Content check — Prealgebra, Chapter 7: The Properties of Real Numbers

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

Chapter 7: The Properties of Real Numbers

348 problems · 4 figures

Be Prepared 7.1 §7.1 source ↗

Write

3.19

as an improper fraction.
If you missed this problem, review Example 5.4.

Example 5.4 in the book ↗

Answer

\frac{319}{100}

Be Prepared 7.2 §7.1 source ↗

Write

\frac{5}{11}

as a decimal.
If you missed this problem, review Example 5.30.

Example 5.30 in the book ↗

Answer

0. \bar{45}

Be Prepared 7.3 §7.1 source ↗

Simplify:

\sqrt{144} .

If you missed this problem, review Example 5.69.

Example 5.69 in the book ↗

Answer

12

Try It 7.1 §7.1 source ↗

Write each as the ratio of two integers: ⓐ

−24

ⓑ

3.57 .

Answer

ⓐ $\frac{−24}{1}$

ⓑ $\frac{357}{100}$

Try It 7.2 §7.1 source ↗

Write each as the ratio of two integers: ⓐ

−19

ⓑ

8.41 .

Answer

ⓐ $\frac{−19}{1}$

ⓑ $\frac{841}{100}$

Try It 7.3 §7.1 source ↗

Identify each of the following as rational or irrational:

ⓐ $0.29$ ⓑ $0.81 \overset{–}{6}$ ⓒ $2.515115111…$

Answer

ⓐ rational

ⓑ rational

Try It 7.4 §7.1 source ↗

Identify each of the following as rational or irrational:

ⓐ $0.2 \overset{–}{3}$ ⓑ $0.125$ ⓒ $0.418302…$

Answer

ⓐ rational

ⓑ rational

Try It 7.5 §7.1 source ↗

Identify each of the following as rational or irrational:

ⓐ $\sqrt{81}$

ⓑ $\sqrt{17}$

Answer

ⓐ rational

ⓑ irrational

Try It 7.6 §7.1 source ↗

Identify each of the following as rational or irrational:

ⓐ $\sqrt{116}$

ⓑ $\sqrt{121}$

Answer

ⓐ irrational

ⓑ rational

Try It 7.7 §7.1 source ↗

Determine whether each number is a ⓐ whole number, ⓑ integer, ⓒ rational number, ⓓ irrational number, and ⓔ real number:

−3,

-

\sqrt{2},

0 . \overset{–}{3},

\frac{9}{5},

4,

\sqrt{49} .

Answer

The table has seven rows and six columns. The first row is a header row that labels each column. The first column is labeled “Number”, the second column “Whole”, the third “Integer”, the fourth “Rational” the fifth “Irrational” and the sixth “Real”. Each row has a number in the “Number” column then an x in each column that corresponds to the type of number it is. The second row has the number negative 3 in the “Number” column and an x marked in the “Integer”, “Rational” and “Real” columns. The third row has the number negative square root of 2 in the “Number” column and an x marked in the “Irrational” and “Real” columns. The fourth row has the number 0.3 repeating in the “Number” column and an x marked in the “Rational” and “Real” columns. The fifth row has the number square root of negative 49 in the “Number” column with no other columns marked. The sixth row has the number 4 in the “Number” column and an x marked in the “Whole”, “Integer”, “Rational” and “Real” columns. The last row has the number 9 fifths in the “Number” column and an x marked in the “Rational” and “Real” columns.

Try It 7.8 §7.1 source ↗

Determine whether each number is a ⓐ whole number, ⓑ integer, ⓒ rational number, ⓓ irrational number, and ⓔ real number:

-

\sqrt{25},

-

\frac{3}{8},

−1,

6,

\sqrt{121},

2.041975…

Answer

7.1-1 §7.1 source ↗

Rational Numbers

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

ⓐ $5$

ⓑ $3.19$

Answer

ⓐ $\frac{5}{1}$

ⓑ $\frac{319}{100}$

7.1-3 §7.1 source ↗

Rational Numbers

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

ⓐ $−12$

ⓑ $9.279$

Answer

ⓐ $\frac{−12}{1}$

ⓑ $\frac{9279}{1000}$

7.1-5 §7.1 source ↗

In the following exercises, determine which of the given numbers are rational and which are irrational.

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

Answer

Rational:

0.75, 0.22 \overset{–}{3}

. Irrational:

1.39174…

7.1-7 §7.1 source ↗

In the following exercises, determine which of the given numbers are rational and which are irrational.

$0 . \overset{—}{45}$ , $1.919293…$ , $3.59$

Answer

Rational:

0 . \overset{—}{45}

3.59

. Irrational:

1.919293…

7.1-9 §7.1 source ↗

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

ⓐ $\sqrt{25}$

ⓑ $\sqrt{30}$

Answer

ⓐ rational

ⓑ irrational

7.1-11 §7.1 source ↗

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

ⓐ $\sqrt{164}$

ⓑ $\sqrt{169}$

Answer

ⓐ irrational

ⓑ rational

7.1-13 §7.1 source ↗

Classifying Real Numbers

In the following exercises, determine whether each number is whole, integer, rational, irrational, and real.

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

Answer

7.1-15 §7.1 source ↗

Classifying Real Numbers

In the following exercises, determine whether each number is whole, integer, rational, irrational, and real.

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

Answer

7.1-17 §7.1 source ↗

Classifying Real Numbers

In the following exercises, determine whether each number is whole, integer, rational, irrational, and real.

Child care Serena wants to open a licensed child care center. Her state requires that there be no more than $12$ children for each teacher. She would like her child care center to serve $40$ children.

ⓐ How many teachers will be needed?

ⓑ Why must the answer be a whole number?

Answer

ⓐ 4

ⓑ Teachers cannot be divided

7.1-19 §7.1 source ↗

Classifying Real Numbers

In the following exercises, determine whether each number is whole, integer, rational, irrational, and real.

Explain how the sets of numbers (counting, whole, integer, rational, irrationals, reals) are related to each other.

Answer

Answers will vary.

Be Prepared 7.4 §7.2 source ↗

Simplify:

7 y + 2 + y + 13 .

If you missed this problem, review Example 2.22.

Example 2.22 in the book ↗

Answer

8 y + 15

Be Prepared 7.5 §7.2 source ↗

Multiply:

\frac{2}{3} \cdot 18 .

If you missed this problem, review Example 4.28.

Example 4.28 in the book ↗

Answer

12

Be Prepared 7.6 §7.2 source ↗

Find the opposite of

15 .

If you missed this problem, review Example 3.3.

Example 3.3 in the book ↗

Answer

- 15

Try It 7.9 §7.2 source ↗

Use the commutative properties to rewrite the following:

ⓐ $−4 + 7 =_____$

ⓑ $6 \cdot 12 =_____$

Answer

ⓐ −4 + 7 = 7 + (−4)

ⓑ 6 · 12 = 12 · 6

Try It 7.10 §7.2 source ↗

Use the commutative properties to rewrite the following:

ⓐ $14 +$ $(−2) =$ $_____$

ⓑ $3 (−5) =_____$

Answer

ⓐ 14 + (−2) = −2 + 14

ⓑ 3(−5) = (−5)3

Try It 7.11 §7.2 source ↗

Use the associative properties to rewrite the following:
ⓐ

(1 + 0.7) +

0.3 =

__________

ⓑ

(−9 \cdot 8) \cdot \frac{3}{4} =

__________

Answer

ⓐ $(1 + 0.7) +$ $0.3 =$ $1 +$ $(0.7 + 0.3)$

ⓑ $(−9 \cdot 8) \cdot \frac{3}{4} =$ $−9 (8 \cdot \frac{3}{4})$

Try It 7.12 §7.2 source ↗

Use the associative properties to rewrite the following:
ⓐ

(4 + 0.6) +

0.4 =

__________

ⓑ

(−2 \cdot 12) \cdot \frac{5}{6} =

__________

Answer

ⓐ $(4 + 0.6) +$ $0.4 =$ $4 +$ $(0.6 + 0.4)$

ⓑ $(−2 \cdot 12) \cdot \frac{5}{6} =$ $−2 (12 \cdot \frac{5}{6})$

Try It 7.13 §7.2 source ↗

Use the Associative Property of Multiplication to simplify the given expression:

8 (4 x) .

Answer

8(4x) = (8 · 4)x = 32x

Try It 7.14 §7.2 source ↗

Use the Associative Property of Multiplication to simplify the given expression:

−9 (7 y) .

Answer

−9(7y) = (−9 · 7)y = −63y

Try It 7.15 §7.2 source ↗

Evaluate each expression when

y = \frac{3}{8} :

ⓐ

y + 0.84 + (- y)

ⓑ

y +

(- y) +

0.84 .

Answer

ⓐ 0.84

ⓑ 0.84

Try It 7.16 §7.2 source ↗

Evaluate each expression when

f = \frac{17}{20} :

ⓐ

f +

0.975 +

(- f)

ⓑ

f +

(- f) +

0.975 .

Answer

ⓐ 0.975

ⓑ 0.975

Try It 7.17 §7.2 source ↗

Evaluate each expression when

p = 24 :

ⓐ

\frac{5}{9} (\frac{9}{5} p)

ⓑ

(\frac{5}{9} \cdot \frac{9}{5}) p .

Answer

ⓐ 24

ⓑ 24

Try It 7.18 §7.2 source ↗

Evaluate each expression when

q = 15 :

ⓐ

\frac{7}{11} (\frac{11}{7} q)

ⓑ

(\frac{7}{11} \cdot \frac{11}{7}) q

Answer

ⓐ 15

ⓑ 15

Try It 7.19 §7.2 source ↗

Simplify:

−27 a +

(−48 a) +

27 a .

Answer

−48a

Try It 7.20 §7.2 source ↗

Simplify:

39 x +

(−92 x) +

(−39 x) .

Answer

−92x

Try It 7.21 §7.2 source ↗

Simplify:

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

Answer

\frac{5}{49}

Try It 7.22 §7.2 source ↗

Simplify:

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

Answer

\frac{11}{25}

Try It 7.23 §7.2 source ↗

Simplify:

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

\frac{3}{8} .

Answer

\frac{22}{15}

Try It 7.24 §7.2 source ↗

Simplify:

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

\frac{5}{12} .

Answer

\frac{11}{9}

Try It 7.25 §7.2 source ↗

Simplify:

(5.58 c + 8.75 c) +

1.25 c .

Answer

15.58c

Try It 7.26 §7.2 source ↗

Simplify:

(8.79 d + 3.55 d) +

5.45 d .

Answer

17.79d

Try It 7.27 §7.2 source ↗

Simplify:

[1.17 (4)] (2.25) .

Answer

10.53

Try It 7.28 §7.2 source ↗

Simplify:

[3.52 (8)] (2.5) .

Answer

70.4

Try It 7.29 §7.2 source ↗

Simplify:

8 (3 y) .

Answer

24y

Try It 7.30 §7.2 source ↗

Simplify:

12 (5 z) .

Answer

60z

Try It 7.31 §7.2 source ↗

Simplify:

23 r +

14 s +

9 r +

(−15 s) .

Answer

32r − s

Try It 7.32 §7.2 source ↗

Simplify:

37 m +

21 n +

4 m +

(−15 n) .

Answer

41m + 6n

7.2-21 §7.2 source ↗

Use the Commutative and Associative Properties

In the following exercises, use the commutative properties to rewrite the given expression.

$7 + 6 =___$

Answer

7 + 6 = 6 + 7

7.2-23 §7.2 source ↗

Use the Commutative and Associative Properties

In the following exercises, use the commutative properties to rewrite the given expression.

$7 (−13) =___$

Answer

7(−13) = (−13)7

7.2-25 §7.2 source ↗

Use the Commutative and Associative Properties

In the following exercises, use the commutative properties to rewrite the given expression.

$(−12) (−18) =$ $___$

Answer

(−12)(−18) = (−18)(−12)

7.2-27 §7.2 source ↗

Use the Commutative and Associative Properties

In the following exercises, use the commutative properties to rewrite the given expression.

$−15 + 7 =___$

Answer

−15 + 7 = 7 + (−15)

7.2-29 §7.2 source ↗

Use the Commutative and Associative Properties

In the following exercises, use the commutative properties to rewrite the given expression.

$y + 1 =___$

Answer

y + 1 = 1 + y

7.2-31 §7.2 source ↗

Use the Commutative and Associative Properties

In the following exercises, use the commutative properties to rewrite the given expression.

$−3 m =___$

Answer

−3m = m(−3)

7.2-33 §7.2 source ↗

In the following exercises, use the associative properties to rewrite the given expression.

$(21 + 14) +$ $9 =$ $___$

Answer

(21 + 14) + 9 = 21 + (14 + 9)

7.2-35 §7.2 source ↗

In the following exercises, use the associative properties to rewrite the given expression.

$(14 \cdot 6) \cdot 9 =$ $___$

Answer

(14 · 6) · 9 = 14(6 · 9)

7.2-37 §7.2 source ↗

In the following exercises, use the associative properties to rewrite the given expression.

$(−2 + 6) +$ $7 =$ $___$

Answer

(−2 + 6) + 7 = −2 + (6 + 7)

7.2-39 §7.2 source ↗

In the following exercises, use the associative properties to rewrite the given expression.

$(13 \cdot \frac{2}{3}) \cdot 18 =$ $___$

Answer

(13 \cdot \frac{2}{3}) \cdot 18 =

13 (\frac{2}{3} \cdot 18)

7.2-41 §7.2 source ↗

In the following exercises, use the associative properties to rewrite the given expression.

$4 (7 x) =___$

Answer

4(7x) = (4 · 7)x

7.2-43 §7.2 source ↗

In the following exercises, use the associative properties to rewrite the given expression.

$(17 + y) +$ $33 =$ $___$

Answer

(17 + y) + 33 = 17 + (y + 33)

7.2-45 §7.2 source ↗

Evaluate Expressions using the Commutative and Associative Properties

In the following exercises, evaluate each expression for the given value.

If $z = \frac{7}{8},$ evaluate:

ⓐ $z + 0.97 + (- z)$

ⓑ $z + (- z) + 0.97$

Answer

ⓐ 0.97

ⓑ 0.97

7.2-47 §7.2 source ↗

Evaluate Expressions using the Commutative and Associative Properties

In the following exercises, evaluate each expression for the given value.

If $d = - \frac{9}{4},$ evaluate:

ⓐ $d +$ $2.375 +$ $(- d)$

ⓑ $d +$ $(- d) +$ $2.375$

Answer

ⓐ 2.375

ⓑ 2.375

7.2-49 §7.2 source ↗

Evaluate Expressions using the Commutative and Associative Properties

In the following exercises, evaluate each expression for the given value.

If $k = 21,$ evaluate:

ⓐ $\frac{4}{13} (\frac{13}{4} k)$

ⓑ $(\frac{4}{13} \cdot \frac{13}{4}) k$

Answer

ⓐ 21

ⓑ 21

7.2-51 §7.2 source ↗

Evaluate Expressions using the Commutative and Associative Properties

In the following exercises, evaluate each expression for the given value.

If $n = −8,$ evaluate:

ⓐ $- \frac{5}{21} (\frac{21}{5} n)$

ⓑ $(- \frac{5}{21} \cdot \frac{21}{5}) n$

Answer

ⓐ 8

ⓑ 8

7.2-53 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$9 y + 23 + (−9 y)$

Answer

7.2-55 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$\frac{2}{5} +$ $\frac{5}{12} +$ $(- \frac{2}{5})$

Answer

\frac{5}{12}

7.2-57 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$\frac{13}{18} \cdot \frac{25}{7} \cdot \frac{18}{13}$

Answer

\frac{25}{7}

7.2-59 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$\frac{3}{10} \cdot \frac{13}{23} \cdot \frac{50}{3}$

Answer

\frac{65}{23}

7.2-61 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$−36 \cdot 11 \cdot \frac{4}{9}$

Answer

−176

7.2-63 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$(\frac{1}{12} + \frac{4}{9}) + \frac{5}{9}$

Answer

\frac{13}{12}

7.2-65 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$\frac{8}{15} + \frac{5}{7} + \frac{2}{7}$

Answer

\frac{23}{15}

7.2-67 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$(5.89 d + 2.75 d) +$ $1.25 d$

Answer

9.89d

7.2-69 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$36 (0.2) (5)$

Answer

7.2-71 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$[9.731 (4)] (0.75)$

Answer

29.193

7.2-73 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$9 (8 w)$

Answer

72w

7.2-75 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$−23 (2 n)$

Answer

−46n

7.2-77 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$20 (\frac{3}{5} q)$

Answer

12q

7.2-79 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$15 u +$ $11 v +$ $27 u +$ $19 v$

Answer

42u + 30v

7.2-81 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$−22 p +$ $17 q +$ $(−35 p) +$ $(−27 q)$

Answer

−57p + (−10q)

7.2-83 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$\frac{5}{6} a +$ $\frac{3}{10} b +$ $\frac{1}{6} a +$ $\frac{9}{10} b$

Answer

a + \frac{6}{5} b

7.2-85 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

$9.6 m +$ $7.22 n +$ $(−2.19 m) +$ $(−0.65 n)$

Answer

7.41m + 6.57n

7.2-87 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

Counting Cash Grant is totaling up the cash from a fundraising dinner. In one envelope, he has twenty-three $$5$ bills, eighteen $$10$ bills, and thirty-four $$20$ bills. In another envelope, he has fourteen $$5$ bills, nine $$10$ bills, and twenty-seven $$20$ bills.

ⓐ How much money is in the first envelope?

ⓑ How much money is in the second envelope?

ⓓ What is the value of all the $$5$ bills?

ⓔ What is the value of all $$10$ bills?

ⓕ What is the value of all $$20$ bills?

Answer

ⓐ $975

ⓑ $700

ⓓ $185

ⓔ $270

ⓕ $1220

7.2-89 §7.2 source ↗

Simplify Expressions Using the Commutative and Associative Properties

In the following exercises, simplify.

In your own words, state the Associative Property of Multiplication and explain why it is useful.

Answer

Answers will vary.

Be Prepared 7.7 §7.3 source ↗

Multiply:

3 (0.25) .

If you missed this problem, review Example 5.15

Example 5.15 in the book ↗

Answer

0.75

Be Prepared 7.8 §7.3 source ↗

Simplify:

10 - (−2) (3) .

If you missed this problem, review Example 3.51

Example 3.51 in the book ↗

Answer

16

Be Prepared 7.9 §7.3 source ↗

Combine like terms:

9 y + 17 + 3 y - 2 .

If you missed this problem, review Example 2.22.

Example 2.22 in the book ↗

Answer

12 y + 15

Try It 7.33 §7.3 source ↗

Simplify:

4 (x + 2) .

Answer

4x + 8

Try It 7.34 §7.3 source ↗

Simplify:

6 (x + 7) .

Answer

6x + 42

Try It 7.35 §7.3 source ↗

Simplify:

9 (3 y + 8) .

Answer

27y + 72

Try It 7.36 §7.3 source ↗

Simplify:

5 (5 w + 9) .

Answer

25w + 45

Try It 7.37 §7.3 source ↗

Simplify:

7 (x - 6) .

Answer

7x − 42

Try It 7.38 §7.3 source ↗

Simplify:

8 (x - 5) .

Answer

8x − 40

Try It 7.39 §7.3 source ↗

Simplify:

\frac{2}{5} (p + 10) .

Answer

\frac{2}{5} p + 4

Try It 7.40 §7.3 source ↗

Simplify:

\frac{3}{7} (u + 21) .

Answer

\frac{3}{7} u + 9

Try It 7.41 §7.3 source ↗

Simplify:

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

Answer

5y + 3

Try It 7.42 §7.3 source ↗

Simplify:

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

Answer

4n + 9

Try It 7.43 §7.3 source ↗

Simplify:

100 (0.7 + 0.15 p) .

Answer

70 + 15p

Try It 7.44 §7.3 source ↗

Simplify:

100 (0.04 + 0.35 d) .

Answer

4 + 35d

Try It 7.45 §7.3 source ↗

Simplify:

r (s - 2) .

Answer

rs − 2r

Try It 7.46 §7.3 source ↗

Simplify:

y (z - 8) .

Answer

yz − 8y

Try It 7.47 §7.3 source ↗

Simplify:

(x + 2) p .

Answer

xp + 2p

Try It 7.48 §7.3 source ↗

Simplify:

(y + 4) q .

Answer

yq + 4q

Try It 7.49 §7.3 source ↗

Simplify:

−3 (6 m + 5) .

Answer

−18m − 15

Try It 7.50 §7.3 source ↗

Simplify:

−6 (8 n + 11) .

Answer

−48n − 66

Try It 7.51 §7.3 source ↗

Simplify:

−5 (2 - 3 a) .

Answer

−10 + 15a

Try It 7.52 §7.3 source ↗

Simplify:

−7 (8 - 15 y) .

Answer

−56 + 105y

Try It 7.53 §7.3 source ↗

Simplify:

- (z - 11) .

Answer

−z + 11

Try It 7.54 §7.3 source ↗

Simplify:

- (x - 4) .

Answer

−x + 4

Try It 7.55 §7.3 source ↗

Simplify:

9 - 3 (x + 2) .

Answer

−3x + 3

Try It 7.56 §7.3 source ↗

Simplify:

7 x - 5 (x + 4) .

Answer

2x − 20

Try It 7.57 §7.3 source ↗

Simplify:

6 (x - 9) -

(x + 12) .

Answer

5x − 66

Try It 7.58 §7.3 source ↗

Simplify:

8 (x - 1) -

(x + 5) .

Answer

7x − 13

Try It 7.59 §7.3 source ↗

Evaluate when

w = 3 :

ⓐ

5 (5 w + 9)

ⓑ

5 \cdot 5 w + 5 \cdot 9 .

Answer

ⓐ 120

ⓑ 120

Try It 7.60 §7.3 source ↗

Evaluate when

y = 2 :

ⓐ

9 (3 y + 8)

ⓑ

9 \cdot 3 y + 9 \cdot 8 .

Answer

ⓐ 126

ⓑ 126

Try It 7.61 §7.3 source ↗

Evaluate when

n = −2 :

ⓐ

−6 (8 n + 11)

ⓑ

−6 \cdot 8 n +

(−6) \cdot 11 .

Answer

ⓐ 30

ⓑ 30

Try It 7.62 §7.3 source ↗

Evaluate when

m = −1 :

ⓐ

−3 (6 m + 5)

ⓑ

−3 \cdot 6 m +

(−3) \cdot 5 .

Answer

ⓐ 3

ⓑ 3

Try It 7.63 §7.3 source ↗

Evaluate when

x = 36 :

ⓐ

- (x - 4)

ⓑ

- x + 4

to show that

-

(x - 4) =

-

x +

4 .

Answer

ⓐ −32

ⓑ −32

Try It 7.64 §7.3 source ↗

Evaluate when

z = 55 :

ⓐ

- (z - 10)

ⓑ

- z + 10

to show that

-

(z - 10) =

-

z +

10 .

Answer

ⓐ −45

ⓑ −45

7.3-91 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$3 (a + 9)$

Answer

3a + 27

7.3-93 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$9 (3 w + 7)$

Answer

27w + 63

7.3-95 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$7 (y - 13)$

Answer

7y − 91

7.3-97 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$5 (7 u - 4)$

Answer

35u − 20

7.3-99 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$\frac{1}{3} (u + 9)$

Answer

\frac{1}{3} u + 3

7.3-101 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$\frac{1}{5} (4 m + 20)$

Answer

\frac{4}{5} m + 4

7.3-103 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$10 (\frac{3}{10} x - \frac{2}{5})$

Answer

3x − 4

7.3-105 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$12 (\frac{1}{6} + \frac{3}{4} s)$

Answer

2 + 9s

7.3-107 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$u (v - 10)$

Answer

uv − 10u

7.3-109 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$(a + 7) x$

Answer

ax + 7x

7.3-111 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$−3 (a + 11)$

Answer

−3a − 33

7.3-113 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$−9 (9 a + 4)$

Answer

−81a − 36

7.3-115 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$−4 (q - 7)$

Answer

−4q + 28

7.3-117 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$−6 (7 x - 8)$

Answer

−42x + 48

7.3-119 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$- (q + 11)$

Answer

−q − 11

7.3-121 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$- (5 p - 4)$

Answer

−5p + 4

7.3-123 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$12 + 8 (u - 1)$

Answer

8u + 4

7.3-125 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$18 - 4 (x + 2)$

Answer

−4x + 10

7.3-127 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$9 - 6 (7 n - 5)$

Answer

−42n + 39

7.3-129 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$8 - (r - 7)$

Answer

−r + 15

7.3-131 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$−4 - (c - 10)$

Answer

−c + 6

7.3-133 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$(4 y - 1) -$ $(y - 2)$

Answer

3y + 1

7.3-135 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$9 (5 u + 8) +$ $2 (u - 6)$

Answer

47u + 60

7.3-137 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$4 (6 x - 1) -$ $(−8)$

Answer

24x + 4

7.3-139 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$11 (n - 7) -$ $5 (n - 1)$

Answer

6n − 72

7.3-141 §7.3 source ↗

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

$7 (3 n + 9) -$ $(4 n - 13)$

Answer

17n + 76

7.3-143 §7.3 source ↗

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

If $u = −1,$ evaluate

ⓐ $8 (5 u + 12)$

ⓑ $8 \cdot 5 u + 8 \cdot 12$

Answer

ⓐ 56

ⓑ 56

7.3-145 §7.3 source ↗

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

If $y = \frac{3}{4},$ evaluate

ⓐ $4 (y + \frac{3}{8})$

ⓑ $4 \cdot y + 4 \cdot \frac{3}{8}$

Answer

ⓐ $\frac{9}{2}$

ⓑ $\frac{9}{2}$

7.3-147 §7.3 source ↗

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

If $p = \frac{23}{30},$ evaluate

ⓐ $−6 (5 p + 11)$

ⓑ $−6 \cdot 5 p +$ $(−6) \cdot 11$

Answer

ⓐ −89

ⓑ −89

7.3-149 §7.3 source ↗

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

If $n = 0.75,$ evaluate

ⓐ $−100 (5 n + 1.5)$

ⓑ $−100 \cdot 5 n +$ $(−100) (1.5)$

Answer

ⓐ −525

ⓑ −525

7.3-151 §7.3 source ↗

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

If $w = −80,$ evaluate

ⓐ $- (w - 80)$

ⓑ $- w + 80$

Answer

ⓐ 160

ⓑ 160

7.3-153 §7.3 source ↗

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

If $q = 0.55,$ evaluate

ⓐ $- (q + 0.48)$

ⓑ $- q - 0.48$

Answer

ⓐ −1.03

ⓑ −1.03

7.3-155 §7.3 source ↗

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

Multi-pack purchase Adele’s shampoo sells for $$3.97$ per bottle at the drug store. At the warehouse store, the same shampoo is sold as a $3-pack$ for $$10.49 .$

ⓐ Show how you can use the distributive property to find the cost of $3$ bottles bought individually at the drug store.

ⓑ How much would Adele save by buying the $3-pack$ at the warehouse store?

Answer

ⓐ 3(4 − 0.03) = 11.91

ⓑ $1.42

7.3-157 §7.3 source ↗

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

Explain how you can multiply $4 ($5.97)$ without paper or a calculator by thinking of $$5.97$ as $6 - 0.03$ and then using the distributive property.

Answer

Answers will vary.

Be Prepared 7.10 §7.4 source ↗

Find the opposite of

−4 .

If you missed this problem, review Example 3.3.

Example 3.3 in the book ↗

Answer

4

Be Prepared 7.11 §7.4 source ↗

Find the reciprocal of

\frac{5}{2} .

If you missed this problem, review Example 4.29.

Example 4.29 in the book ↗

Answer

\frac{2}{5}

Be Prepared 7.12 §7.4 source ↗

Multiply:

\frac{3 a}{5} \cdot \frac{9}{2 a} .

If you missed this problem, review Example 4.27.

Example 4.27 in the book ↗

Answer

\frac{27}{10}

Try It 7.65 §7.4 source ↗

Identify whether each equation demonstrates the identity property of addition or multiplication:

ⓐ $23 + 0 = 23$ ⓑ $−37 (1) = −37 .$

Answer

ⓐ identity property of addition

ⓑ identity property of multiplication

Try It 7.66 §7.4 source ↗

Identify whether each equation demonstrates the identity property of addition or multiplication:

ⓐ $1 \cdot 29 = 29$ ⓑ $14 + 0 = 14 .$

Answer

ⓐ identity property of multiplication

ⓑ identity property of addition

Try It 7.67 §7.4 source ↗

Find the additive inverse: ⓐ

18

ⓑ

\frac{7}{9}

ⓒ

1.2

Answer

ⓐ $−18$

ⓑ $- \frac{7}{9}$

Try It 7.68 §7.4 source ↗

Find the additive inverse: ⓐ

47

ⓑ

\frac{7}{13}

ⓒ

8.4

Answer

ⓐ $−47$

ⓑ $- \frac{7}{13}$

Try It 7.69 §7.4 source ↗

Find the multiplicative inverse: ⓐ

5

ⓑ

- \frac{1}{7}

ⓒ

0.3

Answer

ⓐ $\frac{1}{5}$

ⓑ $−7$

Try It 7.70 §7.4 source ↗

Find the multiplicative inverse: ⓐ

18

ⓑ

- \frac{4}{5}

ⓒ

0.6

Answer

ⓐ $\frac{1}{18}$

ⓑ $- \frac{5}{4}$

Try It 7.71 §7.4 source ↗

Simplify: ⓐ

−14 \cdot 0

ⓑ

0 \cdot \frac{2}{3}

ⓒ

(16.5) \cdot 0 .

Answer

ⓐ 0

ⓑ 0

ⓒ 0

Try It 7.72 §7.4 source ↗

Simplify: ⓐ

(1.95) \cdot 0

ⓑ

0 (−17)

ⓒ

0 \cdot \frac{5}{4} .

Answer

ⓐ 0

ⓑ 0

ⓒ 0

Try It 7.73 §7.4 source ↗

Simplify: ⓐ

0 \div 11

ⓑ

\frac{0}{−6}

ⓒ

0 \div \frac{3}{10}

Answer

ⓐ 0

ⓑ 0

ⓒ 0

Try It 7.74 §7.4 source ↗

Simplify: ⓐ

0 \div \frac{8}{3}

ⓑ

0 \div (−10)

ⓒ

0 \div 12.75

Answer

ⓐ 0

ⓑ 0

ⓒ 0

Try It 7.75 §7.4 source ↗

Simplify: ⓐ

16.4 \div 0

ⓑ

\frac{−2}{0}

ⓒ

\frac{1}{5} \div 0

Answer

ⓐ undefined

ⓑ undefined

Try It 7.76 §7.4 source ↗

Simplify: ⓐ

\frac{−5}{0}

ⓑ

96.9 \div 0

ⓒ

\frac{4}{15} \div 0

Answer

ⓐ undefined

ⓑ undefined

Try It 7.77 §7.4 source ↗

Simplify:

−12 z + 9 + 12 z .

Answer

Try It 7.78 §7.4 source ↗

Simplify:

−25 u -

18 +

25 u .

Answer

−18

Try It 7.79 §7.4 source ↗

Simplify:

2 (0.5 p) .

Answer

Try It 7.80 §7.4 source ↗

Simplify:

25 (0.04 r) .

Answer

Try It 7.81 §7.4 source ↗

Simplify:

\frac{0}{m + 7}

, where

m \neq −7

Answer

Try It 7.82 §7.4 source ↗

Simplify:

\frac{0}{d - 4}

, where

d \neq 4

Answer

Try It 7.83 §7.4 source ↗

Simplify:

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

Answer

undefined

Try It 7.84 §7.4 source ↗

Simplify:

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

Answer

undefined

Try It 7.85 §7.4 source ↗

Simplify:

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

Answer

20y + 50

Try It 7.86 §7.4 source ↗

Simplify:

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

Answer

12z + 16

7.4-159 §7.4 source ↗

Recognize the Identity Properties of Addition and Multiplication

In the following exercises, identify whether each example is using the identity property of addition or multiplication.

$\frac{3}{5} (1) = \frac{3}{5}$

Answer

identity property of multiplication

7.4-161 §7.4 source ↗

Recognize the Identity Properties of Addition and Multiplication

In the following exercises, identify whether each example is using the identity property of addition or multiplication.

$0 + 64 = 64$

Answer

identity property of addition

7.4-163 §7.4 source ↗

Use the Inverse Properties of Addition and Multiplication

In the following exercises, find the multiplicative inverse.

$14$

Answer

\frac{1}{14}

7.4-165 §7.4 source ↗

Use the Inverse Properties of Addition and Multiplication

In the following exercises, find the multiplicative inverse.

$−19$

Answer

- \frac{1}{19}

7.4-167 §7.4 source ↗

Use the Inverse Properties of Addition and Multiplication

In the following exercises, find the multiplicative inverse.

$\frac{8}{13}$

Answer

\frac{13}{8}

7.4-169 §7.4 source ↗

Use the Inverse Properties of Addition and Multiplication

In the following exercises, find the multiplicative inverse.

$- \frac{5}{12}$

Answer

- \frac{12}{5}

7.4-171 §7.4 source ↗

Use the Inverse Properties of Addition and Multiplication

In the following exercises, find the multiplicative inverse.

$0.4$

Answer

\frac{5}{2}

7.4-173 §7.4 source ↗

Use the Inverse Properties of Addition and Multiplication

In the following exercises, find the multiplicative inverse.

$−0.5$

Answer

−2

7.4-175 §7.4 source ↗

Use the Properties of Zero

In the following exercises, simplify using the properties of zero.

$\frac{0}{6}$

Answer

7.4-177 §7.4 source ↗

Use the Properties of Zero

In the following exercises, simplify using the properties of zero.

$22 \cdot 0$

Answer

7.4-179 §7.4 source ↗

Use the Properties of Zero

In the following exercises, simplify using the properties of zero.

$\frac{6}{0}$

Answer

undefined

7.4-181 §7.4 source ↗

Use the Properties of Zero

In the following exercises, simplify using the properties of zero.

$0 \div \frac{7}{15}$

Answer

7.4-183 §7.4 source ↗

Use the Properties of Zero

In the following exercises, simplify using the properties of zero.

$(−3.14) (0)$

Answer

7.4-185 §7.4 source ↗

Use the Properties of Zero

In the following exercises, simplify using the properties of zero.

$\frac{\frac{1}{10}}{0}$

Answer

undefined

7.4-187 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$27 c + 16 - 27 c$

Answer

7.4-189 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$92 + 31 s - 92$

Answer

31s

7.4-191 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$100 (0.01 p)$

Answer

7.4-193 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$40 (0.05 n)$

Answer

7.4-195 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$\frac{0}{s + 13}$ , where $s \neq −13$

Answer

7.4-197 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$\frac{0}{v - 65.1}$ , where $v \neq 65.1$

Answer

7.4-199 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$0 \div (y - \frac{1}{6})$ , where $y \neq \frac{1}{6}$

Answer

7.4-201 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$\frac{28 - 9 b}{0}$ , where $28 - 9 b \neq 0$

Answer

undefined

7.4-203 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$\frac{1.75 + 9 f}{0}$ , where $1.75 + 9 f \neq 0$

Answer

undefined

7.4-205 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$(\frac{5}{16} n - \frac{3}{7}) \div 0$ , where $\frac{5}{16} n - \frac{3}{7} \neq 0$

Answer

undefined

7.4-207 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$\frac{5}{7} \cdot \frac{7}{5} (20 q - 35)$

Answer

20q − 35

7.4-209 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$18 \cdot \frac{5}{6} (15 h + 24)$

Answer

225h + 360

7.4-211 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

Cooking time Helen bought a $24-pound$ turkey for her family’s Thanksgiving dinner and wants to know what time to put the turkey in the oven. She wants to allow $20$ minutes per pound cooking time.

ⓐ Calculate the length of time needed to roast the turkey by multiplying $24 \cdot 20$ to find the number of minutes and then multiplying the product by $\frac{1}{60}$ to convert minutes into hours.

ⓑ Multiply $24 (20 \cdot \frac{1}{60}) .$

Answer

ⓐ 8 hours

ⓑ 8

7.4-213 §7.4 source ↗

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

How can the use of the properties of real numbers make it easier to simplify expressions?

Answer

Answers will vary.

Be Prepared 7.13 §7.5 source ↗

Multiply:

4.29 (1000) .

If you missed this problem, review Example 5.18.

Example 5.18 in the book ↗

Answer

4, 290

Be Prepared 7.14 §7.5 source ↗

Simplify:

\frac{30}{54} .

If you missed this problem, review Example 4.20.

Example 4.20 in the book ↗

Answer

\frac{5}{9}

Be Prepared 7.15 §7.5 source ↗

Multiply:

\frac{7}{15} \cdot \frac{25}{28} .

If you missed this problem, review Example 4.27.

Example 4.27 in the book ↗

Answer

\frac{5}{12}

Try It 7.87 §7.5 source ↗

Lexie is

30

inches tall. Convert her height to feet.

Answer

2.5 feet

Try It 7.88 §7.5 source ↗

Rene bought a hose that is

18

yards long. Convert the length to feet.

Answer

54 feet

Try It 7.89 §7.5 source ↗

Arnold’s SUV weighs about

4.3

tons. Convert the weight to pounds.

Answer

8600 pounds

Try It 7.90 §7.5 source ↗

A cruise ship weighs

51,000

tons. Convert the weight to pounds.

Answer

102,000,000 pounds

Try It 7.91 §7.5 source ↗

The distance between Earth and the moon is about

250,000

miles. Convert this length to yards.

Answer

440,000,000 yards

Try It 7.92 §7.5 source ↗

A team of astronauts spends

15

weeks in space. Convert the time to minutes.

Answer

151,200 minutes

Try It 7.93 §7.5 source ↗

How many cups are in

1

gallon?

Answer

16 cups

Try It 7.94 §7.5 source ↗

How many teaspoons are in

1

cup?

Answer

48 teaspoons

Try It 7.95 §7.5 source ↗

Laura gave birth to triplets weighing

3

pounds

12

ounces,

3

pounds

3

ounces, and

2

pounds

9

ounces. What was the total birth weight of the three babies?

Answer

9 lbs. 8 oz

Try It 7.96 §7.5 source ↗

Seymour 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 7.97 §7.5 source ↗

Henri wants to triple his spaghetti sauce recipe, which calls for

1

pound

8

ounces of ground turkey. How many pounds of ground turkey will he need?

Answer

4 lbs. 8 oz.

Try It 7.98 §7.5 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 qts.

Try It 7.99 §7.5 source ↗

Sandy completed her first

5-km

race. How many meters did she run?

Answer

5000 m

Try It 7.100 §7.5 source ↗

Herman bought a rug

2.5

meters in length. How many centimeters is the length?

Answer

250 cm

Try It 7.101 §7.5 source ↗

Kari’s newborn baby weighed

2800

grams. How many kilograms did the baby weigh?

Answer

2.8 kilograms

Try It 7.102 §7.5 source ↗

Anderson received a package that was marked

4500

grams. How many kilograms did this package weigh?

Answer

4.5 kilograms

Try It 7.103 §7.5 source ↗

Convert: ⓐ

7.25

L to kL ⓑ

6.3

L to mL.

Answer

ⓐ 0.00725 kL

ⓑ 6300 mL

Try It 7.104 §7.5 source ↗

Convert: ⓐ

350

hL to L ⓑ

4.1

L to cL.

Answer

ⓐ 35,000 L

ⓑ 410 cL

Try It 7.105 §7.5 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 cm

Try It 7.106 §7.5 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 m

Try It 7.107 §7.5 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 L

Try It 7.108 §7.5 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 kg

Try It 7.109 §7.5 source ↗

How many quarts of soda are in a

2-liter

bottle?

Answer

2.12 quarts

Try It 7.110 §7.5 source ↗

How many liters are in

4

quarts of milk?

Answer

3.8 liters

Try It 7.111 §7.5 source ↗

The height of Mount Kilimanjaro is

5,895

meters. Convert the height to feet. Round to the nearest foot.

Answer

19,336 ft

Try It 7.112 §7.5 source ↗

The flight distance from New York City to London is

5,586

kilometers. Convert the distance to miles. Round to the nearest mile.

Answer

3,470 mi

Try It 7.113 §7.5 source ↗

Convert the Fahrenheit temperatures to degrees Celsius:

59 °F .

Answer

15°C

Try It 7.114 §7.5 source ↗

Convert the Fahrenheit temperatures to degrees Celsius:

41 °F .

Answer

5°C

Try It 7.115 §7.5 source ↗

Convert the Celsius temperatures to degrees Fahrenheit:

The temperature in Helsinki, Finland was $15 °C .$

Answer

59°F

Try It 7.116 §7.5 source ↗

Convert the Celsius temperatures to degrees Fahrenheit:

The temperature in Sydney, Australia was $10 °C .$

Answer

50°F

7.5-215 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

A floor tile is $2$ feet wide. Convert the width to inches.

Answer

24 inches

7.5-217 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Carson is $45$ inches tall. Convert his height to feet.

Answer

3.75 feet

7.5-219 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Faye is $4$ feet $10$ inches tall. Convert her height to inches.

Answer

58 inches

7.5-221 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

On a baseball diamond, the distance from home plate to first base is $30$ yards. Convert the distance to feet.

Answer

90 feet

7.5-223 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Denver, Colorado, is $5,183$ feet above sea level. Convert the height to miles.

Answer

0.98 miles

7.5-225 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Blue whales can weigh as much as $150$ tons. Convert the weight to pounds.

Answer

300,000 pounds

7.5-227 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

At take-off, an airplane weighs $220,000$ pounds. Convert the weight to tons.

Answer

110 tons

7.5-229 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Lynn’s cruise lasted $6$ days and $18$ hours. Convert the time to hours.

Answer

162 hours

7.5-231 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Misty’s surgery lasted $2 \frac{1}{4}$ hours. Convert the time to seconds.

Answer

8100 seconds

7.5-233 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

How many tablespoons are in a gallon?

Answer

256 tablespoons

7.5-235 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

April’s dog, Beans, weighs $8$ pounds. Convert his weight to ounces.

Answer

128 ounces

7.5-237 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Baby Audrey weighed $6$ pounds $15$ ounces at birth. Convert her weight to ounces.

Answer

111 ounces

7.5-239 §7.5 source ↗

Make Unit Conversions in the U.S. System

In the following exercises, convert the units.

Lance needs $500$ cups of water for the runners in a race. Convert the volume to gallons.

Answer

31.25 gallons

7.5-241 §7.5 source ↗

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

In the following exercises, solve and write your answer in mixed units.

Judy bought $1$ pound $6$ ounces of almonds, $2$ pounds $3$ ounces of walnuts, and $8$ ounces of cashews. What was the total weight of the nuts?

Answer

4 lbs. 1 oz.

7.5-243 §7.5 source ↗

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

In the following exercises, solve and write your answer in mixed units.

Last year Eric went on $6$ business trips. The number of days of each was $5,$ $2,$ $8,$ $12,$ $6,$ $and 3.$ How much time (in weeks and days) did Eric spend on business trips last year?

Answer

5 weeks and 1 day

7.5-245 §7.5 source ↗

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

In the following exercises, solve and write your answer in mixed units.

Fawzi’s SUV is $6$ feet $4$ inches tall. If he puts a $2-foot-10-inch$ box on top of his SUV, what is the total height of the SUV and the box?

Answer

9 ft 2 in

7.5-247 §7.5 source ↗

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

In the following exercises, solve and write your answer in mixed units.

Mireille needs to cut $24$ inches of ribbon for each of the $12$ girls in her dance class. How many yards of ribbon will she need altogether?

Answer

8 yards

7.5-249 §7.5 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

Kitaka hiked $8$ kilometers. Convert the length to meters.

Answer

8000 meters

7.5-251 §7.5 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

The width of the wading pool is $2.45$ meters. Convert the width to centimeters.

Answer

245 centimeters

7.5-253 §7.5 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

The depth of the Mariana Trench is $10,911$ meters. Convert the depth to kilometers.

Answer

10.911 kilometers

7.5-255 §7.5 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

A typical ruby-throated hummingbird weights $3$ grams. Convert this to milligrams.

Answer

3000 milligrams

7.5-257 §7.5 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

One serving of gourmet ice cream has $25$ grams of fat. Convert this to milligrams.

Answer

25,000 milligrams

7.5-259 §7.5 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

Dimitri’s daughter weighed $3.8$ kilograms at birth. Convert this to grams.

Answer

3800 grams

7.5-261 §7.5 source ↗

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

A bottle of medicine contained $300$ milliliters. Convert this to liters.

Answer

0.3 liters

7.5-263 §7.5 source ↗

Use Mixed Units of Measurement in the Metric System

In the following exercises, solve and write your answer in mixed units.

Stavros is $1.6$ meters tall. His sister is $95$ centimeters tall. How much taller, in centimeters, is Stavros than his sister?

Answer

65 centimeters

7.5-265 §7.5 source ↗

Use Mixed Units of Measurement in the Metric System

In the following exercises, solve and write your answer in mixed units.

Concetta had a $2-kilogram$ bag of flour. She used $180$ grams of flour to make biscotti. How many kilograms of flour are left in the bag?

Answer

1.82 kilograms

7.5-267 §7.5 source ↗

Use Mixed Units of Measurement in the Metric System

In the following exercises, solve and write your answer in mixed units.

One glass of orange juice provides $560$ milligrams of potassium. Linda drinks one glass of orange juice every morning. How many grams of potassium does Linda get from her orange juice in $30$ days?

Answer

16.8 grams

7.5-269 §7.5 source ↗

Use Mixed Units of Measurement in the Metric System

In the following exercises, solve and write your answer in mixed units.

One serving of whole grain sandwich bread provides $6$ grams of protein. How many milligrams of protein are provided by $7$ servings of whole grain sandwich bread?

Answer

42,000 milligrams

7.5-271 §7.5 source ↗

Convert Between U.S. and Metric Systems

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

Frankie is $42$ inches tall. Convert his height to centimeters.

Answer

106.7 centimeters

7.5-273 §7.5 source ↗

Convert Between U.S. and Metric Systems

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

Connie bought $9$ yards of fabric to make drapes. Convert the fabric length to meters.

Answer

8.2 meters

7.5-275 §7.5 source ↗

Convert Between U.S. and Metric Systems

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

An average American will throw away $90,000$ pounds of trash over his or her lifetime. Convert this weight to kilograms (2.20 pounds = 1 kilogram).

Answer

40,900 kilograms

7.5-277 §7.5 source ↗

Convert Between U.S. and Metric Systems

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

Kathryn is $1.6$ meters tall. Convert her height to feet.

Answer

5.2 feet

7.5-279 §7.5 source ↗

Convert Between U.S. and Metric Systems

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

Jackson’s backpack weighs $15$ kilograms. Convert the weight to pounds.

Answer

33 pounds

7.5-281 §7.5 source ↗

Convert Between U.S. and Metric Systems

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

Bernard bought $8$ gallons of paint. Convert the volume to liters.

Answer

30.2 liters

7.5-283 §7.5 source ↗

Convert between Fahrenheit and Celsius

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

$77 °F$

Answer

25°C

7.5-285 §7.5 source ↗

Convert between Fahrenheit and Celsius

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

$14 °F$

Answer

−10°C

7.5-287 §7.5 source ↗

Convert between Fahrenheit and Celsius

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

$4 °F$

Answer

−15.6°C

7.5-289 §7.5 source ↗

Convert between Fahrenheit and Celsius

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

$120 °F$

Answer

48.9°C

7.5-291 §7.5 source ↗

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

$25 °C$

Answer

77°F

7.5-293 §7.5 source ↗

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

$−15 °C$

Answer

5°F

7.5-295 §7.5 source ↗

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

$8 °C$

Answer

46.4°F

7.5-297 §7.5 source ↗

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

$16 °C$

Answer

60.8°F

7.5-299 §7.5 source ↗

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

Reflectors The reflectors in each lane-marking stripe on a highway are spaced $16$ yards apart. How many reflectors are needed for a one-mile-long stretch of highway?

Answer

110 reflectors

7.R-303 §7.R source ↗

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

$−5$

Answer

\frac{- 5}{1}

7.R-305 §7.R source ↗

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

$1.8$

Answer

\frac{18}{10}

7.R-307 §7.R source ↗

In the following exercises, determine which of the numbers is rational.

$0.75319…,$ $0. \overset{—}{16},$ $1.95$

Answer

0. \overset{—}{16}, 1.95

7.R-309 §7.R source ↗

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

ⓐ $\sqrt{72}$ ⓑ $\sqrt{64}$

Answer

ⓐ irrational

ⓑ rational

7.R-311 §7.R source ↗

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

$−5,$ $-$ $2 \frac{1}{4},$ $-$ $\sqrt{4},$ $0. \overset{—}{25},$ $\frac{13}{5},$ $4$

Answer

ⓐ $4$

ⓑ $- 5, - \sqrt{4}, 4$

ⓓ none

ⓔ $-$ $5,$ $-$ $2 \frac{1}{4},$ $-$ $\sqrt{4},$ $0. \overset{—}{25},$ $\frac{13}{5},$ $4$

7.R-313 §7.R source ↗

In the following exercises, use the commutative property to rewrite the given expression.

$−14 \cdot 5 =____$

Answer

−14·5 = 5(−14)

7.R-315 §7.R source ↗

In the following exercises, use the commutative property to rewrite the given expression.

$a + 8 =____$

Answer

a + 8 = 8 + a

7.R-317 §7.R source ↗

In the following exercises, use the associative property to rewrite the given expression.

$(22 + 7) +$ $3 =$ $_____$

Answer

(22 + 7) + 3 = 22 + (7 + 3)

7.R-319 §7.R source ↗

In the following exercises, use the associative property to rewrite the given expression.

$\frac{1}{2} (22 y) =$ $_____$

Answer

\frac{1}{2} (22 y) =

(\frac{1}{2} \cdot 22) y

7.R-321 §7.R source ↗

In the following exercises, evaluate each expression for the given value.

If $z = - \frac{5}{3},$ evaluate:
ⓐ $z + 5.39 + (- z)$
ⓑ $z + (- z) + 5.39$

Answer

ⓐ 5.39

ⓑ 5.39

7.R-323 §7.R source ↗

In the following exercises, evaluate each expression for the given value.

If $m = −13,$ evaluate:
ⓐ $- \frac{2}{5} (\frac{5}{2} m)$
ⓑ $(- \frac{2}{5} \cdot \frac{5}{2}) m$

Answer

ⓐ 13

ⓑ 13

7.R-325 §7.R source ↗

In the following exercises, simplify using the commutative and associative properties.

$\frac{1}{4} +$ $\frac{11}{15} +$ $(- \frac{1}{4})$

Answer

\frac{11}{15}

7.R-327 §7.R source ↗

In the following exercises, simplify using the commutative and associative properties.

$−18 \cdot 15 \cdot \frac{2}{9}$

Answer

−60

7.R-329 §7.R source ↗

In the following exercises, simplify using the commutative and associative properties.

$(3.98 d + 0.75 d) +$ $1.25 d$

Answer

5.98 d

7.R-331 §7.R source ↗

In the following exercises, simplify using the commutative and associative properties.

$30 (\frac{5}{6} q)$

Answer

25 q

7.R-333 §7.R source ↗

In the following exercises, simplify using the commutative and associative properties.

$52 m +$ $(−20 n) +$ $(−18 m) +$ $(−5 n)$

Answer

34 m + (−25 n)

7.R-335 §7.R source ↗

In the following exercises, simplify using the distributive property.

$9 (u - 4)$

Answer

9y − 36

7.R-337 §7.R source ↗

In the following exercises, simplify using the distributive property.

$−8 (−7 a - 12)$

Answer

56a + 96

7.R-339 §7.R source ↗

In the following exercises, simplify using the distributive property.

$(y + 10) \cdot p$

Answer

yp + 10p

7.R-341 §7.R source ↗

In the following exercises, simplify using the distributive property.

$4 (x + 3) -$ $8 (x - 7)$

Answer

−4x + 68

7.R-343 §7.R source ↗

In the following exercises, evaluate using the distributive property.

If $n = \frac{7}{8},$ evaluate
ⓐ $8 (n + \frac{1}{4})$ and
ⓑ $8 \cdot n + 8 \cdot \frac{1}{4}$ to show that $8 (n + \frac{1}{4}) =$ $8 \cdot n +$ $8 \cdot \frac{1}{4}$

Answer

ⓐ 9

ⓑ 9

7.R-345 §7.R source ↗

In the following exercises, evaluate using the distributive property.

If $y = −18,$ evaluate
ⓐ $- (y - 18)$ and
ⓑ $- y + 18$ to show that $-$ $(y - 18) =$ $-$ $y +$ $18$

Answer

ⓐ 36

ⓑ 36

7.R-347 §7.R source ↗

In the following exercises, identify whether each example is using the identity property of addition or multiplication.

$29 + 0 = 29$

Answer

identity property of addition

7.R-349 §7.R source ↗

In the following exercises, identify whether each example is using the identity property of addition or multiplication.

$9 \cdot 1 +$ $(- 3) =$ $9 +$ $(- 3)$

Answer

identity property of multiplication

7.R-351 §7.R source ↗

In the following exercises, find the additive inverse.

$19.4$

Answer

−19.4

7.R-353 §7.R source ↗

In the following exercises, find the additive inverse.

$- \frac{7}{15}$

Answer

\frac{7}{15}

7.R-355 §7.R source ↗

In the following exercises, find the multiplicative inverse.

$−5$

Answer

- \frac{1}{5}

7.R-357 §7.R source ↗

In the following exercises, find the multiplicative inverse.

$- \frac{4}{9}$

Answer

- \frac{9}{4}

7.R-359 §7.R source ↗

In the following exercises, simplify.

$\frac{0}{9}$

Answer

7.R-361 §7.R source ↗

In the following exercises, simplify.

$0 \div \frac{2}{3}$

Answer

7.R-363 §7.R source ↗

In the following exercises, simplify.

$(n + 6.75) +$ $0.25$

Answer

n + 7

7.R-365 §7.R source ↗

In the following exercises, simplify.

$\frac{1}{6} \cdot 17 \cdot 12$

Answer

7.R-367 §7.R source ↗

In the following exercises, simplify.

$9 (6 x - 11) + 15$

Answer

54x − 84

7.R-369 §7.R source ↗

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

A picture frame is $42$ inches wide. Convert the width to feet.

Answer

3.5 feet

7.R-371 §7.R source ↗

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

A playground is $45$ feet wide. Convert the width to yards.

Answer

15 yards

7.R-373 §7.R source ↗

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

Shamu weighs $4.5$ tons. Convert the weight to pounds.

Answer

9000 pounds

7.R-375 §7.R source ↗

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

How many tablespoons are in a quart?

Answer

64 tablespoons

7.R-377 §7.R source ↗

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

Trinh needs $30$ cups of paint for her class art project. Convert the volume to gallons.

Answer

1.9 gallons

7.R-379 §7.R source ↗

In the following exercises, solve, and state your answer in mixed units.

Every day last week, Pedro recorded the amount of time he spent reading. He read for $50,$ $25,$ $83,$ $45,$ $32,$ $60,$ $and 135$ minutes. How much time, in hours and minutes, did Pedro spend reading?

Answer

7 hours 10 minutes

7.R-381 §7.R source ↗

In the following exercises, solve, and state your answer in mixed units.

Dalila wants to make pillow covers. Each cover takes $30$ inches of fabric. How many yards and inches of fabric does she need for $4$ pillow covers?

Answer

3 yards, 12 inches

7.R-383 §7.R source ↗

In the following exercises, convert between metric units.

Mount Everest is $8,850$ meters tall. Convert the height to kilometers.

Answer

8.85 kilometers

7.R-385 §7.R source ↗

In the following exercises, convert between metric units.

One cup of yogurt contains $13$ grams of protein. Convert this to milligrams.

Answer

13,000 milligrams

7.R-387 §7.R source ↗

In the following exercises, convert between metric units.

A bottle of water contained $650$ milliliters. Convert this to liters.

Answer

0.65 liters

7.R-389 §7.R source ↗

In the following exercises, solve.

Selma had a $1-liter$ bottle of water. If she drank $145$ milliliters, how much water, in milliliters, was left in the bottle?

Answer

855 milliliters

7.R-391 §7.R source ↗

In the following exercises, solve.

One ounce of tofu provides $2$ grams of protein. How many milligrams of protein are provided by $5$ ounces of tofu?

Answer

10,000 milligrams

7.R-393 §7.R source ↗

In the following exercises, convert between U.S. and metric units. Round to the nearest tenth.

A college basketball court is $84$ feet long. Convert this length to meters.

Answer

25.6 meters

7.R-395 §7.R source ↗

In the following exercises, convert between U.S. and metric units. Round to the nearest tenth.

Lucas weighs $78$ kilograms. Convert his weight to pounds.

Answer

171.6 pounds

7.R-397 §7.R source ↗

In the following exercises, convert between U.S. and metric units. Round to the nearest tenth.

A box of books weighs $25$ pounds. Convert this weight to kilograms.

Answer

11.4 kilograms

7.R-399 §7.R source ↗

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

$23 °F$

Answer

−5°C

7.R-401 §7.R source ↗

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

$64 °F$

Answer

17.8°C

7.R-403 §7.R source ↗

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

$−5 °C$

Answer

23°F

7.R-405 §7.R source ↗

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

$24 °C$

Answer

75.2°F

7.T-407 §7.T source ↗

\sqrt{144}

rational or irrational?

Answer

\sqrt{144} =

12 therefore rational.

7.T-409 §7.T source ↗

Rewrite using the commutative property:

x \cdot 14 =

_________

Answer

x·14 = 14·x

7.T-411 §7.T source ↗

Rewrite the expression using the associative property:

(8 \cdot 2) \cdot 5 =

___________

Answer

(8·2)·5 = 8·(2·5)

7.T-413 §7.T source ↗

For the number

\frac{2}{5}

find the ⓐ additive inverse ⓑ multiplicative inverse.

Answer

ⓐ $- \frac{2}{5}$

ⓑ $\frac{5}{2}$

7.T-415 §7.T source ↗

In the following exercises, simplify the given expression.

$−3 + 15 y + 3$

Answer

15y

7.T-417 §7.T source ↗

In the following exercises, simplify the given expression.

$(\frac{8}{15} + \frac{2}{9}) + \frac{7}{9}$

Answer

\frac{23}{15}

7.T-419 §7.T source ↗

In the following exercises, simplify the given expression.

$14 y +$ $(−6 z) +$ $16 y +$ $2 z$

Answer

30y − 4z

7.T-421 §7.T source ↗

In the following exercises, simplify the given expression.

$6 (5 x - 4)$

Answer

30x − 24

7.T-423 §7.T source ↗

In the following exercises, simplify the given expression.

$\frac{1}{4} (8 a + 12)$

Answer

2a + 3

7.T-425 §7.T source ↗

In the following exercises, simplify the given expression.

$8 (6 p - 1) +$ $2 (9 p + 3)$

Answer

66p − 2

7.T-427 §7.T source ↗

In the following exercises, simplify the given expression.

$\frac{0}{8}$

Answer

7.T-429 §7.T source ↗

In the following exercises, simplify the given expression.

$0 \div (\frac{2}{3})$

Answer

7.T-431 §7.T source ↗

In the following exercises, solve using the appropriate unit conversions.

One cup of milk contains $276$ milligrams of calcium. Convert this to grams. $(1 milligram = 0.001 gram)$

Answer

.276 grams

7.T-433 §7.T source ↗

In the following exercises, solve using the appropriate unit conversions.

Janice ran $15$ kilometers. Convert this distance to miles. Round to the nearest hundredth of a mile. $(1 mile = 1.61 kilometers)$

Answer

9.317 miles

7.T-435 §7.T source ↗

In the following exercises, solve using the appropriate unit conversions.

Use the formula $F = \frac{9}{5} C + 32$ to convert $35 °C$ to degrees $F$

Answer

95°F

Loading chapter 8…

Problems and answers are adapted from Prealgebra 2e by Lynn Marecek, MaryAnne Anthony-Smith and Andrea Honeycutt Mathis, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/prealgebra-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.