Chapter 1: FoundationsContent check — Intermediate Algebra, Chapter 1: Foundations

Is 4,962 divisible by ⓐ 2? ⓑ 3? ⓒ 5? ⓓ 6? ⓔ 10?

Is 3,765 divisible by ⓐ 2? ⓑ 3? ⓒ 5? ⓓ 6? ⓔ 10?

Find the prime factorization of $80.$

Find the prime factorization of $60.$

Find the LCM of 9 and 12 using the Prime Factors Method.

Find the LCM of 18 and 24 using the Prime Factors Method.

Simplify: $30÷5+$ $10(3-2).$

Simplify: $70÷10+$ $4(6-2).$

Simplify: $9+$ $5^3-$ $\left[4\right(9+3\left)\right].$

Simplify: $7^2-$ $2\left[4\right(5+1\left)\right].$

Evaluate when $x=3,$ ⓐ $x^2$ ⓑ $4^x$ ⓒ $3x^2+4x+1.$

Evaluate when $x=6,$ ⓐ $x^3$ ⓑ $2^x$ ⓒ $6x^2-4x-7.$

Simplify: $3x^2+$ $7x+$ $9+$ $7x^2+$ $9x+$ $8.$

Simplify: $4y^2+$ $5y+$ $2+$ $8y^2+$ $4y+$ $5.$

Translate the English phrase into an algebraic expression:

ⓐ the difference of $14x^2$ and 13 ⓑ the quotient of $12x$ and 2 ⓒ 13 more than $z$
ⓓ 18 less than $8x$

Translate the English phrase into an algebraic expression:

ⓐ the sum of $17y^2$ and 19 ⓑ the product of $7$ and y ⓒ Eleven more than x ⓓ Fourteen less than 11a

Translate the English phrase into an algebraic expression:

ⓐ four times the sum of p and q
ⓑ the sum of four times p and q

Translate the English phrase into an algebraic expression:

ⓐ the difference of two times x and 8
ⓑ two times the difference of x and 8

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.

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.

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.

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.

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.

84

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.

896

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.

22,335

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

86

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

455

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

432

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

8, 12

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

28, 40

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

55, 88

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

$2^3-12÷(9-5)$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

$2+8(6+1)$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

$20÷4+6\left(5-1\right)$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

$3(1+9·6)-4^2$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

$2\left[1+3\left(10-2\right)\right]$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

$8+$ $2[7-2(5-3\left)\right]-$ $3^2$

Evaluate an Expression

In the following exercises, evaluate the following expressions.

When $x=2,$
ⓐ $x^6$
ⓑ $4^x$
ⓒ $2x^2+3x-7$

Evaluate an Expression

In the following exercises, evaluate the following expressions.

When $x=4,y=1$
$x^2+3xy-7y^2$

Evaluate an Expression

In the following exercises, evaluate the following expressions.

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

Simplify Expressions by Combining Like Terms

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

$7x+2+3x+4$

Simplify Expressions by Combining Like Terms

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

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

Simplify Expressions by Combining Like Terms

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

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

Translate an English Phrase to an Algebraic Expression

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

ⓐ the difference of $5x^2$ and $6xy$
ⓑ the quotient of $6y^2$ and $5x$
ⓒ Twenty-one more than $y^2$
ⓓ $6x$ less than $81x^2$

Translate an English Phrase to an Algebraic Expression

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

ⓐ the sum of $4a{b}^2$ and $3a^{2}b$
ⓑ the product of $4y^2$ and $5x$
ⓒ Fifteen more than $m$
ⓓ $9x$ less than $121x^2$

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
ⓑ the difference of eight times $y$ and 9

Translate an English Phrase to an Algebraic Expression

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

ⓐ five times the sum of $3x$ and $y$
ⓑ the sum of five times $3x$ and $y$

Translate an English Phrase to an Algebraic Expression

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

Eric has rock and country songs on his playlist. The number of rock songs is 14 more than twice the number of country songs. Let c represent the number of country songs. Write an expression for the number of rock songs.

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 three times the number of nickels. Let n represent the number of nickels. Write an expression for the number of pennies.

Translate an English Phrase to an Algebraic Expression

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

Explain in your own words how to find the prime factorization of a composite number.

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 $8a^2+$ $4a+$ $9-$ $a^2-$ $1.$

Fill in $<,>,$ or $=$ for each of the following pairs of numbers:

ⓐ $\mathrm{-9}\_\_-\left|\mathrm{-9}\right|$ ⓑ $2\_\_-\left|\mathrm{-2}\right|$ ⓒ $\mathrm{-8}\_\_\left|\mathrm{-8}\right|$ ⓓ $\text{−}\left(\mathrm{-9}\right)\_\_\left|\mathrm{-9}\right|.$

Fill in $<,>,$ or $=$ for each of the following pairs of numbers:

ⓐ $7\_\_-\left|\mathrm{-7}\right|$ ⓑ $\text{−}\left(\mathrm{-10}\right)\_\_\left|\mathrm{-10}\right|$ ⓒ $\left|\mathrm{-4}\right|\_\_-\left|\mathrm{-4}\right|$ ⓓ $\mathrm{-1}\_\_\left|\mathrm{-1}\right|.$

Simplify:$19-$ $|11-$ $4(3-1)|.$

Simplify: $9-$ $|8-$ $4(7-5)|.$

Add: ⓐ $\mathrm{-2}+\left(\mathrm{-4}\right)$ ⓑ $\mathrm{-2}+4$ ⓒ $2+\left(\mathrm{-4}\right).$

Add: ⓐ $\mathrm{-2}+\left(\mathrm{-5}\right)$ ⓑ $\mathrm{-2}+5$ ⓒ $2+\left(\mathrm{-5}\right).$

Subtract: ⓐ $6-4$ ⓑ $\mathrm{-6}-(\mathrm{-4})$ ⓒ $\mathrm{-6}-4$ ⓓ $6-\left(\mathrm{-4}\right).$

Subtract: ⓐ $7-4$ ⓑ $\mathrm{-7}-(\mathrm{-4})$ ⓒ $\mathrm{-7}-4$ ⓓ $7-\left(\mathrm{-4}\right).$

Simplify: ⓐ $21-13$ and $21+\left(\mathrm{-13}\right)$ ⓑ $\mathrm{-11}-7$ and $\mathrm{-11}+(\mathrm{-7})$ ⓒ $6-\left(\mathrm{-13}\right)$ and $6+13$ ⓓ $\mathrm{-5}-\left(\mathrm{-1}\right)$ and $\mathrm{-5}+1.$

Simplify: ⓐ $15-7$ and $15+\left(\mathrm{-7}\right)$ ⓑ $\mathrm{-14}-8$ and $\mathrm{-14}+(\mathrm{-8})$ ⓒ $4-\left(\mathrm{-19}\right)$ and $4+19$ ⓓ $\mathrm{-4}-\left(\mathrm{-7}\right)$ and $\mathrm{-4}+7.$

Simplify: $8-\left(\mathrm{-3}-1\right)-9.$

Simplify: $12-$ $(\mathrm{-9}-6)-$ $14.$

Multiply or divide: ⓐ $\mathrm{-115}÷\left(\mathrm{-5}\right)$ ⓑ $5·12$ ⓒ $9\left(\mathrm{-7}\right)$ ⓓ $\mathrm{-63}÷7.$

Multiply or divide: ⓐ $\mathrm{-117}÷\left(\mathrm{-3}\right)$ ⓑ $3·13$ ⓒ $7\left(\mathrm{-4}\right)$ ⓓ $\mathrm{-42}÷6.$

Simplify: ⓐ ${\left(\mathrm{-3}\right)}^4$ ⓑ $\text{−}{3}^4.$

Simplify: ⓐ ${\left(\mathrm{-7}\right)}^2$ ⓑ $\text{−}{7}^2.$

Simplify: ⓐ $12\left(\mathrm{-9}\right)÷{\left(\mathrm{-3}\right)}^3$ ⓑ $\mathrm{-27}÷3+$ $\left(\mathrm{-5}\right)\left(\mathrm{-6}\right).$

Simplify: ⓐ $18\left(\mathrm{-4}\right)÷{\left(\mathrm{-2}\right)}^3$ ⓑ $\mathrm{-32}÷4+$ $\left(\mathrm{-2}\right)\left(\mathrm{-7}\right).$

Evaluate: $3x^2-2xy+6y^2$ when $x=1,y=\mathrm{-2}.$

Evaluate: $4x^2-xy+5y^2$ when $x=\mathrm{-2},y=3.$

Translate and simplify the sum of 9 and $\mathrm{-16},$ increased by 4.

Translate and simplify the sum of $\mathrm{-8}$ and $\mathrm{-12},$ increased by 7.

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?

The temperature in Denver was $\mathrm{-6}$ degrees at lunchtime. By sunset the temperature had dropped to $\mathrm{-15}$ degrees. What was the difference in the lunchtime and sunset temperatures?

Simplify Expressions with Absolute Value

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

ⓐ $\left|\mathrm{-7}\right|\_\_\_-$ $\left|\mathrm{-7}\right|$
ⓑ $6\_\_\_-\left|\mathrm{-6}\right|$
ⓒ $\left|\mathrm{-11}\right|\_\_\_-11$
ⓓ $\text{−}\left(\mathrm{-13}\right)\_\_\_-$ $\left|\mathrm{-13}\right|$

Simplify Expressions with Absolute Value

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

ⓐ $\text{−}\left|2\right|\_\_\_-$ $\left|\mathrm{-2}\right|$
ⓑ $\mathrm{-12}\_\_\_-$ $\left|\mathrm{-12}\right|$
ⓒ $\left|\mathrm{-3}\right|\_\_\_-3$
ⓓ $\left|\mathrm{-19}\right|\_\_\_-$ $\left(\mathrm{-19}\right)$

In the following exercises, simplify.

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

In the following exercises, simplify.

$18-\left|2\left(8-3\right)\right|$

In the following exercises, simplify.

$18-$ $|12-$ $4(4-1)+$ $3|$

In the following exercises, simplify.

$10-$ $3|9-$ $3(3-1)|$

Add and Subtract Integers

In the following exercises, simplify each expression.

ⓐ $\mathrm{-7}+\left(\mathrm{-4}\right)$
ⓑ $\mathrm{-7}+4$
ⓒ $7+\left(\mathrm{-4}\right).$

Add and Subtract Integers

In the following exercises, simplify each expression.

$48+\left(\mathrm{-16}\right)$

Add and Subtract Integers

In the following exercises, simplify each expression.

$\mathrm{-14}+\left(\mathrm{-12}\right)+4$

Add and Subtract Integers

In the following exercises, simplify each expression.

$19+2\left(\mathrm{-3}+8\right)$

Add and Subtract Integers

In the following exercises, simplify each expression.

ⓐ $13-7$
ⓑ $\mathrm{-13}-(\mathrm{-7})$
ⓒ $\mathrm{-13}-7$
ⓓ $13-\left(\mathrm{-7}\right)$

Add and Subtract Integers

In the following exercises, simplify each expression.

$\mathrm{-17}-42$

Add and Subtract Integers

In the following exercises, simplify each expression.

$\mathrm{-14}-\left(\mathrm{-27}\right)+9$

Add and Subtract Integers

In the following exercises, simplify each expression.

ⓐ $44-28$ ⓑ $44+\left(\mathrm{-28}\right)$

Add and Subtract Integers

In the following exercises, simplify each expression.

ⓐ $27-\left(\mathrm{-18}\right)$ ⓑ $27+18$

Add and Subtract Integers

In the following exercises, simplify each expression.

$\left(2-7\right)-\left(3-8\right)$

Add and Subtract Integers

In the following exercises, simplify each expression.

$\text{−}(6-8)-$ $(2-4)$

Add and Subtract Integers

In the following exercises, simplify each expression.

$25-$ $[10-(3-12\left)\right]$

Multiply and Divide Integers

In the following exercises, multiply or divide.

ⓐ $\mathrm{-4}·8$
ⓑ $13\left(\mathrm{-5}\right)$
ⓒ $\mathrm{-24}÷6$
ⓓ $\mathrm{-52}÷\left(\mathrm{-4}\right)$

Multiply and Divide Integers

In the following exercises, multiply or divide.

ⓐ $\mathrm{-28}÷7$
ⓑ $\mathrm{-180}÷15$
ⓒ $3\left(\mathrm{-13}\right)$
ⓓ $\mathrm{-1}\left(\mathrm{-14}\right)$

Simplify and Evaluate Expressions with Integers

In the following exercises, simplify each expression.

ⓐ ${\left(\mathrm{-2}\right)}^6$ ⓑ $\text{−}{2}^6$

Simplify and Evaluate Expressions with Integers

In the following exercises, simplify each expression.

$5\left(\mathrm{-6}\right)+$ $7\left(\mathrm{-2}\right)-$ $3$

Simplify and Evaluate Expressions with Integers

In the following exercises, simplify each expression.

$\mathrm{-3}\left(\mathrm{-5}\right)\left(6\right)$

Simplify and Evaluate Expressions with Integers

In the following exercises, simplify each expression.

$\left(8-11\right)\left(9-12\right)$

Simplify and Evaluate Expressions with Integers

In the following exercises, simplify each expression.

$26-3\left(2-7\right)$

Simplify and Evaluate Expressions with Integers

In the following exercises, simplify each expression.

$65÷\left(\mathrm{-5}\right)+$ $\left(\mathrm{-28}\right)÷\left(\mathrm{-7}\right)$

Simplify and Evaluate Expressions with Integers

In the following exercises, simplify each expression.

$9-$ $2[3-8(\mathrm{-2}\left)\right]$

Simplify and Evaluate Expressions with Integers

In the following exercises, simplify each expression.

$8-$ $|2-$ $4(4-1)+$ $3|$

Simplify and Evaluate Expressions with Integers

In the following exercises, simplify each expression.

$9-$ $3\left|2\right(2-6)-$ $(3-7)|$

Simplify and Evaluate Expressions with Integers

In the following exercises, simplify each expression.

${\left(\mathrm{-3}\right)}^2-$ $24÷(8-2)$

In the following exercises, evaluate each expression.

$y+\left(\mathrm{-14}\right)$ when
ⓐ $y=\mathrm{-33}$ ⓑ $y=30$

In the following exercises, evaluate each expression.

${\left(x+y\right)}^2$ when
$x=\mathrm{-3},y=14$

In the following exercises, evaluate each expression.

$9a-2b-8$ when
$a=\mathrm{-6}$ and $b=\mathrm{-3}$

In the following exercises, evaluate each expression.

$3x^2-4xy+2y^2$ when
$x=\mathrm{-2},y=\mathrm{-3}$

Translate English Phrases to Algebraic Expressions

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

the sum of 3 and $\mathrm{-15},$ increased by 7

Translate English Phrases to Algebraic Expressions

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

ⓐ the difference of $10$ and $\mathrm{-18}$
ⓑ subtract $11$ from $\mathrm{-25}$

Translate English Phrases to Algebraic Expressions

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

the quotient of $\mathrm{-6}$ and the sum of $a$ and $b$

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 $\text{−}12\text{°}.$ What was the difference between the temperature in Anaheim and the temperature in Embarrass?

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?

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?

Use Integers in Applications

In the following exercises, solve.

Explain why the sum of $\mathrm{-8}$ and 2 is negative, but the sum of 8 and $\mathrm{-2}$ is positive.

Use Integers in Applications

In the following exercises, solve.

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

Simplify: $-\frac{69}{120}.$

Simplify: $-\frac{120}{192}.$

Multiply: $\frac{11}{3}\left(\mathrm{-9}a\right).$

Multiply: $\frac{13}{7}\left(\mathrm{-14}b\right).$

Divide: $-$ $\frac{7}{27}÷(-\frac{35}{36}).$

Divide: $-$ $\frac{5}{14}÷(-\frac{15}{28}).$

Simplify: $\frac{\frac{a}{8}}{\frac{ab}{6}}.$

Simplify: $\frac{\frac{p}{2}}{\frac{pq}{8}}.$

Add: $\frac{7}{12}+\frac{11}{15}.$

Add: $\frac{13}{15}+\frac{17}{20}.$

Simplify: ⓐ $\frac{3a}{4}-\frac{8}{9}$ ⓑ $\frac{3a}{4}·\frac{8}{9}.$

Simplify: ⓐ $\frac{4k}{5}-\frac{1}{6}$ ⓑ $\frac{4k}{5}·\frac{1}{6}.$

Simplify: $\frac{8\left(-2\right)+4\left(-3\right)}{-5\left(2\right)+3}.$

Simplify: $\frac{7\left(-1\right)+9\left(-3\right)}{-5\left(3\right)-2}.$

Simplify: $\frac{{\left(\frac{1}{3}\right)}^2}{2^3+2}.$

Simplify: $\frac{1+4^2}{{\left(\frac{1}{4}\right)}^2}.$

Simplify: $\frac{\frac{1}{3}+\frac{1}{2}}{\frac{3}{4}-\frac{1}{3}}.$

Simplify: $\frac{\frac{2}{3}-\frac{1}{2}}{\frac{1}{4}+\frac{1}{3}}.$

Evaluate $3a{b}^2$ when $a=-\frac{2}{3}$ and $b=-\frac{1}{2}.$

Evaluate $4c^{3}d$ when $c=-\frac{1}{2}$ and $d=-\frac{4}{3}.$

Simplify Fractions

In the following exercises, simplify.

$-\frac{108}{63}$

Simplify Fractions

In the following exercises, simplify.

$\frac{120}{252}$

Simplify Fractions

In the following exercises, simplify.

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

Simplify Fractions

In the following exercises, simplify.

$-\frac{210a^2}{110b^2}$

Multiply and Divide Fractions

In the following exercises, perform the indicated operation.

$-\frac{3}{4}\left(-\frac{4}{9}\right)$

Multiply and Divide Fractions

In the following exercises, perform the indicated operation.

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

Multiply and Divide Fractions

In the following exercises, perform the indicated operation.

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

Multiply and Divide Fractions

In the following exercises, perform the indicated operation.

$\frac{3}{7}·21n$

Multiply and Divide Fractions

In the following exercises, perform the indicated operation.

$\frac{3}{4}÷\frac{x}{11}$

Multiply and Divide Fractions

In the following exercises, perform the indicated operation.

$\frac{5}{18}÷\left(-\frac{15}{24}\right)$

Multiply and Divide Fractions

In the following exercises, perform the indicated operation.

$\frac{8u}{15}÷\frac{12v}{25}$

Multiply and Divide Fractions

In the following exercises, perform the indicated operation.

$\frac{3}{4}÷\left(\mathrm{-12}\right)$

In the following exercises, simplify.

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

In the following exercises, simplify.

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

In the following exercises, simplify.

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

Add and Subtract Fractions

In the following exercises, add or subtract.

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

Add and Subtract Fractions

In the following exercises, add or subtract.

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

Add and Subtract Fractions

In the following exercises, add or subtract.

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

Add and Subtract Fractions

In the following exercises, add or subtract.

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

Add and Subtract Fractions

In the following exercises, add or subtract.

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

Add and Subtract Fractions

In the following exercises, add or subtract.

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

Add and Subtract Fractions

In the following exercises, add or subtract.

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

Add and Subtract Fractions

In the following exercises, add or subtract.

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

Add and Subtract Fractions

In the following exercises, add or subtract.

ⓐ $-\frac{4x}{9}-\frac{5}{6}$
ⓑ $-\frac{4k}{9}·\frac{5}{6}$

Add and Subtract Fractions

In the following exercises, add or subtract.

ⓐ $-\frac{5a}{3}+\left(-\frac{10}{6}\right)$
ⓑ $-\frac{5a}{3}÷\left(-\frac{10}{6}\right)$

Use the Order of Operations to Simplify Fractions

In the following exercises, simplify.

$\frac{5·6-3·4}{4·5-2·3}$

Use the Order of Operations to Simplify Fractions

In the following exercises, simplify.

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

Use the Order of Operations to Simplify Fractions

In the following exercises, simplify.

$\frac{7·4-2\left(8-5\right)}{9·3-3·5}$

Use the Order of Operations to Simplify Fractions

In the following exercises, simplify.

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

Use the Order of Operations to Simplify Fractions

In the following exercises, simplify.

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

Use the Order of Operations to Simplify Fractions

In the following exercises, simplify.

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

Use the Order of Operations to Simplify Fractions

In the following exercises, simplify.

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

Use the Order of Operations to Simplify Fractions

In the following exercises, simplify.

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

Mixed Practice

In the following exercises, simplify.

$-\frac{3}{8}÷\left(-\frac{3}{10}\right)$

Mixed Practice

In the following exercises, simplify.

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

Mixed Practice

In the following exercises, simplify.

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

Mixed Practice

In the following exercises, simplify.

$\frac{11}{12a}·\frac{9a}{16}$

Mixed Practice

In the following exercises, simplify.

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

Mixed Practice

In the following exercises, simplify.

$1-\frac{3}{5}÷\frac{1}{10}$

Mixed Practice

In the following exercises, simplify.

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

Mixed Practice

In the following exercises, simplify.

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

Mixed Practice

In the following exercises, simplify.

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

Mixed Practice

In the following exercises, simplify.

$\left(\frac{5}{9}+\frac{1}{6}\right)÷\left(\frac{2}{3}-\frac{1}{2}\right)$

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

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

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

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

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

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

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

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

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

Explain how you find the reciprocal of a fraction.

Round $6.582$ to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

Round $15.2175$ to the nearest ⓐ thousandth ⓑ hundredth ⓒ tenth.

Add or subtract: ⓐ $\mathrm{-4.8}-11.69$ ⓑ $9.58-10.$

Add or subtract: ⓐ $\mathrm{-5.123}-$ $18.47$ ⓑ $37.42-50.$