

Answer

- \frac{1}{4}

Try It 1.176 §1.6 source ↗

Evaluate

- \frac{3}{8} - y

when

y = - \frac{5}{2} .

Answer

- \frac{17}{8}

Try It 1.177 §1.6 source ↗

Evaluate

3 a b^{2}

when

a = - \frac{2}{3}

and

b = - \frac{1}{2} .

Answer

- \frac{1}{2}

Try It 1.178 §1.6 source ↗

Evaluate

4 c^{3} d

when

c = - \frac{1}{2}

and

d = - \frac{4}{3} .

Answer

\frac{2}{3}

Try It 1.179 §1.6 source ↗

Evaluate

\frac{a + b}{c}

when

a =

−8,

b =

−7,

and c =

6 .

Answer

- \frac{5}{2}

Try It 1.180 §1.6 source ↗

Evaluate

\frac{x + y}{z}

when

x =

9,

y =

−18,

and z =

−6 .

Answer

\frac{3}{2}

1.6-425 §1.6 source ↗

Add and Subtract Fractions with a Common Denominator

In the following exercises, add.

$\frac{6}{13} + \frac{5}{13}$

Answer

\frac{11}{13}

1.6-427 §1.6 source ↗

Add and Subtract Fractions with a Common Denominator

In the following exercises, add.

$\frac{x}{4} + \frac{3}{4}$

Answer

\frac{x + 3}{4}

1.6-429 §1.6 source ↗

Add and Subtract Fractions with a Common Denominator

In the following exercises, add.

$- \frac{3}{16} + (- \frac{7}{16})$

Answer

- \frac{5}{8}

1.6-431 §1.6 source ↗

Add and Subtract Fractions with a Common Denominator

In the following exercises, add.

$- \frac{8}{17} + \frac{15}{17}$

Answer

\frac{7}{17}

1.6-433 §1.6 source ↗

Add and Subtract Fractions with a Common Denominator

In the following exercises, add.

$\frac{6}{13} +$ $(- \frac{10}{13}) +$ $(- \frac{12}{13})$

Answer

- \frac{16}{13}

1.6-435 §1.6 source ↗

In the following exercises, subtract.

$\frac{11}{15} - \frac{7}{15}$

Answer

\frac{4}{15}

1.6-437 §1.6 source ↗

In the following exercises, subtract.

$\frac{11}{12} - \frac{5}{12}$

Answer

\frac{1}{2}

1.6-439 §1.6 source ↗

In the following exercises, subtract.

$\frac{19}{21} - \frac{4}{21}$

Answer

\frac{5}{7}

1.6-441 §1.6 source ↗

In the following exercises, subtract.

$\frac{5 y}{8} - \frac{7}{8}$

Answer

\frac{5 y - 7}{8}

1.6-443 §1.6 source ↗

In the following exercises, subtract.

$- \frac{23}{u} - \frac{15}{u}$

Answer

- \frac{38}{u}

1.6-445 §1.6 source ↗

In the following exercises, subtract.

$- \frac{3}{5} - (- \frac{4}{5})$

Answer

\frac{1}{5}

1.6-447 §1.6 source ↗

In the following exercises, subtract.

$- \frac{7}{9} - (- \frac{5}{9})$

Answer

- \frac{2}{9}

1.6-449 §1.6 source ↗

Mixed Practice

In the following exercises, simplify.

$- \frac{5}{18} \cdot \frac{9}{10}$

Answer

- \frac{1}{4}

1.6-451 §1.6 source ↗

Mixed Practice

In the following exercises, simplify.

$\frac{n}{5} - \frac{4}{5}$

Answer

\frac{n - 4}{5}

1.6-453 §1.6 source ↗

Mixed Practice

In the following exercises, simplify.

$- \frac{7}{24} + \frac{2}{24}$

Answer

- \frac{5}{24}

1.6-455 §1.6 source ↗

Mixed Practice

In the following exercises, simplify.

$\frac{8}{15} \div \frac{12}{5}$

Answer

\frac{2}{9}

1.6-457 §1.6 source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$\frac{1}{2} + \frac{1}{7}$

Answer

\frac{9}{14}

1.6-459 §1.6 source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$\frac{1}{3} - (- \frac{1}{9})$

Answer

\frac{4}{9}

1.6-461 §1.6 source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$\frac{7}{12} + \frac{5}{8}$

Answer

\frac{29}{24}

1.6-463 §1.6 source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$\frac{7}{12} - \frac{9}{16}$

Answer

\frac{1}{48}

1.6-465 §1.6 source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$\frac{2}{3} - \frac{3}{8}$

Answer

\frac{7}{24}

1.6-467 §1.6 source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$- \frac{11}{30} + \frac{27}{40}$

Answer

\frac{37}{120}

1.6-469 §1.6 source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$- \frac{13}{30} + \frac{25}{42}$

Answer

\frac{17}{105}

1.6-471 §1.6 source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$- \frac{39}{56} - \frac{22}{35}$

Answer

- \frac{53}{40}

1.6-473 §1.6 source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$- \frac{2}{3} - (- \frac{3}{4})$

Answer

\frac{1}{12}

1.6-475 §1.6 source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$1 + \frac{7}{8}$

Answer

\frac{15}{8}

1.6-477 §1.6 source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$\frac{x}{3} + \frac{1}{4}$

Answer

\frac{4 x + 3}{12}

1.6-479 §1.6 source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$\frac{y}{4} - \frac{3}{5}$

Answer

\frac{5 y - 12}{20}

1.6-481 §1.6 source ↗

Mixed Practice

In the following exercises, simplify.

ⓐ $\frac{2}{3} + \frac{1}{6}$ ⓑ $\frac{2}{3} \div \frac{1}{6}$

Answer

ⓐ

\frac{5}{6}

ⓑ 4

1.6-483 §1.6 source ↗

Mixed Practice

In the following exercises, simplify.

ⓐ $\frac{5 n}{6} \div \frac{8}{15}$ ⓑ $\frac{5 n}{6} - \frac{8}{15}$

Answer

ⓐ

\frac{25 n}{16}

ⓑ

\frac{25 n - 16}{30}

1.6-485 §1.6 source ↗

Mixed Practice

In the following exercises, simplify.

$- \frac{3}{8} \div (- \frac{3}{10})$

Answer

\frac{5}{4}

1.6-487 §1.6 source ↗

Mixed Practice

In the following exercises, simplify.

$- \frac{3}{8} + \frac{5}{12}$

Answer

\frac{1}{24}

1.6-489 §1.6 source ↗

Mixed Practice

In the following exercises, simplify.

$\frac{5}{6} - \frac{1}{9}$

Answer

\frac{13}{18}

1.6-491 §1.6 source ↗

Mixed Practice

In the following exercises, simplify.

$- \frac{7}{15} - \frac{y}{4}$

Answer

\frac{−28 - 15 y}{60}

1.6-493 §1.6 source ↗

Mixed Practice

In the following exercises, simplify.

$\frac{11}{12 a} \cdot \frac{9 a}{16}$

Answer

\frac{33}{64}

1.6-495 §1.6 source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$\frac{2^{3} + 4^{2}}{{(\frac{2}{3})}^{2}}$

Answer

1.6-497 §1.6 source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$\frac{{(\frac{3}{5})}^{2}}{{(\frac{3}{7})}^{2}}$

Answer

\frac{49}{25}

1.6-499 §1.6 source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$\frac{2}{\frac{1}{3} + \frac{1}{5}}$

Answer

\frac{15}{4}

1.6-501 §1.6 source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$\frac{\frac{7}{8} - \frac{2}{3}}{\frac{1}{2} + \frac{3}{8}}$

Answer

\frac{5}{21}

1.6-503 §1.6 source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$\frac{1}{2} + \frac{2}{3} \cdot \frac{5}{12}$

Answer

\frac{7}{9}

1.6-505 §1.6 source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$1 - \frac{3}{5} \div \frac{1}{10}$

Answer

−5

1.6-507 §1.6 source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$\frac{2}{3} + \frac{1}{6} + \frac{3}{4}$

Answer

\frac{19}{12}

1.6-509 §1.6 source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$\frac{3}{8} - \frac{1}{6} + \frac{3}{4}$

Answer

\frac{23}{24}

1.6-511 §1.6 source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$12 (\frac{9}{20} - \frac{4}{15})$

Answer

\frac{11}{5}

1.6-513 §1.6 source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$\frac{\frac{5}{8} + \frac{1}{6}}{\frac{19}{24}}$

Answer

1.6-515 §1.6 source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$(\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2})$

Answer

\frac{13}{3}

1.6-517 §1.6 source ↗

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

$x + (- \frac{5}{6})$ when
ⓐ $x = \frac{1}{3}$
ⓑ $x = - \frac{1}{6}$

Answer

ⓐ

- \frac{1}{2}

ⓑ

−1

1.6-519 §1.6 source ↗

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

$x - \frac{2}{5}$ when ⓐ $x = \frac{3}{5}$ ⓑ $x = - \frac{3}{5}$

Answer

ⓐ

\frac{1}{5}

ⓑ

−1

1.6-521 §1.6 source ↗

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

$\frac{7}{10} - w$ when ⓐ $w = \frac{1}{2}$ ⓑ $w = - \frac{1}{2}$

Answer

ⓐ

\frac{1}{5}

ⓑ

\frac{6}{5}

1.6-523 §1.6 source ↗

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

$2 x^{2} y^{3}$ when $x = - \frac{2}{3}$ and $y = - \frac{1}{2}$

Answer

- \frac{1}{9}

1.6-525 §1.6 source ↗

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

$\frac{a + b}{a - b}$ when $a = −3, b = 8$

Answer

- \frac{5}{11}

1.6-527 §1.6 source ↗

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

Decorating Laronda is making covers for the throw pillows on her sofa. For each pillow cover, she needs $\frac{1}{2}$ yard of print fabric and $\frac{3}{8}$ yard of solid fabric. What is the total amount of fabric Laronda needs for each pillow cover?

Answer

\frac{7}{8}

yard

1.6-529 §1.6 source ↗

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

Why do you need a common denominator to add or subtract fractions? Explain.

Answer

Answers may vary

Try It 1.181 §1.7 source ↗

Name the decimal:

6.7 .

Answer

six and seven tenths

Try It 1.182 §1.7 source ↗

Name the decimal:

5.8 .

Answer

five and eight tenths

Try It 1.183 §1.7 source ↗

Name the decimal:

−13.461 .

Answer

negative thirteen and four hundred sixty-one thousandths

Try It 1.184 §1.7 source ↗

Name the decimal:

−2.053 .

Answer

negative two and fifty-three thousandths

Try It 1.185 §1.7 source ↗

Write as a decimal: thirteen and sixty-eight thousandths.

Answer

13.068

Try It 1.186 §1.7 source ↗

Write as a decimal: five and ninety-four thousandths.

Answer

5.094

Try It 1.187 §1.7 source ↗

Round to the nearest hundredth:

1.047 .

Answer

1.05

Try It 1.188 §1.7 source ↗

Round to the nearest hundredth:

9.173 .

Answer

9.17

Try It 1.189 §1.7 source ↗

Round

6.582

to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

Answer

ⓐ 6.58 ⓑ 6.6 ⓒ 7

Try It 1.190 §1.7 source ↗

Round

15.2175

to the nearest ⓐ thousandth ⓑ hundredth ⓒ tenth.

Answer

ⓐ 15.218 ⓑ 15.22 ⓒ 15.2

Try It 1.191 §1.7 source ↗

Add:

4.8 + 11.69 .

Answer

16.49

Try It 1.192 §1.7 source ↗

Add:

5.123 +

18.47 .

Answer

23.593

Try It 1.193 §1.7 source ↗

Subtract:

10 - 9.58 .

Answer

0.42

Try It 1.194 §1.7 source ↗

Subtract:

50 - 37.42 .

Answer

12.58

Try It 1.195 §1.7 source ↗

Multiply:

−4.5 (6.107) .

Answer

−27.4815

Try It 1.196 §1.7 source ↗

Multiply:

−10.79 (8.12) .

Answer

−87.6148

Try It 1.197 §1.7 source ↗

Multiply 2.58 ⓐ by 10 ⓑ by 100 ⓒ by 1,000.

Answer

ⓐ 25.8 ⓑ 258 ⓒ 2,580

Try It 1.198 §1.7 source ↗

Multiply 14.2 ⓐ by 10 ⓑ by 100 ⓒ by 1,000.

Answer

ⓐ 142 ⓑ 1,420 ⓒ 14,200

Try It 1.199 §1.7 source ↗

Divide:

−23.492 \div (−0.04) .

Answer

587.3

Try It 1.200 §1.7 source ↗

Divide:

−4.11 \div (−0.12) .

Answer

34.25

Try It 1.201 §1.7 source ↗

Divide:

$6.99 \div 36 .

Answer

$0.19

Try It 1.202 §1.7 source ↗

Divide:

$4.99 \div 12 .

Answer

$0.42

Try It 1.203 §1.7 source ↗

Write 0.234 as a fraction.

Answer

\frac{117}{500}

Try It 1.204 §1.7 source ↗

Write 0.024 as a fraction.

Answer

\frac{3}{125}

Try It 1.205 §1.7 source ↗

Write

- \frac{7}{8}

as a decimal.

Answer

−0.875

Try It 1.206 §1.7 source ↗

Write

- \frac{3}{8}

as a decimal.

Answer

−0.375

Try It 1.207 §1.7 source ↗

Write

\frac{27}{11}

as a decimal.

Answer

2. \overset{—}{45}

Try It 1.208 §1.7 source ↗

Write

\frac{51}{22}

as a decimal.

Answer

2.3 \overset{—}{18}

Try It 1.209 §1.7 source ↗

Simplify:

\frac{3}{8} + 4.9 .

Answer

5.275

Try It 1.210 §1.7 source ↗

Simplify:

5.7 + \frac{13}{20} .

Answer

6.35

Try It 1.211 §1.7 source ↗

Convert each percent to a decimal: ⓐ

9%

ⓑ

87%

Answer

ⓐ 0.09 ⓑ 0.87 ⓒ 0.039

Try It 1.212 §1.7 source ↗

Convert each percent to a decimal: ⓐ 3% ⓑ 91% ⓒ 8.3%.

Answer

ⓐ 0.03 ⓑ 0.91 ⓒ 0.083

Try It 1.213 §1.7 source ↗

Convert each decimal to a percent: ⓐ 0.17 ⓑ 1.75 ⓒ 0.0825.

Answer

ⓐ 17% ⓑ 175% ⓒ 8.25%

Try It 1.214 §1.7 source ↗

Convert each decimal to a percent: ⓐ 0.41 ⓑ 2.25 ⓒ 0.0925.

Answer

ⓐ 41% ⓑ 225% ⓒ 9.25%

1.7-531 §1.7 source ↗

Name and Write Decimals

In the following exercises, write as a decimal.

Twenty-nine and eighty-one hundredths

Answer

29.81

1.7-533 §1.7 source ↗

Name and Write Decimals

In the following exercises, write as a decimal.

Seven tenths

Answer

0.7

1.7-535 §1.7 source ↗

Name and Write Decimals

In the following exercises, write as a decimal.

Twenty-nine thousandth

Answer

0.029

1.7-537 §1.7 source ↗

Name and Write Decimals

In the following exercises, write as a decimal.

Negative eleven and nine ten-thousandths

Answer

−11.0009

1.7-539 §1.7 source ↗

In the following exercises, name each decimal.

5.5

Answer

five and five tenths

1.7-541 §1.7 source ↗

In the following exercises, name each decimal.

8.71

Answer

eight and seventy-one hundredths

1.7-543 §1.7 source ↗

In the following exercises, name each decimal.

0.002

Answer

two thousandths

1.7-545 §1.7 source ↗

In the following exercises, name each decimal.

$− 17 .9$

Answer

negative seventeen and nine tenths

1.7-547 §1.7 source ↗

Round Decimals

In the following exercises, round each number to the nearest tenth.

0.67

Answer

0.7

1.7-549 §1.7 source ↗

Round Decimals

In the following exercises, round each number to the nearest tenth.

2.84

Answer

2.8

1.7-551 §1.7 source ↗

In the following exercises, round each number to the nearest hundredth.

0.845

Answer

0.85

1.7-553 §1.7 source ↗

In the following exercises, round each number to the nearest hundredth.

0.299

Answer

0.30

1.7-555 §1.7 source ↗

In the following exercises, round each number to the nearest hundredth.

4.098

Answer

4.10

1.7-557 §1.7 source ↗

In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

5.781

Answer

ⓐ 5.78 ⓑ 5.8 ⓒ 6

1.7-559 §1.7 source ↗

In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

63.479

Answer

ⓐ 63.48 ⓑ 63.5 ⓒ 63

1.7-561 §1.7 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$16.92 + 7.56$

Answer

24.48

1.7-563 §1.7 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$21.76 - 30.99$

Answer

−9.23

1.7-565 §1.7 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$−16.53 -$ $24.38$

Answer

−40.91

1.7-567 §1.7 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$−38.69 +$ $31.47$

Answer

−7.22

1.7-569 §1.7 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$72.5 - 100$

Answer

−27.5

1.7-571 §1.7 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$15 + 0.73$

Answer

15.73

1.7-573 §1.7 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$91.95 -$ $(−10.462)$

Answer

102.412

1.7-575 §1.7 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$55.01 - 3.7$

Answer

51.31

1.7-577 §1.7 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$2.51 - 7.4$

Answer

−4.89

1.7-579 §1.7 source ↗

Multiply and Divide Decimals

In the following exercises, multiply.

$(0.24) (0.6)$

Answer

0.144

1.7-581 §1.7 source ↗

Multiply and Divide Decimals

In the following exercises, multiply.

$(5.9) (7.12)$

Answer

42.008

1.7-583 §1.7 source ↗

Multiply and Divide Decimals

In the following exercises, multiply.

$(−4.3) (2.71)$

Answer

−11.653

1.7-585 §1.7 source ↗

Multiply and Divide Decimals

In the following exercises, multiply.

$(−5.18) (−65.23)$

Answer

337.8914

1.7-587 §1.7 source ↗

Multiply and Divide Decimals

In the following exercises, multiply.

$(0.06) (21.75)$

Answer

1.305

1.7-589 §1.7 source ↗

Multiply and Divide Decimals

In the following exercises, multiply.

$(9.24) (10)$

Answer

92.4

1.7-591 §1.7 source ↗

Multiply and Divide Decimals

In the following exercises, multiply.

$(55.2) (1000)$

Answer

55,200

1.7-593 §1.7 source ↗

In the following exercises, divide.

$4.75 \div 25$

Answer

0.19

1.7-595 §1.7 source ↗

In the following exercises, divide.

$$117.25 \div 48$

Answer

$2.44

1.7-597 §1.7 source ↗

In the following exercises, divide.

$0.6 \div 0.2$

Answer

1.7-599 §1.7 source ↗

In the following exercises, divide.

$1.44 \div (−0.3)$

Answer

−4.8

1.7-601 §1.7 source ↗

In the following exercises, divide.

$−1.75 \div (−0.05)$

Answer

1.7-603 §1.7 source ↗

In the following exercises, divide.

$5.2 \div 2.5$

Answer

2.08

1.7-605 §1.7 source ↗

In the following exercises, divide.

$11 \div 0.55$

Answer

1.7-607 §1.7 source ↗

Convert Decimals, Fractions and Percents

In the following exercises, write each decimal as a fraction.

0.04

Answer

\frac{1}{25}

1.7-609 §1.7 source ↗

Convert Decimals, Fractions and Percents

In the following exercises, write each decimal as a fraction.

0.52

Answer

\frac{13}{25}

1.7-611 §1.7 source ↗

Convert Decimals, Fractions and Percents

In the following exercises, write each decimal as a fraction.

1.25

Answer

\frac{5}{4}

1.7-613 §1.7 source ↗

Convert Decimals, Fractions and Percents

In the following exercises, write each decimal as a fraction.

0.375

Answer

\frac{3}{8}

1.7-615 §1.7 source ↗

Convert Decimals, Fractions and Percents

In the following exercises, write each decimal as a fraction.

0.095

Answer

\frac{19}{200}

1.7-617 §1.7 source ↗

In the following exercises, convert each fraction to a decimal.

$\frac{17}{20}$

Answer

0.85

1.7-619 §1.7 source ↗

In the following exercises, convert each fraction to a decimal.

$\frac{11}{4}$

Answer

2.75

1.7-621 §1.7 source ↗

In the following exercises, convert each fraction to a decimal.

$- \frac{310}{25}$

Answer

−12.4

1.7-623 §1.7 source ↗

In the following exercises, convert each fraction to a decimal.

$\frac{15}{11}$

Answer

1. \overset{—}{36}

1.7-625 §1.7 source ↗

In the following exercises, convert each fraction to a decimal.

$\frac{15}{111}$

Answer

0. \overset{—}{135}

1.7-627 §1.7 source ↗

In the following exercises, convert each fraction to a decimal.

$2.4 + \frac{5}{8}$

Answer

3.025

1.7-629 §1.7 source ↗

In the following exercises, convert each percent to a decimal.

Answer

0.01

1.7-631 §1.7 source ↗

In the following exercises, convert each percent to a decimal.

63%

Answer

0.63

1.7-633 §1.7 source ↗

In the following exercises, convert each percent to a decimal.

150%

Answer

1.5

1.7-635 §1.7 source ↗

In the following exercises, convert each percent to a decimal.

21.4%

Answer

0.214

1.7-637 §1.7 source ↗

In the following exercises, convert each percent to a decimal.

7.8%

Answer

0.078

1.7-639 §1.7 source ↗

In the following exercises, convert each decimal to a percent.

0.01

Answer

1.7-641 §1.7 source ↗

In the following exercises, convert each decimal to a percent.

1.35

Answer

135%

1.7-643 §1.7 source ↗

In the following exercises, convert each decimal to a percent.

Answer

300%

1.7-645 §1.7 source ↗

In the following exercises, convert each decimal to a percent.

0.0875

Answer

8.75%

1.7-647 §1.7 source ↗

In the following exercises, convert each decimal to a percent.

2.254

Answer

225.4%

1.7-649 §1.7 source ↗

In the following exercises, convert each decimal to a percent.

Salary Increase Danny got a raise and now makes $58,965.95 a year. Round this number to the nearest ⓐ dollar ⓑ thousand dollars ⓒ ten thousand dollars.

Answer

ⓐ $58,966 ⓑ $59,000 ⓒ $60,000

1.7-651 §1.7 source ↗

In the following exercises, convert each decimal to a percent.

Sales Tax Hyo Jin lives in San Diego. She bought a refrigerator for $1,624.99 and when the clerk calculated the sales tax it came out to exactly $142.186625. Round the sales tax to the nearest ⓐ penny and ⓑ dollar.

Answer

ⓐ $142.19; ⓑ $142

1.7-653 §1.7 source ↗

In the following exercises, convert each decimal to a percent.

Paycheck Annie has two jobs. She gets paid $14.04 per hour for tutoring at City College and $8.75 per hour at a coffee shop. Last week she tutored for 8 hours and worked at the coffee shop for 15 hours. ⓐ How much did she earn? ⓑ If she had worked all 23 hours as a tutor instead of working both jobs, how much more would she have earned?

Answer

ⓐ $243.57 ⓑ $79.35

1.7-655 §1.7 source ↗

In the following exercises, convert each decimal to a percent.

How does knowing about US money help you learn about decimals?

Answer

Answers may vary

1.7-657 §1.7 source ↗

In the following exercises, convert each decimal to a percent.

Without solving the problem “44 is 80% of what number” think about what the solution might be. Should it be a number that is greater than 44 or less than 44? Explain your reasoning.

Answer

Answers may vary

Try It 1.215 §1.8 source ↗

Simplify: ⓐ

\sqrt{36}

ⓑ

\sqrt{169} .

Answer

ⓐ 6 ⓑ 13

Try It 1.216 §1.8 source ↗

Simplify: ⓐ

\sqrt{16}

ⓑ

\sqrt{196} .

Answer

ⓐ 4 ⓑ 14

Try It 1.217 §1.8 source ↗

Simplify: ⓐ

− \sqrt{4}

ⓑ

− \sqrt{225} .

Answer

ⓐ

−2

ⓑ

−15

Try It 1.218 §1.8 source ↗

Simplify: ⓐ

− \sqrt{81}

ⓑ

− \sqrt{100} .

Answer

ⓐ

−9

ⓑ

−10

Try It 1.219 §1.8 source ↗

Write as the ratio of two integers: ⓐ

−24

ⓑ 3.57.

Answer

ⓐ

\frac{−24}{1}

ⓑ

\frac{357}{100}

Try It 1.220 §1.8 source ↗

Write as the ratio of two integers: ⓐ

−19

ⓑ 8.41.

Answer

ⓐ

\frac{−19}{1}

ⓑ

\frac{841}{100}

Try It 1.221 §1.8 source ↗

For the given numbers list the ⓐ rational numbers ⓑ irrational numbers:

0.29,

0.81 \overset{–}{6},

2.515115111 … .

Answer

ⓐ

0.29, 0.81 \overset{–}{6}

ⓑ

2.515115111 …

Try It 1.222 §1.8 source ↗

For the given numbers list the ⓐ rational numbers ⓑ irrational numbers:

2.6 \overset{–}{3},

0.125,

0.418302 …

Answer

ⓐ

2.6 \overset{–}{3}, 0.125

ⓑ

0.418302 …

Try It 1.223 §1.8 source ↗

For each number given, identify whether it is rational or irrational: ⓐ

\sqrt{81}

ⓑ

\sqrt{17} .

Answer

ⓐ rational ⓑ irrational

Try It 1.224 §1.8 source ↗

For each number given, identify whether it is rational or irrational: ⓐ

\sqrt{116}

ⓑ

\sqrt{121} .

Answer

ⓐ irrational ⓑ rational

Try It 1.225 §1.8 source ↗

For each number given, identify whether it is a real number or not a real number: ⓐ

\sqrt{−196}

ⓑ

− \sqrt{81} .

Answer

ⓐ not a real number ⓑ real number

Try It 1.226 §1.8 source ↗

For each number given, identify whether it is a real number or not a real number: ⓐ

− \sqrt{49}

ⓑ

\sqrt{−121} .

Answer

ⓐ real number ⓑ not a real number

Try It 1.227 §1.8 source ↗

For the given numbers, list the ⓐ whole numbers ⓑ integers ⓒ rational numbers ⓓ irrational numbers ⓔ real numbers:

−3,

− \sqrt{2},

0. \overset{–}{3},

\frac{9}{5},

4,

\sqrt{49} .

Answer

ⓐ

4, \sqrt{49}

ⓑ

−3, 4, \sqrt{49}

ⓒ

−3,

0. \overset{–}{3},

\frac{9}{5},

4,

\sqrt{49}

ⓓ

− \sqrt{2}

ⓔ

−3,

− \sqrt{2},

0. \overset{–}{3},

\frac{9}{5},

4,

\sqrt{49}

Try It 1.228 §1.8 source ↗

For the given numbers, list the ⓐ whole numbers ⓑ integers ⓒ rational numbers ⓓ irrational numbers ⓔ real numbers:

− \sqrt{25},

-

\frac{3}{8},

−1,

6,

\sqrt{121},

2.041975 …

Answer

ⓐ

6, \sqrt{121}

ⓑ

− \sqrt{25},

−1,

6,

\sqrt{121}

ⓒ

− \sqrt{25},

-

\frac{3}{8},

−1,

6,

\sqrt{121}

ⓓ

2.041975 …

ⓔ

− \sqrt{25},

-

\frac{3}{8},

−1,

6,

\sqrt{121},

2.041975 …

Try It 1.229 §1.8 source ↗

Locate and label the following on a number line:

−1,

\frac{1}{3},

\frac{6}{5},

-

\frac{7}{4},

\frac{9}{2},

5,

-

\frac{8}{3} .

Answer

Try It 1.230 §1.8 source ↗

Locate and label the following on a number line:

−2,

\frac{2}{3},

\frac{7}{5},

-

\frac{7}{4},

\frac{7}{2},

3,

-

\frac{7}{3} .

Answer

Try It 1.231 §1.8 source ↗

Order each of the following pairs of numbers, using < or >:

ⓐ $- \frac{1}{3}___−1$ ⓑ $−1 \frac{1}{2}___−2$ ⓒ $- \frac{2}{3}___- \frac{1}{3}$ ⓓ $−3___- \frac{7}{3} .$

Answer

ⓐ > ⓑ > ⓒ < ⓓ <

Try It 1.232 §1.8 source ↗

Order each of the following pairs of numbers, using < or >:

ⓐ $−1___- \frac{2}{3}$ ⓑ $−2 \frac{1}{4}___−2$ ⓒ $- \frac{3}{5}___- \frac{4}{5}$ ⓓ $−4___- \frac{10}{3} .$

Answer

ⓐ < ⓑ < ⓒ > ⓓ <

Try It 1.233 §1.8 source ↗

Locate on the number line: 0.6.

Answer

Try It 1.234 §1.8 source ↗

Locate on the number line: 0.9.

Answer

Try It 1.235 §1.8 source ↗

Locate on the number line:

−0.6 .

Answer

Try It 1.236 §1.8 source ↗

Locate on the number line:

−0.7 .

Answer

Try It 1.237 §1.8 source ↗

Order each of the following pairs of numbers, using

<

or >

: 0.42___0.4 .

Answer

Try It 1.238 §1.8 source ↗

Order each of the following pairs of numbers, using

<

or >

: 0.18___0.1 .

Answer

Try It 1.239 §1.8 source ↗

Order the following pair of numbers, using

<

or >

: 0.76___0.706 .

Answer

Try It 1.240 §1.8 source ↗

Order the following pair of numbers, using

<

or >

: 0.305___0.35 .

Answer

Try It 1.241 §1.8 source ↗

Order the following pair of numbers, using < or >:

−0.3___−0.5 .

Answer

Try It 1.242 §1.8 source ↗

Order the following pair of numbers, using < or >:

−0.6___−0.7 .

Answer

1.8-659 §1.8 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{36}$

Answer

1.8-661 §1.8 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{64}$

Answer

1.8-663 §1.8 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{9}$

Answer

1.8-665 §1.8 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{100}$

Answer

1.8-667 §1.8 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$− \sqrt{4}$

Answer

−2

1.8-669 §1.8 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$− \sqrt{1}$

Answer

−1

1.8-671 §1.8 source ↗

Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers

In the following exercises, write as the ratio of two integers.

ⓐ 5 ⓑ 3.19

Answer

ⓐ

\frac{5}{1}

ⓑ

\frac{319}{100}

1.8-673 §1.8 source ↗

Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers

In the following exercises, write as the ratio of two integers.

ⓐ $− 12$ ⓑ 9.279

Answer

ⓐ

\frac{−12}{1}

ⓑ

\frac{9279}{1000}

1.8-675 §1.8 source ↗

In the following exercises, list the ⓐ rational numbers, ⓑ irrational numbers

$0.75,$ $0.22 \overset{–}{3},$ $1.39174 …$

Answer

ⓐ

0.75, 0.22 \overset{–}{3}

ⓑ

1.39174 …

1.8-677 §1.8 source ↗

In the following exercises, list the ⓐ rational numbers, ⓑ irrational numbers

$0.4 \overset{–}{5},$ $1.919293 …,$ $3.59$

Answer

ⓐ

0.4 \overset{–}{5}, 3.59

ⓑ

1.919293 …

1.8-679 §1.8 source ↗

In the following exercises, identify whether each number is rational or irrational.

ⓐ $\sqrt{25}$ ⓑ $\sqrt{30}$

Answer

ⓐ rational ⓑ irrational

1.8-681 §1.8 source ↗

In the following exercises, identify whether each number is rational or irrational.

ⓐ $\sqrt{164}$ ⓑ $\sqrt{169}$

Answer

ⓐ irrational ⓑ rational

1.8-683 §1.8 source ↗

In the following exercises, identify whether each number is a real number or not a real number.

ⓐ $− \sqrt{81}$ ⓑ $\sqrt{−121}$

Answer

ⓐ real number ⓑ not a real number

1.8-685 §1.8 source ↗

In the following exercises, identify whether each number is a real number or not a real number.

ⓐ $\sqrt{−36}$ ⓑ $− \sqrt{144}$

Answer

ⓐ not a real number ⓑ real number

1.8-687 §1.8 source ↗

In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.

$−8,$ $0,$ $1.95286 …,$ $\frac{12}{5},$ $\sqrt{36},$ $9$

Answer

ⓐ

0, \sqrt{36}, 9

ⓑ

−8, 0, \sqrt{36}, 9

ⓒ

−8,

0,

\frac{12}{5},

\sqrt{36},

9

ⓓ

1.95286 …

ⓔ

−8,

0,

1.95286 …,

\frac{12}{5},

\sqrt{36},

9

1.8-689 §1.8 source ↗

In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.

$− \sqrt{100},$ $−7,$ $-$ $\frac{8}{3},$ $−1,$ $0.77,$ $3 \frac{1}{4}$

Answer

ⓐ none ⓑ

− \sqrt{100}, −7, −1

ⓒ

− \sqrt{100},

−7,

-

\frac{8}{3},

−1,

0.77,

3 \frac{1}{4}

ⓓ none ⓔ

− \sqrt{100},

−7,

-

\frac{8}{3},

−1,

0.77,

3 \frac{1}{4}

1.8-691 §1.8 source ↗

Locate Fractions on the Number Line

In the following exercises, locate the numbers on a number line.

$\frac{3}{4}, \frac{8}{5}, \frac{10}{3}$

Answer

1.8-693 §1.8 source ↗

Locate Fractions on the Number Line

In the following exercises, locate the numbers on a number line.

$\frac{3}{10},$ $\frac{7}{2},$ $\frac{11}{6},$ $4$

Answer

1.8-695 §1.8 source ↗

Locate Fractions on the Number Line

In the following exercises, locate the numbers on a number line.

$\frac{2}{5}, - \frac{2}{5}$

Answer

1.8-697 §1.8 source ↗

Locate Fractions on the Number Line

In the following exercises, locate the numbers on a number line.

$\frac{3}{4},$ $-$ $\frac{3}{4},$ $1 \frac{2}{3},$ $−1 \frac{2}{3},$ $\frac{5}{2},$ $-$ $\frac{5}{2}$

Answer

1.8-699 §1.8 source ↗

In the following exercises, order each of the pairs of numbers, using < or >.

$−1___- \frac{1}{4}$

Answer

1.8-701 §1.8 source ↗

In the following exercises, order each of the pairs of numbers, using < or >.

$−2 \frac{1}{2}___−3$

Answer

1.8-703 §1.8 source ↗

In the following exercises, order each of the pairs of numbers, using < or >.

$- \frac{5}{12}___- \frac{7}{12}$

Answer

1.8-705 §1.8 source ↗

In the following exercises, order each of the pairs of numbers, using < or >.

$−3___- \frac{13}{5}$

Answer

1.8-707 §1.8 source ↗

Locate Decimals on the Number Line In the following exercises, locate the number on the number line.

0.8

Answer

1.8-709 §1.8 source ↗

Locate Decimals on the Number Line In the following exercises, locate the number on the number line.

$−1.6$

Answer

1.8-711 §1.8 source ↗

In the following exercises, order each pair of numbers, using < or >.

$0.37___0.63$

Answer

1.8-713 §1.8 source ↗

In the following exercises, order each pair of numbers, using < or >.

$0.91___0.901$

Answer

1.8-715 §1.8 source ↗

In the following exercises, order each pair of numbers, using < or >.

$−0.5___−0.3$

Answer

1.8-717 §1.8 source ↗

In the following exercises, order each pair of numbers, using < or >.

$−0.62___−0.619$

Answer

1.8-719 §1.8 source ↗

In the following exercises, order each pair of numbers, using < or >.

Field trip All the 5th graders at Lincoln Elementary School will go on a field trip to the science museum. Counting all the children, teachers, and chaperones, there will be 147 people. Each bus holds 44 people.

ⓐ How many busses will be needed?
ⓑ Why must the answer be a whole number?
ⓒ Why shouldn’t you round the answer the usual way, by choosing the whole number closest to the exact answer?

Answer

ⓐ 4 busses ⓑ answers may vary ⓒ answers may vary

1.8-721 §1.8 source ↗

In the following exercises, order each pair of numbers, using < or >.

In your own words, explain the difference between a rational number and an irrational number.

Answer

Answers may vary

Try It 1.243 §1.9 source ↗

Simplify:

23 r +

14 s +

9 r +

15 s .

Answer

32 r + 29 s

Try It 1.244 §1.9 source ↗

Simplify:

37 m +

21 n +

4 m -

15 n .

Answer

41 m + 6 n

Try It 1.245 §1.9 source ↗

Simplify:

(\frac{7}{15} + \frac{5}{8}) +

\frac{3}{8} .

Answer

1 \frac{7}{15}

Try It 1.246 §1.9 source ↗

Simplify:

(\frac{2}{9} + \frac{7}{12}) +

\frac{5}{12} .

Answer

1 \frac{2}{9}

Try It 1.247 §1.9 source ↗

Use the associative property to simplify 8(4x).

Answer

32x

Try It 1.248 §1.9 source ↗

Use the associative property to simplify

−9 (7 y) .

Answer

−63 y

Try It 1.249 §1.9 source ↗

Find the additive inverse of: ⓐ

\frac{7}{9}

ⓑ

1.2

ⓒ

−14

ⓓ

- \frac{9}{4} .

Answer

ⓐ

- \frac{7}{9}

ⓑ

−1.2

ⓒ

14

ⓓ

\frac{9}{4}

Try It 1.250 §1.9 source ↗

Find the additive inverse of: ⓐ

\frac{7}{13}

ⓑ

8.4

ⓒ

−46

ⓓ

- \frac{5}{2} .

Answer

ⓐ

- \frac{7}{13}

ⓑ

−8.4

ⓒ

46

ⓓ

\frac{5}{2}

Try It 1.251 §1.9 source ↗

Find the multiplicative inverse of ⓐ

4

ⓑ

- \frac{1}{7}

ⓒ

0.3

Answer

ⓐ

\frac{1}{4}

ⓑ

−7

ⓒ

\frac{10}{3}

Try It 1.252 §1.9 source ↗

Find the multiplicative inverse of ⓐ

18

ⓑ

- \frac{4}{5}

ⓒ

0.6 .

Answer

ⓐ

\frac{1}{18}

ⓑ

- \frac{5}{4}

ⓒ

\frac{5}{3}

Try It 1.253 §1.9 source ↗

Simplify: ⓐ

−14 \cdot 0

ⓑ

\frac{0}{−6}

ⓒ

\frac{−2}{0} .

Answer

ⓐ 0 ⓑ 0 ⓒ undefined

Try It 1.254 §1.9 source ↗

Simplify: ⓐ

0 (−17)

ⓑ

\frac{0}{−10}

ⓒ

\frac{−5}{0} .

Answer

ⓐ 0 ⓑ 0 ⓒ undefined

Try It 1.255 §1.9 source ↗

Simplify:

−27 a +

(−48 a) +

27 a .

Answer

−48 a

Try It 1.256 §1.9 source ↗

Simplify:

39 x +

(−92 x) +

(−39 x) .

Answer

−92 x

Try It 1.257 §1.9 source ↗

Simplify:

\frac{9}{16} \cdot \frac{5}{49} \cdot \frac{16}{9} .

Answer

\frac{5}{49}

Try It 1.258 §1.9 source ↗

Simplify:

\frac{6}{17} \cdot \frac{11}{25} \cdot \frac{17}{6} .

Answer

\frac{11}{25}

Try It 1.259 §1.9 source ↗

Simplify: ⓐ

\frac{0}{m + 7},

where

m \neq − 7

ⓑ

\frac{18 - 6 c}{0},

where

18 - 6 c \neq 0 .

Answer

ⓐ 0 ⓑ undefined

Try It 1.260 §1.9 source ↗

Simplify: ⓐ

\frac{0}{d - 4},

where d \neq 4

ⓑ

\frac{15 - 4 q}{0},

where 15 -

4 q \neq 0 .

Answer

ⓐ 0 ⓑ undefined

Try It 1.261 §1.9 source ↗

Simplify:

\frac{2}{5} \cdot \frac{5}{2} (20 y + 50) .

Answer

20 y + 50

Try It 1.262 §1.9 source ↗

Simplify:

\frac{3}{8} \cdot \frac{8}{3} (12 z + 16) .

Answer

12 z + 16

Try It 1.263 §1.9 source ↗

Simplify:

4 (x + 2) .

Answer

4 x + 8

Try It 1.264 §1.9 source ↗

Simplify:

6 (x + 7) .

Answer

6 x + 42

Try It 1.265 §1.9 source ↗

Simplify:

6 (\frac{5}{6} y + \frac{1}{2}) .

Answer

5 y + 3

Try It 1.266 §1.9 source ↗

Simplify:

12 (\frac{1}{3} n + \frac{3}{4}) .

Answer

4 n + 9

Try It 1.267 §1.9 source ↗

Simplify:

100 (0.7 + 0.15 p) .

Answer

70 + 15 p

Try It 1.268 §1.9 source ↗

Simplify:

100 (0.04 + 0.35 d) .

Answer

4 + 35 d

Try It 1.269 §1.9 source ↗

Simplify:

−3 (6 m + 5) .

Answer

−18 m - 15

Try It 1.270 §1.9 source ↗

Simplify:

−6 (8 n + 11) .

Answer

−48 n - 66

Try It 1.271 §1.9 source ↗

Simplify:

−5 (2 - 3 a) .

Answer

−10 + 15 a

Try It 1.272 §1.9 source ↗

Simplify:

−7 (8 - 15 y) .

Answer

−56 + 105 y

Try It 1.273 §1.9 source ↗

Simplify:

− (z - 11) .

Answer

− z + 11

Try It 1.274 §1.9 source ↗

Simplify:

− (x - 4) .

Answer

− x + 4

Try It 1.275 §1.9 source ↗

Simplify:

9 - 3 (x + 2) .

Answer

3 - 3 x

Try It 1.276 §1.9 source ↗

Simplify:

7 x - 5 (x + 4) .

Answer

2 x - 20

Try It 1.277 §1.9 source ↗

Simplify:

6 (x - 9) -

(x + 12) .

Answer

5 x - 66

Try It 1.278 §1.9 source ↗

Simplify:

8 (x - 1) -

(x + 5) .

Answer

7 x - 13

1.9-723 §1.9 source ↗

Use the Commutative and Associative Properties

In the following exercises, use the associative property to simplify.

3(4x)

Answer

12x

1.9-725 §1.9 source ↗

Use the Commutative and Associative Properties

In the following exercises, use the associative property to simplify.

$(y + 12) + 28$

Answer

y + 40

1.9-727 §1.9 source ↗

In the following exercises, simplify.

$\frac{1}{2} + \frac{7}{8} + (- \frac{1}{2})$

Answer

\frac{7}{8}

1.9-729 §1.9 source ↗

In the following exercises, simplify.

$\frac{3}{20} \cdot \frac{49}{11} \cdot \frac{20}{3}$

Answer

\frac{49}{11}

1.9-731 §1.9 source ↗

In the following exercises, simplify.

$−24 \cdot 7 \cdot \frac{3}{8}$

Answer

−63

1.9-733 §1.9 source ↗

In the following exercises, simplify.

$(\frac{5}{6} + \frac{8}{15}) +$ $\frac{7}{15}$

Answer

1 \frac{5}{6}

1.9-735 §1.9 source ↗

In the following exercises, simplify.

17(0.25)(4)

Answer

1.9-737 §1.9 source ↗

In the following exercises, simplify.

[2.48(12)](0.5)

Answer

14.88

1.9-739 §1.9 source ↗

In the following exercises, simplify.

7(4a)

Answer

28a

1.9-741 §1.9 source ↗

In the following exercises, simplify.

$−15 (5 m)$

Answer

−75 m

1.9-743 §1.9 source ↗

In the following exercises, simplify.

$12 (\frac{5}{6} p)$

Answer

10p

1.9-745 §1.9 source ↗

In the following exercises, simplify.

$43 m +$ $(−12 n) +$ $(−16 m) +$ $(−9 n)$

Answer

27 m + (−21 n)

1.9-747 §1.9 source ↗

In the following exercises, simplify.

$\frac{3}{8} g +$ $\frac{1}{12} h +$ $\frac{7}{8} g +$ $\frac{5}{12} h$

Answer

\frac{5}{4} g + \frac{1}{2} h

1.9-749 §1.9 source ↗

In the following exercises, simplify.

$6.8 p +$ $9.14 q +$ $(−4.37 p) +$ $(−0.88 q)$

Answer

2.43 p + 8.26 q

1.9-751 §1.9 source ↗

Use the Identity and Inverse Properties of Addition and Multiplication

In the following exercises, find the additive inverse of each number.

ⓐ $\frac{2}{5}$ ⓑ 4.3
ⓒ $−8$
ⓓ $- \frac{10}{3}$

Answer

ⓐ

- \frac{2}{5}

ⓑ

−4.3

\frac{10}{3}

1.9-753 §1.9 source ↗

Use the Identity and Inverse Properties of Addition and Multiplication

In the following exercises, find the additive inverse of each number.

ⓐ $- \frac{7}{6}$ ⓑ $−0.075$ ⓒ 23 ⓓ $\frac{1}{4}$

Answer

ⓐ

\frac{7}{6}

ⓑ 0.075 ⓒ

−23

ⓓ

- \frac{1}{4}

1.9-755 §1.9 source ↗

In the following exercises, find the multiplicative inverse of each number.

ⓐ 6 ⓑ $- \frac{3}{4}$ ⓒ 0.7

Answer

ⓐ

\frac{1}{6}

ⓑ

- \frac{4}{3}

ⓒ

\frac{10}{7}

1.9-757 §1.9 source ↗

In the following exercises, find the multiplicative inverse of each number.

ⓐ $\frac{11}{12}$ ⓑ $−1.1$ ⓒ $−4$

Answer

ⓐ

\frac{12}{11}

ⓑ

- \frac{10}{11}

ⓒ

- \frac{1}{4}

1.9-759 §1.9 source ↗

Use the Properties of Zero

In the following exercises, simplify.

$\frac{0}{6}$

Answer

1.9-761 §1.9 source ↗

Use the Properties of Zero

In the following exercises, simplify.

$0 \div \frac{11}{12}$

Answer

1.9-763 §1.9 source ↗

Use the Properties of Zero

In the following exercises, simplify.

$\frac{0}{3}$

Answer

1.9-765 §1.9 source ↗

Use the Properties of Zero

In the following exercises, simplify.

$(−3.14) (0)$

Answer

1.9-767 §1.9 source ↗

Mixed Practice

In the following exercises, simplify.

$19 a + 44 - 19 a$

Answer

1.9-769 §1.9 source ↗

Mixed Practice

In the following exercises, simplify.

$10 (0.1 d)$

Answer

1.9-771 §1.9 source ↗

Mixed Practice

In the following exercises, simplify.

$\frac{0}{u - 4.99},$ where $u \neq 4.99$

Answer

1.9-773 §1.9 source ↗

Mixed Practice

In the following exercises, simplify.

$0 \div (x - \frac{1}{2}),$ where $x \neq \frac{1}{2}$

Answer

1.9-775 §1.9 source ↗

Mixed Practice

In the following exercises, simplify.

$\frac{32 - 5 a}{0},$ where
$32 - 5 a \neq 0$

Answer

undefined

1.9-777 §1.9 source ↗

Mixed Practice

In the following exercises, simplify.

$(\frac{3}{4} + \frac{9}{10} m) \div 0$ where
$\frac{3}{4} + \frac{9}{10} m \neq 0$

Answer

undefined

1.9-779 §1.9 source ↗

Mixed Practice

In the following exercises, simplify.

$15 \cdot \frac{3}{5} (4 d + 10)$

Answer

36 d + 90

1.9-781 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$8 (4 y + 9)$

Answer

32 y + 72

1.9-783 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$6 (c - 13)$

Answer

6 c - 78

1.9-785 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$\frac{1}{4} (3 q + 12)$

Answer

\frac{3}{4} q + 3

1.9-787 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$9 (\frac{5}{9} y - \frac{1}{3})$

Answer

5 y - 3

1.9-789 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$12 (\frac{1}{4} + \frac{2}{3} r)$

Answer

3 + 8 r

1.9-791 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$r (s - 18)$

Answer

r s - 18 r

1.9-793 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$(y + 4) p$

Answer

y p + 4 p

1.9-795 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$−7 (4 p + 1)$

Answer

−28 p - 7

1.9-797 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$−3 (x - 6)$

Answer

−3 x + 18

1.9-799 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$− (3 x - 7)$

Answer

−3 x + 7

1.9-801 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$16 - 3 (y + 8)$

Answer

−3 y - 8

1.9-803 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$4 - 11 (3 c - 2)$

Answer

−33 c + 26

1.9-805 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$22 - (a + 3)$

Answer

− a + 19

1.9-807 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$(5 m - 3) -$ $(m + 7)$

Answer

4 m - 10

1.9-809 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$5 (2 n + 9) +$ $12 (n - 3)$

Answer

22 n + 9

1.9-811 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$9 (8 x - 3) -$ $(−2)$

Answer

72 x - 25

1.9-813 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$14 (c - 1) -$ $8 (c - 6)$

Answer

6 c + 34

1.9-815 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$6 (7 y + 8) -$ $(30 y - 15)$

Answer

12 y + 63

1.9-817 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

Insurance copayment Carrie had to have 5 fillings done. Each filling cost $80. Her dental insurance required her to pay 20% of the cost as a copay. Calculate Carrie’s copay:

ⓐ First, by multiplying 0.20 by 80 to find her copay for each filling and then multiplying your answer by 5 to find her total copay for 5 fillings.

ⓑ Next, by multiplying [5(0.20)](80)

Answer

1.9-819 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

Buying by the case Trader Joe’s grocery stores sold a bottle of wine they called “Two Buck Chuck” for $1.99. They sold a case of 12 bottles for $23.88. To find the cost of 12 bottles at $1.99, notice that 1.99 is $2 - 0.01 .$

ⓐ Multiply 12(1.99) by using the distributive property to multiply $12 (2 - 0.01) .$

ⓑ Was it a bargain to buy “Two Buck Chuck” by the case?

Answer

ⓐ $23.88 ⓑ no, the price is the same

1.9-821 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

In your own words, state the commutative property of addition.

Answer

Answers may vary

1.9-823 §1.9 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

Simplify $8 (x - \frac{1}{4})$ using the distributive property and explain each step.

Answer

Answers may vary

Try It 1.279 §1.10 source ↗

Lexie is 30 inches tall. Convert her height to feet.

Answer

2.5 feet

Try It 1.280 §1.10 source ↗

Rene bought a hose that is 18 yards long. Convert the length to feet.

Answer

54 feet

Try It 1.281 §1.10 source ↗

Arnold’s SUV weighs about 4.3 tons. Convert the weight to pounds.

Answer

8,600 pounds

Try It 1.282 §1.10 source ↗

The Carnival Destiny cruise ship weighs 51,000 tons. Convert the weight to pounds.

Answer

102,000,000 pounds

Try It 1.283 §1.10 source ↗

The distance between the earth and the moon is about 250,000 miles. Convert this length to yards.

Answer

440,000,000 yards

Try It 1.284 §1.10 source ↗

The astronauts of Expedition 28 on the International Space Station spend 15 weeks in space. Convert the time to minutes.

Answer

151,200 minutes

Try It 1.285 §1.10 source ↗

How many cups are in 1 gallon?

Answer

16 cups

Try It 1.286 §1.10 source ↗

How many teaspoons are in 1 cup?

Answer

48 teaspoons

Try It 1.287 §1.10 source ↗

Laura gave birth to triplets weighing 3 pounds 3 ounces, 3 pounds 3 ounces, and 2 pounds 9 ounces. What was the total birth weight of the three babies?

Answer

8 lbs . 15 oz

Try It 1.288 §1.10 source ↗

Stan cut two pieces of crown molding for his family room that were 8 feet 7 inches and 12 feet 11 inches. What was the total length of the molding?

Answer

21 ft. 6 in.

Try It 1.289 §1.10 source ↗

Henri wants to triple his spaghetti sauce recipe that uses 1 pound 8 ounces of ground turkey. How many pounds of ground turkey will he need?

Answer

4 lbs. 8 oz.

Try It 1.290 §1.10 source ↗

Joellen wants to double a solution of 5 gallons 3 quarts. How many gallons of solution will she have in all?

Answer

11 gal. 2 qt.

Try It 1.291 §1.10 source ↗

Sandy completed her first 5K race! How many meters did she run?

Answer

5,000 meters

Try It 1.292 §1.10 source ↗

Herman bought a rug 2.5 meters in length. How many centimeters is the length?

Answer

250 centimeters

Try It 1.293 §1.10 source ↗

Kari’s newborn baby weighed 2,800 grams. How many kilograms did the baby weigh?

Answer

2.8 kilograms

Try It 1.294 §1.10 source ↗

Anderson received a package that was marked 4,500 grams. How many kilograms did this package weigh?

Answer

4.5 kilograms

Try It 1.295 §1.10 source ↗

Convert: ⓐ 725 L to kiloliters ⓑ 6.3 L to milliliters

Answer

ⓐ 0.725 kiloliters ⓑ 6,300 milliliters

Try It 1.296 §1.10 source ↗

Convert: ⓐ 350 hL to liters ⓑ 4.1 L to centiliters

Answer

ⓐ 35,000 liters ⓑ 410 centiliters

Try It 1.297 §1.10 source ↗

Mariella is 1.58 meters tall. Her daughter is 75 centimeters tall. How much taller is Mariella than her daughter? Write the answer in centimeters.

Answer

83 centimeters

Try It 1.298 §1.10 source ↗

The fence around Hank’s yard is 2 meters high. Hank is 96 centimeters tall. How much shorter than the fence is Hank? Write the answer in meters.

Answer

1.04 meters

Try It 1.299 §1.10 source ↗

A recipe for Alfredo sauce calls for 250 milliliters of milk. Renata is making pasta with Alfredo sauce for a big party and needs to multiply the recipe amounts by 8. How many liters of milk will she need?

Answer

2 liters

Try It 1.300 §1.10 source ↗

To make one pan of baklava, Dorothea needs 400 grams of filo pastry. If Dorothea plans to make 6 pans of baklava, how many kilograms of filo pastry will she need?

Answer

2.4 kilograms

Try It 1.301 §1.10 source ↗

How many quarts of soda are in a 2-L bottle?

Answer

2.12 quarts

Try It 1.302 §1.10 source ↗

How many liters are in 4 quarts of milk?

Answer

3.8 liters

Try It 1.303 §1.10 source ↗

The height of Mount Kilimanjaro is 5,895 meters. Convert the height to feet.

Answer

19,336 feet

Try It 1.304 §1.10 source ↗

The flight distance from New York City to London is 5,586 kilometers. Convert the distance to miles.

Answer

3469.57 miles

Try It 1.305 §1.10 source ↗

Convert the Fahrenheit temperature to degrees Celsius:

59 °

Fahrenheit.

Answer

15 ° C

Try It 1.306 §1.10 source ↗

Convert the Fahrenheit temperature to degrees Celsius:

41 °

Fahrenheit.

Answer

5 ° C

Try It 1.307 §1.10 source ↗

Convert the Celsius temperature to degrees Fahrenheit: the temperature in Helsinki, Finland, was

15 °

Celsius.

Answer

59 ° F

Try It 1.308 §1.10 source ↗

Convert the Celsius temperature to degrees Fahrenheit: the temperature in Sydney, Australia, was

10 °

Celsius.

Answer

50 ° F

1.10-825 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

A park bench is 6 feet long. Convert the length to inches.

Answer

72 inches

1.10-827 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

A ribbon is 18 inches long. Convert the length to feet.

Answer

1.5 feet

1.10-829 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

A football field is 160 feet wide. Convert the width to yards.

Answer

53 \frac{1}{3}

yards

1.10-831 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Ulises lives 1.5 miles from school. Convert the distance to feet.

Answer

7,920 feet

1.10-833 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

A killer whale weighs 4.6 tons. Convert the weight to pounds.

Answer

9,200 pounds

1.10-835 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

An empty bus weighs 35,000 pounds. Convert the weight to tons.

Answer

17 \frac{1}{2}

tons

1.10-837 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Rocco waited $1 \frac{1}{2}$ hours for his appointment. Convert the time to seconds.

Answer

5,400 s

1.10-839 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

How many teaspoons are in a pint?

Answer

96

teaspoons

1.10-841 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

JJ’s cat, Posy, weighs 14 pounds. Convert her weight to ounces.

Answer

224

ounces

1.10-843 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Crista will serve 20 cups of juice at her son’s party. Convert the volume to gallons.

Answer

1 \frac{1}{4}

gallons

1.10-845 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Jon is 6 feet 4 inches tall. Convert his height to inches.

Answer

76 in.

1.10-847 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

The voyage of the Mayflower took 2 months and 5 days. Convert the time to days.

Answer

65 days

1.10-849 §1.10 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Baby Preston weighed 7 pounds 3 ounces at birth. Convert his weight to ounces.

Answer

115 ounces

1.10-851 §1.10 source ↗

Use Mixed Units of Measurement in the U.S. System

In the following exercises, solve.

Eli caught three fish. The weights of the fish were 2 pounds 4 ounces, 1 pound 11 ounces, and 4 pounds 14 ounces. What was the total weight of the three fish?

Answer

8 lbs. 13 oz.

1.10-853 §1.10 source ↗

Use Mixed Units of Measurement in the U.S. System

In the following exercises, solve.

One day Anya kept track of the number of minutes she spent driving. She recorded 45, 10, 8, 65, 20, and 35. How many hours did Anya spend driving?

Answer

3.05 hours

1.10-855 §1.10 source ↗

Use Mixed Units of Measurement in the U.S. System

In the following exercises, solve.

Renee attached a 6 feet 6 inch extension cord to her computer’s 3 feet 8 inch power cord. What was the total length of the cords?

Answer

10 ft. 2 in.

1.10-857 §1.10 source ↗

Use Mixed Units of Measurement in the U.S. System

In the following exercises, solve.

Leilani wants to make 8 placemats. For each placemat she needs 18 inches of fabric. How many yards of fabric will she need for the 8 placemats?

Answer

4 yards

1.10-859 §1.10 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

Ghalib ran 5 kilometers. Convert the length to meters.

Answer

5,000 meters

1.10-861 §1.10 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

Estrella is 1.55 meters tall. Convert her height to centimeters.

Answer

155 centimeters

1.10-863 §1.10 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

Mount Whitney is 3,072 meters tall. Convert the height to kilometers.

Answer

3.072 kilometers

1.10-865 §1.10 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

June’s multivitamin contains 1,500 milligrams of calcium. Convert this to grams.

Answer

1.5 grams

1.10-867 §1.10 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

One stick of butter contains 91.6 grams of fat. Convert this to milligrams.

Answer

91,600 milligrams

1.10-869 §1.10 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

The maximum mass of an airmail letter is 2 kilograms. Convert this to grams.

Answer

2,000 grams

1.10-871 §1.10 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

A bottle of wine contained 750 milliliters. Convert this to liters.

Answer

0.75 liters

1.10-873 §1.10 source ↗

Use Mixed Units of Measurement in the Metric System

In the following exercises, solve.

Matthias is 1.8 meters tall. His son is 89 centimeters tall. How much taller is Matthias than his son?

Answer

91 centimeters

1.10-875 §1.10 source ↗

Use Mixed Units of Measurement in the Metric System

In the following exercises, solve.

A typical dove weighs 345 grams. A typical duck weighs 1.2 kilograms. What is the difference, in grams, of the weights of a duck and a dove?

Answer

855 grams

1.10-877 §1.10 source ↗

Use Mixed Units of Measurement in the Metric System

In the following exercises, solve.

Harry mailed 5 packages that weighed 420 grams each. What was the total weight of the packages in kilograms?

Answer

2.1 kilograms

1.10-879 §1.10 source ↗

Use Mixed Units of Measurement in the Metric System

In the following exercises, solve.

Jonas drinks 200 milliliters of water 8 times a day. How many liters of water does Jonas drink in a day?

Answer

1.6 liters

1.10-881 §1.10 source ↗

Convert Between the U.S. and the Metric Systems of Measurement

In the following exercises, make the unit conversions. Round to the nearest tenth.

Bill is 75 inches tall. Convert his height to centimeters.

Answer

190.5 centimeters

1.10-883 §1.10 source ↗

Convert Between the U.S. and the Metric Systems of Measurement

In the following exercises, make the unit conversions. Round to the nearest tenth.

Marcus passed a football 24 yards. Convert the pass length to meters

Answer

21.9 meters

1.10-885 §1.10 source ↗

Convert Between the U.S. and the Metric Systems of Measurement

In the following exercises, make the unit conversions. Round to the nearest tenth.

Each American throws out an average of 1,650 pounds of garbage per year. Convert this weight to kilograms.

Answer

750 kilograms

1.10-887 §1.10 source ↗

Convert Between the U.S. and the Metric Systems of Measurement

In the following exercises, make the unit conversions. Round to the nearest tenth.

A 5K run is 5 kilometers long. Convert this length to miles.

Answer

3.1 miles

1.10-889 §1.10 source ↗

Convert Between the U.S. and the Metric Systems of Measurement

In the following exercises, make the unit conversions. Round to the nearest tenth.

Dawn’s suitcase weighed 20 kilograms. Convert the weight to pounds.

Answer

44 pounds

1.10-891 §1.10 source ↗

Convert Between the U.S. and the Metric Systems of Measurement

In the following exercises, make the unit conversions. Round to the nearest tenth.

Ozzie put 14 gallons of gas in his truck. Convert the volume to liters.

Answer

53.2 liters

1.10-893 §1.10 source ↗

Convert between Fahrenheit and Celsius Temperatures

In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.

$86 °$ Fahrenheit

Answer

30 ° C

1.10-895 §1.10 source ↗

Convert between Fahrenheit and Celsius Temperatures

In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.

$104 °$ Fahrenheit

Answer

40 ° C

1.10-897 §1.10 source ↗

Convert between Fahrenheit and Celsius Temperatures

In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.

$72 °$ Fahrenheit

Answer

22.2 ° C

1.10-899 §1.10 source ↗

Convert between Fahrenheit and Celsius Temperatures

In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.

$0 °$ Fahrenheit

Answer

− 17.8 ° C

1.10-901 §1.10 source ↗

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

$5 °$ Celsius

Answer

41 ° F

1.10-903 §1.10 source ↗

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

$− 10 °$ Celsius

Answer

14 ° F

1.10-905 §1.10 source ↗

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

$22 °$ Celsius

Answer

71.6 ° F

1.10-907 §1.10 source ↗

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

$43 °$ Celsius

Answer

109.4 ° F

1.10-909 §1.10 source ↗

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

Nutrition Julian drinks one can of soda every day. Each can of soda contains 40 grams of sugar. How many kilograms of sugar does Julian get from soda in 1 year?

Answer

14.6 kilograms

1.10-911 §1.10 source ↗

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

Some people think that $65 ° to 75 °$ Fahrenheit is the ideal temperature range.

ⓐ What is your ideal temperature range? Why do you think so?

ⓑ Convert your ideal temperatures from Fahrenheit to Celsius.

Answer

Answers may vary.

1.R-913 §1.R source ↗

Use Place Value with Whole Number

In the following exercises find the place value of each digit.

26,915

Answer

1.R-915 §1.R source ↗

Use Place Value with Whole Number

In the following exercises find the place value of each digit.

58,129,304

Answer

1.R-917 §1.R source ↗

In the following exercises, name each number.

6,104

Answer

six thousand, one hundred four

1.R-919 §1.R source ↗

In the following exercises, name each number.

3,975,284

Answer

three million, nine hundred seventy-five thousand, two hundred eighty-four

1.R-921 §1.R source ↗

In the following exercises, write each number as a whole number using digits.

three hundred fifteen

Answer

315

1.R-923 §1.R source ↗

In the following exercises, write each number as a whole number using digits.

ninety million, four hundred twenty-five thousand, sixteen

Answer

90,425,016

1.R-925 §1.R source ↗

In the following exercises, round to the indicated place value.

Round to the nearest ten.

ⓐ 407 ⓑ 8,564

Answer

ⓐ

410

ⓑ

8,560

1.R-927 §1.R source ↗

864,951

Answer

ⓐ

865,000

ⓑ

865,000

ⓒ

860,000

1.R-929 §1.R source ↗

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

168

Answer

by 2, 3, 6

1.R-931 §1.R source ↗

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

375

Answer

by 3, 5

1.R-933 §1.R source ↗

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

1430

Answer

by 2, 5, 10

1.R-935 §1.R source ↗

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

420

Answer

2 \cdot 2 \cdot 3 \cdot 5 \cdot 7

1.R-937 §1.R source ↗

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

225

Answer

3 \cdot 3 \cdot 5 \cdot 5

1.R-939 §1.R source ↗

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

1560

Answer

2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 13

1.R-941 §1.R source ↗

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

Answer

2 \cdot 2 \cdot 2 \cdot 3 \cdot 3

1.R-943 §1.R source ↗

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

252

Answer

2 \cdot 2 \cdot 3 \cdot 3 \cdot 7

1.R-945 §1.R source ↗

In the following exercises, find the least common multiple of the following numbers using the multiples method.

6,15

Answer

30

1.R-947 §1.R source ↗

In the following exercises, find the least common multiple of the following numbers using the prime factors method.

24, 30

Answer

120

1.R-949 §1.R source ↗

Use Variables and Algebraic Symbols

In the following exercises, translate the following from algebra to English.

$25 - 7$

Answer

25 minus 7, the difference of twenty-five and seven

1.R-951 §1.R source ↗

Use Variables and Algebraic Symbols

In the following exercises, translate the following from algebra to English.

$45 \div 5$

Answer

45 divided by 5, the quotient of forty-five and five

1.R-953 §1.R source ↗

Use Variables and Algebraic Symbols

In the following exercises, translate the following from algebra to English.

$42 \geq 27$

Answer

forty-two is greater than or equal to twenty-seven

1.R-955 §1.R source ↗

Use Variables and Algebraic Symbols

In the following exercises, translate the following from algebra to English.

$3 \leq 20 \div 4$

Answer

3 is less than or equal to 20 divided by 4, three is less than or equal to the quotient of twenty and four

1.R-957 §1.R source ↗

In the following exercises, determine if each is an expression or an equation.

$6 \cdot 3 + 5$

Answer

expression

1.R-959 §1.R source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

$3^{5}$

Answer

243

1.R-961 §1.R source ↗

In the following exercises, simplify

$6 + 10 / 2 + 2$

Answer

1.R-963 §1.R source ↗

In the following exercises, simplify

$20 \div (4 + 6) \cdot 5$

Answer

1.R-965 §1.R source ↗

In the following exercises, simplify

${(4^{2} + 5^{2})}^{2}$

Answer

1681

1.R-967 §1.R source ↗

Evaluate an Expression

In the following exercises, evaluate the following expressions.

$9 x + 7$ when $x = 3$

Answer

1.R-969 §1.R source ↗

Evaluate an Expression

In the following exercises, evaluate the following expressions.

$x^{4}$ when $x = 3$

Answer

1.R-971 §1.R source ↗

Evaluate an Expression

In the following exercises, evaluate the following expressions.

$x^{2} + 5 x - 8$ when $x = 6$

Answer

1.R-973 §1.R source ↗

Simplify Expressions by Combining Like Terms

In the following exercises, identify the coefficient of each term.

$12 n$

Answer

1.R-975 §1.R source ↗

In the following exercises, identify the like terms.

$3 n,$ $n^{2},$ $12,$ $12 p^{2},$ $3,$ $3 n^{2}$

Answer

12 and 3,

n^{2} and 3 n^{2}

1.R-977 §1.R source ↗

In the following exercises, identify the terms in each expression.

$11 x^{2} + 3 x + 6$

Answer

11 x^{2}, 3 x, 6

1.R-979 §1.R source ↗

In the following exercises, simplify the following expressions by combining like terms.

$17 a + 9 a$

Answer

26 a

1.R-981 §1.R source ↗

In the following exercises, simplify the following expressions by combining like terms.

$9 x + 3 x + 8$

Answer

12 x + 8

1.R-983 §1.R source ↗

In the following exercises, simplify the following expressions by combining like terms.

$7 p + 6 + 5 p - 4$

Answer

12 p + 2

1.R-985 §1.R source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the following phrases into algebraic expressions.

the sum of 8 and 12

Answer

8 + 12

1.R-987 §1.R source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the following phrases into algebraic expressions.

the difference of $x$ and 4

Answer

x - 4

1.R-989 §1.R source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the following phrases into algebraic expressions.

the product of 6 and $y$

Answer

6 y

1.R-991 §1.R source ↗

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the following phrases into algebraic expressions.

Adele bought a skirt and a blouse. The skirt cost $15 more than the blouse. Let $b$ represent the cost of the blouse. Write an expression for the cost of the skirt.

Answer

b + 15

1.R-993 §1.R source ↗

Use Negatives and Opposites of Integers

In the following exercises, order each of the following pairs of numbers, using < or >.

Answer

1.R-995 §1.R source ↗

In the following exercises,, find the opposite of each number.

ⓐ $−8$ ⓑ 1

Answer

ⓐ 8 ⓑ

−1

1.R-997 §1.R source ↗

In the following exercises, simplify.

$− (−19)$

Answer

1.R-999 §1.R source ↗

In the following exercises, simplify.

$− m$ when
ⓐ $m = 3$
ⓑ $m = −3$

Answer

ⓐ

−3

ⓑ 3

1.R-1001 §1.R source ↗

Simplify Expressions with Absolute Value

In the following exercises,, simplify.

Answer

ⓐ 7 ⓑ 25 ⓒ 0

1.R-1003 §1.R source ↗

In the following exercises, fill in <, >, or = for each of the following pairs of numbers.

ⓐ $−8___| −8 |$
ⓑ $− | −2 |___−2$

Answer

ⓐ < ⓑ =

1.R-1005 §1.R source ↗

In the following exercises, simplify.

$| 8 - 4 |$

Answer

1.R-1007 §1.R source ↗

In the following exercises, simplify.

$8 (14 - 2 | −2 |)$

Answer

1.R-1009 §1.R source ↗

In the following exercises, evaluate.

ⓐ $| x |$ when $x = −28$ ⓑ $| x |$ when $x = −15$

Answer

ⓐ 28 ⓑ 15

1.R-1011 §1.R source ↗

Add Integers

In the following exercises, simplify each expression.

$−200 + 65$

Answer

−135

1.R-1013 §1.R source ↗

Add Integers

In the following exercises, simplify each expression.

$2 + (−8) + 6$

Answer

1.R-1015 §1.R source ↗

Add Integers

In the following exercises, simplify each expression.

$140 +$ $(−75) +$ $67$

Answer

132

1.R-1017 §1.R source ↗

Subtract Integers

In the following exercises, simplify.

$9 - 3$

Answer

1.R-1019 §1.R source ↗

Subtract Integers

In the following exercises, simplify.

ⓐ $15 - 6$ ⓑ $15 + (−6)$

Answer

ⓐ 9 ⓑ 9

1.R-1021 §1.R source ↗

Subtract Integers

In the following exercises, simplify.

ⓐ $8 - (−9)$ ⓑ $8 + 9$

Answer

ⓐ 17 ⓑ 17

1.R-1023 §1.R source ↗

In the following exercises, simplify each expression.

$10 - (−19)$

Answer

1.R-1025 §1.R source ↗

In the following exercises, simplify each expression.

$31 - 79$

Answer

−48

1.R-1027 §1.R source ↗

In the following exercises, simplify each expression.

$−31 - 11$

Answer

−42

1.R-1029 §1.R source ↗

In the following exercises, simplify each expression.

$−15 - (−28) + 5$

Answer

1.R-1031 §1.R source ↗

In the following exercises, simplify each expression.

$−16 -$ $(−4 + 1) -$ $7$

Answer

−20

1.R-1033 §1.R source ↗

Multiply Integers

In the following exercises, multiply.

$−5 (7)$

Answer

−35

1.R-1035 §1.R source ↗

Multiply Integers

In the following exercises, multiply.

$−18 (−2)$

Answer

36

1.R-1037 §1.R source ↗

Divide Integers

In the following exercises, divide.

$−28 \div 7$

Answer

−4

1.R-1039 §1.R source ↗

Divide Integers

In the following exercises, divide.

$−120 \div (−20)$

Answer

1.R-1041 §1.R source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$−8 (−2) -$ $3 (−9)$

Answer

1.R-1043 §1.R source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

${(−5)}^{3}$

Answer

−125

1.R-1045 §1.R source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$−4 \cdot 2 \cdot 11$

Answer

−88

1.R-1047 §1.R source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$−10 (−4) \div (−8)$

Answer

−5

1.R-1049 §1.R source ↗

Simplify Expressions with Integers

In the following exercises, simplify each expression.

$31 - 4 (3 - 9)$

Answer

1.R-1051 §1.R source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$x + 8$ when ⓐ $x = −26$ ⓑ $x = −95$

Answer

ⓐ

−18

ⓑ

−87

1.R-1053 §1.R source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

When $b = −11$ , evaluate:ⓐ $b + 6$ ⓑ $− b + 6$

Answer

ⓐ

−5

ⓑ 17

1.R-1055 §1.R source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$p^{2} - 5 p + 2$ when
$p = −1$

Answer

1.R-1057 §1.R source ↗

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

$6 x - 5 y + 15$ when $x = 3$ and $y = −1$

Answer

1.R-1059 §1.R source ↗

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

the sum of $−4$ and $−17$ , increased by 32

Answer

(−4 + (−17)) +

32;

11

1.R-1061 §1.R source ↗

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

the quotient of $−45$ and $−9$

Answer

\frac{−45}{−9}; 5

1.R-1063 §1.R source ↗

Use Integers in Applications

In the following exercises, solve.

Temperature The high temperature one day in Miami Beach, Florida, was $76 °$ . That same day, the high temperature in Buffalo, New York was $− 8 °$ . What was the difference between the temperature in Miami Beach and the temperature in Buffalo?

Answer

84 degrees

1.R-1065 §1.R source ↗

Find Equivalent Fractions

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

$\frac{1}{4}$

Answer

\frac{2}{8}, \frac{3}{12}, \frac{4}{16}

answers may vary

1.R-1067 §1.R source ↗

Find Equivalent Fractions

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

$\frac{5}{6}$

Answer

\frac{10}{12},

\frac{15}{18},

\frac{20}{24}

answers may vary

1.R-1069 §1.R source ↗

Simplify Fractions

In the following exercises, simplify.

$\frac{7}{21}$

Answer

\frac{1}{3}

1.R-1071 §1.R source ↗

Simplify Fractions

In the following exercises, simplify.

$\frac{15}{20}$

Answer

\frac{3}{4}

1.R-1073 §1.R source ↗

Simplify Fractions

In the following exercises, simplify.

$- \frac{168}{192}$

Answer

- \frac{7}{8}

1.R-1075 §1.R source ↗

Simplify Fractions

In the following exercises, simplify.

$\frac{11 x}{11 y}$

Answer

\frac{x}{y}

1.R-1077 §1.R source ↗

Multiply Fractions

In the following exercises, multiply.

$\frac{2}{5} \cdot \frac{1}{3}$

Answer

\frac{2}{15}

1.R-1079 §1.R source ↗

Multiply Fractions

In the following exercises, multiply.

$\frac{7}{12} (- \frac{8}{21})$

Answer

- \frac{2}{9}

1.R-1081 §1.R source ↗

Multiply Fractions

In the following exercises, multiply.

$−28 p (- \frac{1}{4})$

Answer

7 p

1.R-1083 §1.R source ↗

Multiply Fractions

In the following exercises, multiply.

$\frac{14}{5} (−15)$

Answer

−42

1.R-1085 §1.R source ↗

Divide Fractions

In the following exercises, divide.

$\frac{1}{2} \div \frac{1}{4}$

Answer

1.R-1087 §1.R source ↗

Divide Fractions

In the following exercises, divide.

$- \frac{4}{5} \div \frac{4}{7}$

Answer

- \frac{7}{5}

1.R-1089 §1.R source ↗

Divide Fractions

In the following exercises, divide.

$\frac{5}{8} \div \frac{a}{10}$

Answer

\frac{25}{4 a}

1.R-1091 §1.R source ↗

Divide Fractions

In the following exercises, divide.

$\frac{7 p}{12} \div \frac{21 p}{8}$

Answer

\frac{2}{9}

1.R-1093 §1.R source ↗

Divide Fractions

In the following exercises, divide.

$\frac{2}{5} \div (−10)$

Answer

- \frac{1}{25}

1.R-1095 §1.R source ↗

In the following exercises, simplify.

$\frac{\frac{2}{3}}{\frac{8}{9}}$

Answer

\frac{3}{4}

1.R-1097 §1.R source ↗

In the following exercises, simplify.

$\frac{- \frac{9}{10}}{3}$

Answer

- \frac{3}{10}

1.R-1099 §1.R source ↗

In the following exercises, simplify.

$\frac{\frac{r}{5}}{\frac{s}{3}}$

Answer

\frac{3 r}{5 s}

1.R-1101 §1.R source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{4 + 11}{8}$

Answer

\frac{15}{8}

1.R-1103 §1.R source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{30}{7 - 12}$

Answer

−6

1.R-1105 §1.R source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{22 - 14}{19 - 13}$

Answer

\frac{4}{3}

1.R-1107 §1.R source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{5 \cdot 8}{−10}$

Answer

−4

1.R-1109 §1.R source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{15 \cdot 5 - 5^{2}}{2 \cdot 10}$

Answer

\frac{5}{2}

1.R-1111 §1.R source ↗

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

$\frac{2 + 4 (3)}{−3 - 2^{2}}$

Answer

−2

1.R-1113 §1.R source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

the quotient of c and the sum of d and 9.

Answer

\frac{c}{d + 9}

1.R-1115 §1.R source ↗

Add and Subtract Fractions with a Common Denominator

In the following exercises, add.

$\frac{4}{9} + \frac{1}{9}$

Answer

\frac{5}{9}

1.R-1117 §1.R source ↗

Add and Subtract Fractions with a Common Denominator

In the following exercises, add.

$\frac{y}{3} + \frac{2}{3}$

Answer

\frac{y + 2}{3}

1.R-1119 §1.R source ↗

Add and Subtract Fractions with a Common Denominator

In the following exercises, add.

$- \frac{1}{8} + (- \frac{3}{8})$

Answer

- \frac{1}{2}

1.R-1121 §1.R source ↗

In the following exercises, subtract.

$\frac{4}{5} - \frac{1}{5}$

Answer

\frac{3}{5}

1.R-1123 §1.R source ↗

In the following exercises, subtract.

$\frac{y}{17} - \frac{9}{17}$

Answer

\frac{y - 9}{17}

1.R-1125 §1.R source ↗

In the following exercises, subtract.

$- \frac{8}{d} - \frac{3}{d}$

Answer

- \frac{11}{d}

1.R-1127 §1.R source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$\frac{1}{3} + \frac{1}{5}$

Answer

\frac{8}{15}

1.R-1129 §1.R source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$\frac{1}{5} - (- \frac{1}{10})$

Answer

\frac{3}{10}

1.R-1131 §1.R source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$\frac{2}{3} + \frac{3}{4}$

Answer

\frac{17}{12}

1.R-1133 §1.R source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$\frac{11}{12} - \frac{3}{8}$

Answer

\frac{13}{24}

1.R-1135 §1.R source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$- \frac{9}{16} - (- \frac{4}{5})$

Answer

\frac{19}{80}

1.R-1137 §1.R source ↗

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$1 + \frac{5}{6}$

Answer

\frac{11}{6}

1.R-1139 §1.R source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$\frac{{(\frac{1}{5})}^{2}}{2 + 3^{2}}$

Answer

\frac{1}{275}

1.R-1141 §1.R source ↗

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$\frac{\frac{2}{3} + \frac{1}{2}}{\frac{3}{4} - \frac{2}{3}}$

Answer

1.R-1143 §1.R source ↗

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

$x + \frac{1}{2}$ when
ⓐ $x = - \frac{1}{8}$
ⓑ $x = - \frac{1}{2}$

Answer

ⓐ

\frac{3}{8}

ⓑ 0

1.R-1145 §1.R source ↗

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

$4 p^{2} q$ when $p = - \frac{1}{2}$ and $q = \frac{5}{9}$

Answer

\frac{5}{9}

1.R-1147 §1.R source ↗

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

$\frac{u + v}{w}$ when
$u =$ $−4,$ $v =$ $−8,$ $w =$ $2$

Answer

−6

1.R-1149 §1.R source ↗

Name and Write Decimals

In the following exercises, write as a decimal.

Eight and three hundredths

Answer

8.03

1.R-1151 §1.R source ↗

Name and Write Decimals

In the following exercises, write as a decimal.

One thousandth

Answer

0.001

1.R-1153 §1.R source ↗

In the following exercises, name each decimal.

7.8

Answer

seven and eight tenths

1.R-1155 §1.R source ↗

In the following exercises, name each decimal.

0.005

Answer

five thousandths

1.R-1157 §1.R source ↗

Round Decimals

5.7932

Answer

1.R-1159 §1.R source ↗

Round Decimals

12.4768

Answer

1.R-1161 §1.R source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$18.37 + 9.36$

Answer

27.73

1.R-1163 §1.R source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$15.35 - 20.88$

Answer

−5.53

1.R-1165 §1.R source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$−4.2 + (−9.3)$

Answer

−13.5

1.R-1167 §1.R source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$100 - 64.2$

Answer

35.8

1.R-1169 §1.R source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$2.51 + 40$

Answer

42.51

1.R-1171 §1.R source ↗

Multiply and Divide Decimals

In the following exercises, multiply.

$(0.3) (0.4)$

Answer

0.12

1.R-1173 §1.R source ↗

Multiply and Divide Decimals

In the following exercises, multiply.

$(8.52) (3.14)$

Answer

26.7528

1.R-1175 §1.R source ↗

Multiply and Divide Decimals

In the following exercises, multiply.

$(0.09) (24.78)$

Answer

2.2302

1.R-1177 §1.R source ↗

In the following exercises, divide.

$0.15 \div 5$

Answer

0.03

1.R-1179 §1.R source ↗

In the following exercises, divide.

$$8.49 \div 12$

Answer

$0.71

1.R-1181 §1.R source ↗

In the following exercises, divide.

$12 \div 0.08$

Answer

150

1.R-1183 §1.R source ↗

Convert Decimals, Fractions, and Percents

In the following exercises, write each decimal as a fraction.

0.08

Answer

\frac{2}{25}

1.R-1185 §1.R source ↗

Convert Decimals, Fractions, and Percents

In the following exercises, write each decimal as a fraction.

0.425

Answer

\frac{17}{40}

1.R-1187 §1.R source ↗

Convert Decimals, Fractions, and Percents

In the following exercises, write each decimal as a fraction.

1.75

Answer

\frac{7}{4}

1.R-1189 §1.R source ↗

In the following exercises, convert each fraction to a decimal.

$\frac{2}{5}$

Answer

0.4

1.R-1191 §1.R source ↗

In the following exercises, convert each fraction to a decimal.

$- \frac{3}{8}$

Answer

−0.375

1.R-1193 §1.R source ↗

In the following exercises, convert each fraction to a decimal.

$\frac{5}{9}$

Answer

0. \overset{–}{5}

1.R-1195 §1.R source ↗

In the following exercises, convert each fraction to a decimal.

$\frac{1}{2} + 6.5$

Answer

1.R-1197 §1.R source ↗

In the following exercises, convert each percent to a decimal.

Answer

0.05

1.R-1199 §1.R source ↗

In the following exercises, convert each percent to a decimal.

40%

Answer

0.4

1.R-1201 §1.R source ↗

In the following exercises, convert each percent to a decimal.

115%

Answer

1.15

1.R-1203 §1.R source ↗

In the following exercises, convert each decimal to a percent.

0.18

Answer

18%

1.R-1205 §1.R source ↗

In the following exercises, convert each decimal to a percent.

0.009

Answer

0.9%

1.R-1207 §1.R source ↗

In the following exercises, convert each decimal to a percent.

1.5

Answer

150%

1.R-1209 §1.R source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{64}$

Answer

1.R-1211 §1.R source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$− \sqrt{25}$

Answer

−5

1.R-1213 §1.R source ↗

Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers

In the following exercises, write as the ratio of two integers.

ⓐ 9 ⓑ 8.47

Answer

ⓐ

\frac{9}{1}

ⓑ

\frac{847}{100}

1.R-1215 §1.R source ↗

In the following exercises, list the ⓐ rational numbers, ⓑ irrational numbers.

$0.84,$ $0.79132 …,$ $1. \overset{–}{3}$

Answer

ⓐ

0.84, 1. \overset{–}{3}

ⓑ

0.79132 …,

1.R-1217 §1.R source ↗

In the following exercises, identify whether each number is rational or irrational.

ⓐ $\sqrt{121}$ ⓑ $\sqrt{48}$

Answer

ⓐ rational ⓑ irrational

1.R-1219 §1.R source ↗

In the following exercises, identify whether each number is a real number or not a real number.

ⓐ $\sqrt{−9}$ ⓑ $− \sqrt{169}$

Answer

ⓐ not a real number ⓑ real number

1.R-1221 §1.R source ↗

In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.

$−4,$ $0,$ $\frac{5}{6},$ $\sqrt{16},$ $\sqrt{18},$ $5.2537 …$

Answer

ⓐ

0, \sqrt{16}

ⓑ

−4, 0, \sqrt{16}

ⓒ

−4, 0, \frac{5}{6}, \sqrt{16}

ⓓ

\sqrt{18}, 5.2537 …

ⓔ

−4,

0,

\frac{5}{6},

\sqrt{16},

\sqrt{18},

5.2537 …

1.R-1223 §1.R source ↗

Locate Fractions on the Number Line

In the following exercises, locate the numbers on a number line.

$\frac{2}{3}, \frac{5}{4}, \frac{12}{5}$

Answer

1.R-1225 §1.R source ↗

Locate Fractions on the Number Line

In the following exercises, locate the numbers on a number line.

$2 \frac{1}{3}, −2 \frac{1}{3}$

Answer

1.R-1227 §1.R source ↗

In the following exercises, order each of the following pairs of numbers, using < or >.

$−1___- \frac{1}{8}$

Answer

1.R-1229 §1.R source ↗

In the following exercises, order each of the following pairs of numbers, using < or >.

$- \frac{7}{9}___- \frac{4}{9}$

Answer

1.R-1231 §1.R source ↗

Locate Decimals on the Number Line

In the following exercises, locate on the number line.

$0.3$

Answer

1.R-1233 §1.R source ↗

Locate Decimals on the Number Line

In the following exercises, locate on the number line.

$−2.5$

Answer

1.R-1235 §1.R source ↗

In the following exercises, order each of the following pairs of numbers, using < or >.

$0.9___0.6$

Answer

1.R-1237 §1.R source ↗

In the following exercises, order each of the following pairs of numbers, using < or >.

$−0.6___−0.59$

Answer

1.R-1239 §1.R source ↗

Use the Commutative and Associative Properties

In the following exercises, use the Associative Property to simplify.

$−12 (4 m)$

Answer

−48 m

1.R-1241 §1.R source ↗

Use the Commutative and Associative Properties

In the following exercises, use the Associative Property to simplify.

$(a + 16) + 31$

Answer

a + 47

1.R-1243 §1.R source ↗

In the following exercises, simplify.

$6 y + 37 + (−6 y)$

Answer

1.R-1245 §1.R source ↗

In the following exercises, simplify.

$\frac{14}{11} +$ $\frac{35}{9} +$ $(- \frac{14}{11})$

Answer

\frac{35}{9}

1.R-1247 §1.R source ↗

In the following exercises, simplify.

$(\frac{7}{12} + \frac{4}{5}) + \frac{1}{5}$

Answer

1 \frac{7}{12}

1.R-1249 §1.R source ↗

In the following exercises, simplify.

$11 x +$ $8 y +$ $16 x +$ $15 y$

Answer

27 x + 23 y

1.R-1251 §1.R source ↗

Use the Identity and Inverse Properties of Addition and Multiplication

In the following exercises, find the additive inverse of each number.

Answer

ⓐ

- \frac{1}{3}

ⓑ

−5.1

\frac{8}{5}

1.R-1253 §1.R source ↗

In the following exercises, find the multiplicative inverse of each number.

Answer

ⓐ

\frac{1}{10}

ⓑ

- \frac{9}{4}

ⓒ

\frac{5}{3}

1.R-1255 §1.R source ↗

Use the Properties of Zero

In the following exercises, simplify.

$83 \cdot 0$

Answer

1.R-1257 §1.R source ↗

Use the Properties of Zero

In the following exercises, simplify.

$\frac{5}{0}$

Answer

undefined

1.R-1259 §1.R source ↗

In the following exercises, simplify.

$43 + 39 + (−43)$

Answer

1.R-1261 §1.R source ↗

In the following exercises, simplify.

$\frac{5}{13} \cdot 57 \cdot \frac{13}{5}$

Answer

1.R-1263 §1.R source ↗

In the following exercises, simplify.

$\frac{2}{3} \cdot 28 \cdot \frac{3}{7}$

Answer

1.R-1265 §1.R source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the Distributive Property.

$7 (x + 9)$

Answer

7 x + 63

1.R-1267 §1.R source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the Distributive Property.

$−3 (6 m - 1)$

Answer

−18 m + 3

1.R-1269 §1.R source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the Distributive Property.

$\frac{1}{3} (15 n - 6)$

Answer

5 n - 2

1.R-1271 §1.R source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the Distributive Property.

$(a - 4) -$ $(6 a + 9)$

Answer

−5 a - 13

1.R-1273 §1.R source ↗

1.1 Define U.S. Units of Measurement and Convert from One Unit to Another

In the following exercises, convert the units. Round to the nearest tenth.

A floral arbor is 7 feet tall. Convert the height to inches.

Answer

84 inches

1.R-1275 §1.R source ↗

1.1 Define U.S. Units of Measurement and Convert from One Unit to Another

In the following exercises, convert the units. Round to the nearest tenth.

Kelly is 5 feet 4 inches tall. Convert her height to inches.

Answer

64 inches

1.R-1277 §1.R source ↗

1.1 Define U.S. Units of Measurement and Convert from One Unit to Another

In the following exercises, convert the units. Round to the nearest tenth.

The height of Mount Shasta is 14,179 feet. Convert the height to miles.

Answer

2.7 miles

1.R-1279 §1.R source ↗

1.1 Define U.S. Units of Measurement and Convert from One Unit to Another

In the following exercises, convert the units. Round to the nearest tenth.

The play lasted $1 \frac{3}{4}$ hours. Convert the time to minutes.

Answer

105 minutes

1.R-1281 §1.R source ↗

1.1 Define U.S. Units of Measurement and Convert from One Unit to Another

In the following exercises, convert the units. Round to the nearest tenth.

Naomi’s baby weighed 5 pounds 14 ounces at birth. Convert the weight to ounces.

Answer

94 ounces

1.R-1283 §1.R source ↗

Use Mixed Units of Measurement in the U.S. System.

In the following exercises, solve.

John caught 4 lobsters. The weights of the lobsters were 1 pound 9 ounces, 1 pound 12 ounces, 4 pounds 2 ounces, and 2 pounds 15 ounces. What was the total weight of the lobsters?

Answer

10 lbs. 6 oz.

1.R-1285 §1.R source ↗

Use Mixed Units of Measurement in the U.S. System.

In the following exercises, solve.

Fouad is 6 feet 2 inches tall. If he stands on a rung of a ladder 8 feet 10 inches high, how high off the ground is the top of Fouad’s head?

Answer

15 feet

1.R-1287 §1.R source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

Donna is 1.7 meters tall. Convert her height to centimeters.

Answer

170 centimeters

1.R-1289 §1.R source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

One cup of yogurt contains 488 milligrams of calcium. Convert this to grams.

Answer

0.488 grams

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Make Unit Conversions in the Metric System

In the following exercises, convert the units.

Sergio weighed 2.9 kilograms at birth. Convert this to grams.

Answer

2,900 grams

1.R-1293 §1.R source ↗

Use Mixed Units of Measurement in the Metric System

In the following exerices, solve.

Minh is 2 meters tall. His daughter is 88 centimeters tall. How much taller is Minh than his daughter?

Answer

1.12 meter

1.R-1295 §1.R source ↗

Use Mixed Units of Measurement in the Metric System

In the following exerices, solve.

One serving of cranberry juice contains 30 grams of sugar. How many kilograms of sugar are in 30 servings of cranberry juice?

Answer

0.9 kilograms

1.R-1297 §1.R source ↗

Convert between the U.S. and the Metric Systems of Measurement

In the following exercises, make the unit conversions. Round to the nearest tenth.

Majid is 69 inches tall. Convert his height to centimeters.

Answer

175.3 centimeters

1.R-1299 §1.R source ↗

Convert between the U.S. and the Metric Systems of Measurement

In the following exercises, make the unit conversions. Round to the nearest tenth.

Caroline walked 2.5 kilometers. Convert this length to miles.

Answer

1.6 miles

1.R-1301 §1.R source ↗

Convert between the U.S. and the Metric Systems of Measurement

In the following exercises, make the unit conversions. Round to the nearest tenth.

Steve’s car holds 55 liters of gas. Convert this to gallons.

Answer

14.6 gallons

1.R-1303 §1.R source ↗

Convert between Fahrenheit and Celsius Temperatures

In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.

95° Fahrenheit

Answer

35° C

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Convert between Fahrenheit and Celsius Temperatures

In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.

20° Fahrenheit

Answer

–6.7° C

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In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

30° Celsius

Answer

86° F

1.R-1309 §1.R source ↗

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

–12° Celsius

Answer

10.4° F

1.T-1311 §1.T source ↗

Write as a whole number using digits: two hundred five thousand, six hundred seventeen.

Answer

205,617

1.T-1313 §1.T source ↗

Find the Least Common Multiple of 18 and 24.

Answer

1.T-1315 §1.T source ↗

In the following exercises, evaluate.

$− | x |$ when $x = −2$

Answer

−2

1.T-1317 §1.T source ↗

In the following exercises, evaluate.

Translate to an algebraic expression and simplify: twenty less than negative 7.

Answer

−7 - 20; - 27

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In the following exercises, evaluate.

Round 677.1348 to the nearest hundredth.

Answer

677.13

1.T-1321 §1.T source ↗

In the following exercises, evaluate.

Convert 1.85 to a percent.

Answer

185%

1.T-1323 §1.T source ↗

In the following exercises, simplify each expression.

$4 +$ $10 (3 + 9) -$ $5^{2}$

Answer

1.T-1325 §1.T source ↗

In the following exercises, simplify each expression.

$−19 - 25$

Answer

−44

1.T-1327 §1.T source ↗

In the following exercises, simplify each expression.

$−5 (−9) \div 15$

Answer

1.T-1329 §1.T source ↗

In the following exercises, simplify each expression.

$\frac{4}{5} \div \frac{9}{20}$

Answer

\frac{16}{9}

1.T-1331 §1.T source ↗

In the following exercises, simplify each expression.

$\frac{m}{7} + \frac{10}{7}$

Answer

\frac{m + 10}{7}

1.T-1333 §1.T source ↗

In the following exercises, simplify each expression.

$−5.8 + (−4.7)$

Answer

−10.5

1.T-1335 §1.T source ↗

In the following exercises, simplify each expression.

$(0.07) (31.95)$

Answer

2.2365

1.T-1337 §1.T source ↗

In the following exercises, simplify each expression.

$−14 (\frac{5}{7} p)$

Answer

−10 p

1.T-1339 §1.T source ↗

In the following exercises, simplify each expression.

$6 x +$ $(−4 y) +$ $9 x +$ $8 y$

Answer

15 x + 4 y

1.T-1341 §1.T source ↗

In the following exercises, simplify each expression.

$\frac{75}{0}$

Answer

undefined

1.T-1343 §1.T source ↗

In the following exercises, simplify each expression.

A movie lasted $1 \frac{2}{3}$ hours. How many minutes did it last? (1 hour = 60 minutes)

Answer

100 minutes

1.T-1345 §1.T source ↗

In the following exercises, simplify each expression.

Jennifer ran 2.8 miles. Convert this length to kilometers. (1 mile = 1.61 kilometers)

Answer

4.508 km

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Problems and answers are adapted from Elementary Algebra 2e by Lynn Marecek and MaryAnne Anthony-Smith, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/elementary-algebra-2e/pages/1-introduction. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.