# Chapter 1 Review Exercises

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- Contributed by Lynn Marecek
- Professor (Mathematics) at Santa Ana College
- Publisher: OpenStax CNX

## Chapter Review Exercises

__Introduction to Whole Numbers__

**Use Place Value with Whole Number**

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

Exercise \(\PageIndex{1}\)

26,915

- 1
- 2
- 9
- 5
- 6

**Answer**-
- tens
- ten thousands
- hundreds
- ones
- thousands

Exercise \(\PageIndex{2}\)

359,417

- 9
- 3
- 4
- 7
- 1

Exercise \(\PageIndex{3}\)

58,129,304

- 5
- 0
- 1
- 8
- 2

**Answer**-
- ten millions
- tens
- hundred thousands
- millions
- ten thousands

Exercise \(\PageIndex{4}\)

9,430,286,157

- 6
- 4
- 9
- 0
- 5

In the following exercises, name each number.

Exercise \(\PageIndex{5}\)

6,104

**Answer**-
six thousand, one hundred four

Exercise \(\PageIndex{6}\)

493,068

Exercise \(\PageIndex{7}\)

3,975,284

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

Exercise \(\PageIndex{8}\)

85,620,435

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

Exercise \(\PageIndex{9}\)

three hundred fifteen

**Answer**-
315

Exercise \(\PageIndex{10}\)

sixty-five thousand, nine hundred twelve

Exercise \(\PageIndex{11}\)

ninety million, four hundred twenty-five thousand, sixteen

**Answer**-
90,425,016

Exercise \(\PageIndex{12}\)

one billion, forty-three million, nine hundred twenty-two thousand, three hundred eleven

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

Exercise \(\PageIndex{13}\)

Round to the nearest ten.

- 407
- 8,564

**Answer**-
- 410
- 8,560

Exercise \(\PageIndex{14}\)

Round to the nearest hundred.

- 25,846
- 25,864

In the following exercises, round each number to the nearest 1. hundred 2. thousand 3. ten thousand.

Exercise \(\PageIndex{15}\)

864,951

**Answer**-
- 865,000865,000
- 865,000865,000
- 860,000

Exercise \(\PageIndex{16}\)

3,972,849

**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.

Exercise \(\PageIndex{17}\)

168

**Answer**-
by 2,3,6

Exercise \(\PageIndex{18}\)

264

Exercise \(\PageIndex{19}\)

375

**Answer**-
by 3,5

Exercise \(\PageIndex{20}\)

750

Exercise \(\PageIndex{21}\)

1430

**Answer**-
by 2,5,10

Exercise \(\PageIndex{22}\)

1080

**Find Prime Factorizations and Least Common Multiples**

In the following exercises, find the prime factorization.

Exercise \(\PageIndex{23}\)

420

**Answer**-
2\(\cdot 2 \cdot 3 \cdot 5 \cdot 7\)

Exercise \(\PageIndex{24}\)

115

Exercise \(\PageIndex{25}\)

225

**Answer**-
3\(\cdot 3 \cdot 5 \cdot 5\)

Exercise \(\PageIndex{26}\)

2475

Exercise \(\PageIndex{27}\)

1560

**Answer**-
\(2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 13\)

Exercise \(\PageIndex{28}\)

56

Exercise \(\PageIndex{29}\)

72

**Answer**-
\(2 \cdot 2 \cdot 2 \cdot 3 \cdot 3\)

Exercise \(\PageIndex{30}\)

168

Exercise \(\PageIndex{31}\)

252

**Answer**-
\(2 \cdot 2 \cdot 3 \cdot 3 \cdot 7\)

Exercise \(\PageIndex{32}\)

391

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

Exercise \(\PageIndex{33}\)

6,15

**Answer**-
30

Exercise \(\PageIndex{34}\)

60, 75

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

Exercise \(\PageIndex{35}\)

24, 30

**Answer**-
120

Exercise \(\PageIndex{36}\)

70, 84

__Use the Language of Algebra__

**Use Variables and Algebraic Symbols**

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

Exercise \(\PageIndex{37}\)

25−7

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

Exercise \(\PageIndex{38}\)

5\(\cdot 6\)

Exercise \(\PageIndex{39}\)

\(45 \div 5\)

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

Exercise \(\PageIndex{40}\)

x+8

Exercise \(\PageIndex{41}\)

\(42 \geq 27\)

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

Exercise \(\PageIndex{42}\)

3n=24

Exercise \(\PageIndex{43}\)

\(3 \leq 20 \div 4\)

**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

Exercise \(\PageIndex{44}\)

\(a \neq 7 \cdot 4\)

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

Exercise \(\PageIndex{45}\)

\(6 \cdot 3+5\)

**Answer**-
expression

Exercise \(\PageIndex{46}\)

y−8=32

**Simplify Expressions Using the Order of Operations**

In the following exercises, simplify each expression.

Exercise \(\PageIndex{47}\)

\(3^{5}\)

**Answer**-
243

Exercise \(\PageIndex{48}\)

\(10^{8}\)

In the following exercises, simplify

Exercise \(\PageIndex{49}\)

6+10/2+2

**Answer**-
13

Exercise \(\PageIndex{50}\)

9+12/3+4

Exercise \(\PageIndex{51}\)

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

**Answer**-
10

Exercise \(\PageIndex{52}\)

\(33 \div(3+8) \cdot 2\)

Exercise \(\PageIndex{53}\)

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

**Answer**-
41

Exercise \(\PageIndex{54}\)

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

**Evaluate an Expression**

In the following exercises, evaluate the following expressions.

Exercise \(\PageIndex{55}\)

9x+7 when x=3

**Answer**-
34

Exercise \(\PageIndex{56}\)

5x−4 when x=6

Exercise \(\PageIndex{57}\)

\(x^{4}\) when \(x=3\)

**Answer**-
81

Exercise \(\PageIndex{58}\)

\(3^{x}\) when \(x=3\)

Exercise \(\PageIndex{59}\)

\(x^{2}+5 x-8\) when \(x=6\)

**Answer**-
58

Exercise \(\PageIndex{60}\)

\(2 x+4 y-5\) when

\(x=7, y=8\)

**Simplify Expressions by Combining Like Terms**

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

Exercise \(\PageIndex{61}\)

12n

**Answer**-
12

Exercise \(\PageIndex{62}\)

9\(x^{2}\)

In the following exercises, identify the like terms.

Exercise \(\PageIndex{63}\)

\(3 n, n^{2}, 12,12 p^{2}, 3,3 n^{2}\)

**Answer**-
12 and \(3, n^{2}\) and 3\(n^{2}\)

Exercise \(\PageIndex{64}\)

\(5,18 r^{2}, 9 s, 9 r, 5 r^{2}, 5 s\)

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

Exercise \(\PageIndex{65}\)

\(11 x^{2}+3 x+6\)

**Answer**-
\(11 x^{2}, 3 x, 6\)

Exercise \(\PageIndex{66}\)

\(22 y^{3}+y+15\)

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

Exercise \(\PageIndex{67}\)

17a+9a

**Answer**-
26a

Exercise \(\PageIndex{68}\)

18z+9z

Exercise \(\PageIndex{69}\)

9x+3x+8

**Answer**-
12x+8

Exercise \(\PageIndex{70}\)

8a+5a+9

Exercise \(\PageIndex{71}\)

7p+6+5p−4

**Answer**-
12p+2

Exercise \(\PageIndex{72}\)

8x+7+4x−5

**Translate an English Phrase to an Algebraic Expression**

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

Exercise \(\PageIndex{73}\)

the sum of 8 and 12

**Answer**-
8+12

Exercise \(\PageIndex{74}\)

the sum of 9 and 1

Exercise \(\PageIndex{75}\)

the difference of x and 4

**Answer**-
x−4

Exercise \(\PageIndex{76}\)

the difference of x and 3

Exercise \(\PageIndex{77}\)

the product of 6 and y

**Answer**-
6y

Exercise \(\PageIndex{78}\)

the product of 9 and y

Exercise \(\PageIndex{79}\)

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

**Answer**-
b+15

Exercise \(\PageIndex{80}\)

Marcella has 6 fewer boy cousins than girl cousins. Let g represent the number of girl cousins. Write an expression for the number of boy cousins.

__Add and Subtract Integers__

**Use Negatives and Opposites of Integers**

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

Exercise \(\PageIndex{81}\)

- 6___2
- −7___4
- −9___−1
- 9___−3

**Answer**-
- >
- <
- <
- >

Exercise \(\PageIndex{82}\)

- −5___1
- −4___−9
- 6___10
- 3___−8

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

Exercise \(\PageIndex{83}\)

- −8
- 1

**Answer**-
- 8
- −1

Exercise \(\PageIndex{84}\)

- −2
- 6

In the following exercises, simplify.

Exercise \(\PageIndex{85}\)

−(−19)

**Answer**-
19

Exercise \(\PageIndex{86}\)

−(−53)

In the following exercises, simplify.

Exercise \(\PageIndex{87}\)

−m when

- m=3
- m=−3

**Answer**-
- −3
- 3

Exercise \(\PageIndex{88}\)

−p when

- p=6
- p=−6

**Simplify Expressions with Absolute Value**

In the following exercises,, simplify.

Exercise \(\PageIndex{89}\)

- |7|
- |−25|
- |0|

**Answer**-
- 7
- 25
- 0

Exercise \(\PageIndex{90}\)

- |5|
- |0|
- |−19|

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

Exercise \(\PageIndex{91}\)

- −8___|−8|
- −|−2|___−2

**Answer**-
- <
- =

Exercise \(\PageIndex{92}\)

- |−3|___−|−3|
- 4___−|−4|

In the following exercises, simplify.

Exercise \(\PageIndex{93}\)

|8−4|

**Answer**-
4

Exercise \(\PageIndex{94}\)

|9−6|

Exercise \(\PageIndex{95}\)

8(14−2|−2|)

**Answer**-
80

Exercise \(\PageIndex{96}\)

6(13−4|−2|)

In the following exercises, evaluate.

Exercise \(\PageIndex{97}\)

1. |x| when x=−28

**Answer**-
- 28
- 15

Exercise \(\PageIndex{98}\)

- ∣y∣ when y=−37
- |−z| when z=−24

**Add Integers**

In the following exercises, simplify each expression.

Exercise \(\PageIndex{99}\)

−200+65

**Answer**-
−135

Exercise \(\PageIndex{100}\)

−150+45

Exercise \(\PageIndex{101}\)

2+(−8)+6

**Answer**-
0

Exercise \(\PageIndex{102}\)

4+(−9)+7

Exercise \(\PageIndex{103}\)

140+(−75)+67

**Answer**-
132

Exercise \(\PageIndex{104}\)

−32+24+(−6)+10

**Subtract Integers**

In the following exercises, simplify.

Exercise \(\PageIndex{105}\)

9−3

**Answer**-
6

Exercise \(\PageIndex{106}\)

−5−(−1)

Exercise \(\PageIndex{107}\)

- 15−6
- 15+(−6)

**Answer**-
- 9
- 9

Exercise \(\PageIndex{108}\)

- 12−9
- 12+(−9)

Exercise \(\PageIndex{109}\)

- 8−(−9)
- 8+9

**Answer**-
- 17
- 17

Exercise \(\PageIndex{110}\)

- 4−(−4)
- 4+4

In the following exercises, simplify each expression.

Exercise \(\PageIndex{111}\)

10−(−19)

**Answer**-
29

Exercise \(\PageIndex{112}\)

11−(−18)

Exercise \(\PageIndex{113}\)

31−79

**Answer**-
−48

Exercise \(\PageIndex{114}\)

39−81

Exercise \(\PageIndex{115}\)

−31−11

**Answer**-
−42

Exercise \(\PageIndex{116}\)

−32−18

Exercise \(\PageIndex{117}\)

−15−(−28)+5

**Answer**-
18

Exercise \(\PageIndex{118}\)

71+(−10)−8

Exercise \(\PageIndex{119}\)

−16−(−4+1)−7

**Answer**-
-20

Exercise \(\PageIndex{120}\)

−15−(−6+4)−3

**Multiply Integers**

In the following exercises, multiply.

Exercise \(\PageIndex{121}\)

−5(7)

**Answer**-
−35

Exercise \(\PageIndex{122}\)

−8(6)

Exercise \(\PageIndex{123}\)

−18(−2)

**Answer**-
36

Exercise \(\PageIndex{124}\)

−10(−6)

**Divide Integers**

In the following exercises, divide.

Exercise \(\PageIndex{125}\)

\(-28 \div 7\)

**Answer**-
-4

Exercise \(\PageIndex{126}\)

\(56 \div(-7)\)

Exercise \(\PageIndex{127}\)

\(-120 \div(-20)\)

**Answer**-
6

Exercise \(\PageIndex{128}\)

\(-200 \div 25\)

**Simplify Expressions with Integers**

In the following exercises, simplify each expression.

Exercise \(\PageIndex{129}\)

−8(−2)−3(−9)

**Answer**-
43

Exercise \(\PageIndex{130}\)

−7(−4)−5(−3)

Exercise \(\PageIndex{131}\)

\((-5)^{3}\)

**Answer**-
−125

Exercise \(\PageIndex{132}\)

\((-4)^{3}\)

Exercise \(\PageIndex{133}\)

\(-4 \cdot 2 \cdot 11\)

**Answer**-
−88

Exercise \(\PageIndex{134}\)

\(-5 \cdot 3 \cdot 10\)

Exercise \(\PageIndex{135}\)

\(-10(-4) \div(-8)\)

**Answer**-
-5

Exercise \(\PageIndex{136}\)

\(-8(-6) \div(-4)\)

Exercise \(\PageIndex{137}\)

31−4(3−9)

**Answer**-
55

Exercise \(\PageIndex{138}\)

24−3(2−10)

**Evaluate Variable Expressions with Integers**

In the following exercises, evaluate each expression.

Exercise \(\PageIndex{139}\)

x+8 when

- x=−26
- x=−95

**Answer**-
- −18
- −87

Exercise \(\PageIndex{140}\)

y+9 when

- y=−29
- y=−84

Exercise \(\PageIndex{141}\)

When b=−11, evaluate:

- b+6
- −b+6

**Answer**-
- −5
- 17

Exercise \(\PageIndex{142}\)

When c=−9, evaluate:

- c+(−4)c+(−4)
- −c+(−4)

Exercise \(\PageIndex{143}\)

\(p^{2}-5 p+2\) when

\(p=-1\)

**Answer**-
8

Exercise \(\PageIndex{144}\)

\(q^{2}-2 q+9\) when \(q=-2\)

Exercise \(\PageIndex{145}\)

\(6 x-5 y+15\) when \(x=3\) and \(y=-1\)

**Answer**-
38

Exercise \(\PageIndex{146}\)

\(3 p-2 q+9\) when \(p=8\) and \(q=-2\)

**Translate English Phrases to Algebraic Expressions**

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

Exercise \(\PageIndex{147}\)

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

**Answer**-
(−4+(−17))+32;11

Exercise \(\PageIndex{148}\)

- the difference of 15 and −7
- subtract 15 from −7

Exercise \(\PageIndex{149}\)

the quotient of −45 and −9

**Answer**-
\(\frac{-45}{-9} ; 5\)

Exercise \(\PageIndex{150}\)

the product of −12 and the difference of c and d

**Use Integers in Applications**

In the following exercises, solve.

Exercise \(\PageIndex{151}\)

**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

Exercise \(\PageIndex{152}\)

**Checking** **Account** Adrianne has a balance of −$22 in her checking account. She deposits $301 to the account. What is the new balance?

__Visualize Fractions__

**Find Equivalent Fractions**

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

Exercise \(\PageIndex{153}\)

\(\frac{1}{4}\)

**Answer**-
\(\frac{2}{8}, \frac{3}{12}, \frac{4}{16}\) answers may vary

Exercise \(\PageIndex{154}\)

\(\frac{1}{3}\)

Exercise \(\PageIndex{155}\)

\(\frac{5}{6}\)

**Answer**-
\(\frac{10}{12}, \frac{15}{18}, \frac{20}{24}\) answers may vary

Exercise \(\PageIndex{156}\)

\(\frac{2}{7}\)

**Simplify Fractions**

In the following exercises, simplify.

Exercise \(\PageIndex{157}\)

\(\frac{7}{21}\)

**Answer**-
\(\frac{1}{3}\)

Exercise \(\PageIndex{158}\)

\(\frac{8}{24}\)

Exercise \(\PageIndex{159}\)

\(\frac{15}{20}\)

**Answer**-
\(\frac{3}{4}\)

Exercise \(\PageIndex{160}\)

\(\frac{12}{18}\)

Exercise \(\PageIndex{161}\)

\(-\frac{168}{192}\)

**Answer**-
\(-\frac{7}{8}\)

Exercise \(\PageIndex{162}\)

\(-\frac{140}{224}\)

Exercise \(\PageIndex{163}\)

\(\frac{11 x}{11 y}\)

**Answer**-
\(\frac{x}{y}\)

Exercise \(\PageIndex{164}\)

\(\frac{15 a}{15 b}\)

**Multiply Fractions**

In the following exercises, multiply.

Exercise \(\PageIndex{165}\)

\(\frac{2}{5} \cdot \frac{1}{3}\)

**Answer**-
\(\frac{2}{15}\)

Exercise \(\PageIndex{166}\)

\(\frac{1}{2} \cdot \frac{3}{8}\)

Exercise \(\PageIndex{167}\)

\(\frac{7}{12}\left(-\frac{8}{21}\right)\)

**Answer**-
\(-\frac{2}{9}\)

Exercise \(\PageIndex{168}\)

\(\frac{5}{12}\left(-\frac{8}{15}\right)\)

Exercise \(\PageIndex{169}\)

\(-28 p\left(-\frac{1}{4}\right)\)

**Answer**-
7p

Exercise \(\PageIndex{170}\)

\(-51 q\left(-\frac{1}{3}\right)\)

Exercise \(\PageIndex{172}\)

\(\frac{14}{5}(-15)\)

**Answer**-
−42

Exercise \(\PageIndex{173}\)

\(-1\left(-\frac{3}{8}\right)\)

**Divide Fractions**

In the following exercises, divide

Exercise \(\PageIndex{174}\)

\(\frac{1}{2} \div \frac{1}{4}\)

**Answer**-
2

Exercise \(\PageIndex{175}\)

\(\frac{1}{2} \div \frac{1}{8}\)

Exercise \(\PageIndex{176}\)

\(-\frac{4}{5} \div \frac{4}{7}\)

**Answer**-
\(-\frac{7}{5}\)

Exercise \(\PageIndex{177}\)

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

Exercise \(\PageIndex{178}\)

\(\frac{5}{8} \div \frac{a}{10}\)

**Answer**-
\(\frac{25}{4 a}\)

Exercise \(\PageIndex{179}\)

\(\frac{5}{6} \div \frac{c}{15}\)

Exercise \(\PageIndex{180}\)

\(\frac{7 p}{12} \div \frac{21 p}{8}\)

**Answer**-
\(\frac{2}{9}\)

Exercise \(\PageIndex{181}\)

\(\frac{5 q}{12} \div \frac{15 q}{8}\)

Exercise \(\PageIndex{182}\)

\(\frac{2}{5} \div(-10)\)

**Answer**-
\(-\frac{1}{25}\)

Exercise \(\PageIndex{183}\)

\(-18 \div-\left(\frac{9}{2}\right)\)

In the following exercises, simplify.

Exercise \(\PageIndex{184}\)

\(\frac{\frac{2}{3}}{\frac{8}{9}}\)

**Answer**-
\(\frac{3}{4}\)

Exercise \(\PageIndex{185}\)

\(\frac{\frac{4}{5}}{\frac{8}{15}}\)

Exercise \(\PageIndex{186}\)

\(\frac{-\frac{9}{10}}{3}\)

**Answer**-
\(-\frac{3}{10}\)

Exercise \(\PageIndex{187}\)

\(\frac{2}{\frac{5}{8}}\)

Exercise \(\PageIndex{188}\)

\(\frac{\frac{r}{5}}{\frac{s}{3}}\)

**Answer**-
\(\frac{3 r}{5 s}\)

Exercise \(\PageIndex{189}\)

\(\frac{-\frac{x}{6}}{-\frac{8}{9}}\)

**Simplify Expressions Written with a Fraction Bar**

In the following exercises, simplify.

Exercise \(\PageIndex{190}\)

\(\frac{4+11}{8}\)

**Answer**-
\(\frac{15}{8}\)

Exercise \(\PageIndex{191}\)

\(\frac{9+3}{7}\)

Exercise \(\PageIndex{192}\)

\(\frac{30}{7-12}\)

**Answer**-
-6

Exercise \(\PageIndex{193}\)

\(\frac{15}{4-9}\)

Exercise \(\PageIndex{194}\)

\(\frac{22-14}{19-13}\)

**Answer**-
\(\frac{4}{3}\)

Exercise \(\PageIndex{195}\)

\(\frac{15+9}{18+12}\)

Exercise \(\PageIndex{196}\)

\(\frac{5 \cdot 8}{-10}\)

**Answer**-
-4

Exercise \(\PageIndex{197}\)

\(\frac{3 \cdot 4}{-24}\)

Exercise \(\PageIndex{198}\)

\(\frac{15 \cdot 5-5^{2}}{2 \cdot 10}\)

**Answer**-
\(\frac{5}{2}\)

Exercise \(\PageIndex{199}\)

\(\frac{12 \cdot 9-3^{2}}{3 \cdot 18}\)

Exercise \(\PageIndex{200}\)

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

**Answer**-
-2

Exercise \(\PageIndex{201}\)

\(\frac{7+3(5)}{-2-3^{2}}\)

**Translate Phrases to Expressions with Fractions**

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

Exercise \(\PageIndex{202}\)

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

**Answer**-
\(\frac{c}{d+9}\)

Exercise \(\PageIndex{203}\)

the quotient of the difference of *h* and *k*, and −5.

__Add and Subtract Fractions__

**Add and Subtract Fractions with a Common Denominator**

In the following exercises, add.

Exercise \(\PageIndex{204}\)

\(\frac{4}{9}+\frac{1}{9}\)

**Answer**-
\(\frac{5}{9}\)

Exercise \(\PageIndex{205}\)

\(\frac{2}{9}+\frac{5}{9}\)

Exercise \(\PageIndex{206}\)

\(\frac{y}{3}+\frac{2}{3}\)

**Answer**-
\(\frac{y+2}{3}\)

Exercise \(\PageIndex{207}\)

\(\frac{7}{p}+\frac{9}{p}\)

Exercise \(\PageIndex{208}\)

\(-\frac{1}{8}+\left(-\frac{3}{8}\right)\)

**Answer**-
\(-\frac{1}{2}\)

Exercise \(\PageIndex{209}\)

\(-\frac{1}{8}+\left(-\frac{5}{8}\right)\)

In the following exercises, subtract.

Exercise \(\PageIndex{210}\)

\(\frac{4}{5}-\frac{1}{5}\)

**Answer**-
\(\frac{3}{5}\)

Exercise \(\PageIndex{211}\)

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

Exercise \(\PageIndex{212}\)

\(\frac{y}{17}-\frac{9}{17}\)

**Answer**-
\(\frac{y-9}{17}\)

Exercise \(\PageIndex{213}\)

\(\frac{x}{19}-\frac{8}{19}\)

Exercise \(\PageIndex{214}\)

\(-\frac{8}{d}-\frac{3}{d}\)

**Answer**-
\(-\frac{11}{d}\)

Exercise \(\PageIndex{215}\)

\(-\frac{7}{c}-\frac{7}{c}\)

**Add or Subtract Fractions with Different Denominators**

In the following exercises, add or subtract.

Exercise \(\PageIndex{216}\)

\(\frac{1}{3}+\frac{1}{5}\)

**Answer**-
\(\frac{8}{15}\)

Exercise \(\PageIndex{217}\)

\(\frac{1}{4}+\frac{1}{5}\)

Exercise \(\PageIndex{218}\)

\(\frac{1}{5}-\left(-\frac{1}{10}\right)\)

**Answer**-
\(\frac{3}{10}\)

Exercise \(\PageIndex{219}\)

\(\frac{1}{2}-\left(-\frac{1}{6}\right)\)

Exercise \(\PageIndex{220}\)

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

**Answer**-
\(\frac{17}{12}\)

Exercise \(\PageIndex{221}\)

\(\frac{3}{4}+\frac{2}{5}\)

Exercise \(\PageIndex{222}\)

\(\frac{11}{12}-\frac{3}{8}\)

**Answer**-
\(\frac{13}{24}\)

Exercise \(\PageIndex{223}\)

\(\frac{5}{8}-\frac{7}{12}\)

Exercise \(\PageIndex{224}\)

\(-\frac{9}{16}-\left(-\frac{4}{5}\right)\)

**Answer**-
\(\frac{19}{80}\)

Exercise \(\PageIndex{225}\)

\(-\frac{7}{20}-\left(-\frac{5}{8}\right)\)

Exercise \(\PageIndex{226}\)

\(1+\frac{5}{6}\)

**Answer**-
\(\frac{11}{6}\)

Exercise \(\PageIndex{227}\)

\(1-\frac{5}{9}\)

**Use the Order of Operations to Simplify Complex Fractions**

In the following exercises, simplify.

Exercise \(\PageIndex{228}\)

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

**Answer**-
\(\frac{1}{275}\)

Exercise \(\PageIndex{229}\)

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

Exercise \(\PageIndex{230}\)

\(\frac{\frac{2}{3}+\frac{1}{2}}{\frac{3}{4}-\frac{2}{3}}\)

**Answer**-
14

Exercise \(\PageIndex{231}\)

\(\frac{\frac{3}{4}+\frac{1}{2}}{\frac{5}{6}-\frac{2}{3}}\)

**Evaluate Variable Expressions with Fractions**

In the following exercises, evaluate.

Exercise \(\PageIndex{232}\)

\(x+\frac{1}{2}\) when

- \(x=-\frac{1}{8}\)
- \(x=-\frac{1}{2}\)

**Answer**-
- \(\frac{3}{8}\)
- \(0\)

Exercise \(\PageIndex{233}\)

\(x+\frac{2}{3}\) when

- \(x=-\frac{1}{6}\)
- \(x=-\frac{5}{3}\)

Exercise \(\PageIndex{234}\)

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

**Answer**-
\(\frac{5}{9}\)

Exercise \(\PageIndex{235}\)

5\(m^{2} n\) when \(m=-\frac{2}{5}\) and \(n=\frac{1}{3}\)

Exercise \(\PageIndex{236}\)

\(\frac{u+v}{w}\) when

\(u=-4, v=-8, w=2\)

**Answer**-
-6

Exercise \(\PageIndex{237}\)

\(\frac{m+n}{p}\) when

\(m=-6, n=-2, p=4\)

__Decimals__

**Name and Write Decimals**

In the following exercises, write as a decimal.

Exercise \(\PageIndex{238}\)

Eight and three hundredths

**Answer**-
8.03

Exercise \(\PageIndex{239}\)

Nine and seven hundredths

Exercise \(\PageIndex{240}\)

One thousandth

**Answer**-
0.001

Exercise \(\PageIndex{241}\)

Nine thousandths

In the following exercises, name each decimal.

Exercise \(\PageIndex{242}\)

7.8

**Answer**-
seven and eight tenths

Exercise \(\PageIndex{243}\)

5.01

Exercise \(\PageIndex{244}\)

0.005

**Answer**-
five thousandths

Exercise \(\PageIndex{245}\)

0.381

**Round Decimals**

In the following exercises, round each number to the nearest

- hundredth
- tenth
- whole number.

Exercise \(\PageIndex{246}\)

5.7932

**Answer**-
- 5.79
- 5.8
- 6

Exercise \(\PageIndex{247}\)

3.6284

Exercise \(\PageIndex{248}\)

12.4768

**Answer**-
- 12.48
- 12.5
- 12

Exercise \(\PageIndex{249}\)

25.8449

**Add and Subtract Decimals**

In the following exercises, add or subtract.

Exercise \(\PageIndex{250}\)

18.37+9.36

**Answer**-
27.73

Exercise \(\PageIndex{251}\)

256.37−85.49

Exercise \(\PageIndex{252}\)

15.35−20.88

**Answer**-
−5.53

Exercise \(\PageIndex{253}\)

37.5+12.23

Exercise \(\PageIndex{254}\)

−4.2+(−9.3)

**Answer**-
−13.5

Exercise \(\PageIndex{255}\)

−8.6+(−8.6)

Exercise \(\PageIndex{256}\)

100−64.2

**Answer**-
35.8

Exercise \(\PageIndex{257}\)

100−65.83

Exercise \(\PageIndex{258}\)

2.51+40

**Answer**-
42.51

Exercise \(\PageIndex{259}\)

9.38+60

**Multiply and Divide Decimals**

In the following exercises, multiply.

Exercise \(\PageIndex{260}\)

(0.3)(0.4)

**Answer**-
0.12

Exercise \(\PageIndex{261}\)

(0.6)(0.7)

Exercise \(\PageIndex{262}\)

(8.52)(3.14)

**Answer**-
26.7528

Exercise \(\PageIndex{263}\)

(5.32)(4.86)

Exercise \(\PageIndex{264}\)

(0.09)(24.78)

**Answer**-
2.2302

Exercise \(\PageIndex{265}\)

(0.04)(36.89)

In the following exercises, divide.

Exercise \(\PageIndex{266}\)

\(0.15 \div 5\)

**Answer**-
0.03

Exercise \(\PageIndex{267}\)

\(0.27 \div 3\)

Exercise \(\PageIndex{268}\)

\(\$ 8.49 \div 12\)

**Answer**-
$0.71

Exercise \(\PageIndex{269}\)

\(\$ 16.99 \div 9\)

Exercise \(\PageIndex{270}\)

\(12 \div 0.08\)

**Answer**-
150

Exercise \(\PageIndex{271}\)

\(5 \div 0.04\)

**Convert Decimals, Fractions, and Percents**

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

Exercise \(\PageIndex{272}\)

0.08

**Answer**-
\(\frac{2}{25}\)

Exercise \(\PageIndex{273}\)

0.17

Exercise \(\PageIndex{274}\)

0.425

**Answer**-
\(\frac{17}{40}\)

Exercise \(\PageIndex{275}\)

0.184

Exercise \(\PageIndex{276}\)

1.75

**Answer**-
\(\frac{7}{4}\)

Exercise \(\PageIndex{277}\)

0.035

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

Exercise \(\PageIndex{278}\)

\(\frac{2}{5}\)

**Answer**-
0.4

Exercise \(\PageIndex{279}\)

\(\frac{4}{5}\)

Exercise \(\PageIndex{280}\)

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

**Answer**-
−0.375

Exercise \(\PageIndex{281}\)

\(-\frac{5}{8}\)

Exercise \(\PageIndex{282}\)

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

**Answer**-
\(0 . \overline{5}\)

Exercise \(\PageIndex{283}\)

\(\frac{2}{9}\)

Exercise \(\PageIndex{284}\)

\(\frac{1}{2}+6.5\)

**Answer**-
7

Exercise \(\PageIndex{285}\)

\(\frac{1}{4}+10.75\)

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

Exercise \(\PageIndex{286}\)

5%

**Answer**-
0.05

Exercise \(\PageIndex{287}\)

9%

Exercise \(\PageIndex{288}\)

40%

**Answer**-
0.4

Exercise \(\PageIndex{289}\)

50%

Exercise \(\PageIndex{290}\)

115%

**Answer**-
1.15

Exercise \(\PageIndex{291}\)

125%

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

Exercise \(\PageIndex{292}\)

0.18

**Answer**-
18%

Exercise \(\PageIndex{293}\)

0.15

Exercise \(\PageIndex{294}\)

0.009

**Answer**-
0.9%

Exercise \(\PageIndex{295}\)

0.008

Exercise \(\PageIndex{296}\)

1.5

**Answer**-
150%

Exercise \(\PageIndex{297}\)

2.2

__The Real Numbers__

**Simplify Expressions with Square Roots**

In the following exercises, simplify.

Exercise \(\PageIndex{298}\)

\(\sqrt{64}\)

**Answer**-
8

Exercise \(\PageIndex{299}\)

\(\sqrt{144}\)

Exercise \(\PageIndex{300}\)

\(-\sqrt{25}\)

**Answer**-
-5

Exercise \(\PageIndex{301}\)

\(-\sqrt{81}\)

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

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

Exercise \(\PageIndex{302}\)

- 9
- 8.47

**Answer**-
- \(\frac{9}{1}\)
- \(\frac{847}{100}\)

Exercise \(\PageIndex{303}\)

- −15
- 3.591

In the following exercises, list the

- rational numbers,
- irrational numbers.

Exercise \(\PageIndex{304}\)

\(0.84,0.79132 \ldots, 1 . \overline{3}\)

**Answer**-
- \(0.84,1.3\)
- \(0.79132 \ldots\)

Exercise \(\PageIndex{305}\)

\(2.3 \overline{8}, 0.572,4.93814 \ldots\)

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

Exercise \(\PageIndex{306}\)

- \(\sqrt{121}\)
- \(\sqrt{48}\)

**Answer**-
- rational
- irrational

Exercise \(\PageIndex{307}\)

- \(\sqrt{56}\)
- \(\sqrt{16}\)

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

Exercise \(\PageIndex{308}\)

- \(\sqrt{-9}\)
- \(-\sqrt{169}\)

**Answer**-
- not a real number
- real number

Exercise \(\PageIndex{309}\)

- \(\sqrt{-64}\)
- \(-\sqrt{81}\)

In the following exercises, list the

- whole numbers,
- integers,
- rational numbers,
- irrational numbers,
- real numbers for each set of numbers.

Exercise \(\PageIndex{310}\)

\(-4,0, \frac{5}{6}, \sqrt{16}, \sqrt{18}, 5.2537 \ldots\)

**Answer**-
- \(0, \sqrt{16}\)
- \(-4,0, \sqrt{16}\)
- \(-4,0, \frac{5}{6}, \sqrt{16}\)
- \(\sqrt{18}, 5.2537 \ldots\)
- \(-4,0, \frac{5}{6}, \sqrt{16}, \sqrt{18}, 5.2537 \ldots\)

Exercise \(\PageIndex{311}\)

\(-\sqrt{4}, 0 . \overline{36}, \frac{13}{3}, 6.9152 \ldots, \sqrt{48}, 10 \frac{1}{2}\)

**Locate Fractions on the Number Line**

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

Exercise \(\PageIndex{312}\)

\(\frac{2}{3}, \frac{5}{4}, \frac{12}{5}\)

**Answer**

Exercise \(\PageIndex{313}\)

\(\frac{1}{3}, \frac{7}{4}, \frac{13}{5}\)

Exercise \(\PageIndex{314}\)

\(2 \frac{1}{3},-2 \frac{1}{3}\)

**Answer**

Exercise \(\PageIndex{315}\)

\(1 \frac{3}{5},-1 \frac{3}{5}\)

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

Exercise \(\PageIndex{316}\)

−1___\(-\frac{1}{8}\)

**Answer**-
<

Exercise \(\PageIndex{317}\)

\(-3 \frac{1}{4}\)___−4

Exercise \(\PageIndex{318}\)

\(-\frac{7}{9}\) ___ \(\frac{4}{9}\)

**Answer**-
>

Exercise \(\PageIndex{319}\)

\(-2\) ___ \(\frac{19}{8}\)

**Locate Decimals on the Number Line**

In the following exercises, locate on the number line.

Exercise \(\PageIndex{320}\)

0.3

**Answer**

Exercise \(\PageIndex{321}\)

−0.2

Exercise \(\PageIndex{322}\)

−2.5

**Answer**

Exercise \(\PageIndex{323}\)

2.7

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

Exercise \(\PageIndex{324}\)

0.9___0.6

**Answer**-
>

Exercise \(\PageIndex{325}\)

0.7___0.8

Exercise \(\PageIndex{326}\)

−0.6___−0.59

**Answer**-
>

Exercise \(\PageIndex{327}\)

−0.27___−0.3

__Properties of Real Numbers__

**Use the Commutative and Associative Properties**

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

Exercise \(\PageIndex{328}\)

−12(4m)

**Answer**-
−48m

Exercise \(\PageIndex{329}\)

30\(\left(\frac{5}{6} q\right)\)

Exercise \(\PageIndex{330}\)

(a+16)+31

**Answer**-
a+47

Exercise \(\PageIndex{331}\)

(c+0.2)+0.7

In the following exercises, simplify.

Exercise \(\PageIndex{332}\)

6y+37+(−6y)

**Answer**-
37

Exercise \(\PageIndex{333}\)

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

Exercise \(\PageIndex{334}\)

\(\frac{14}{11} \cdot \frac{35}{9} \cdot \frac{14}{11}\)

**Answer**-
\(\frac{35}{9}\)

Exercise \(\PageIndex{335}\)

\(-18 \cdot 15 \cdot \frac{2}{9}\)

Exercise \(\PageIndex{336}\)

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

**Answer**-
1\(\frac{7}{12}\)

Exercise \(\PageIndex{337}\)

(3.98d+0.75d)+1.25d

Exercise \(\PageIndex{338}\)

11x+8y+16x+15y

**Answer**-
27x+23y

Exercise \(\PageIndex{339}\)

52m+(−20n)+(−18m)+(−5n)

**Use the Identity and Inverse Properties of Addition and Multiplication**

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

Exercise \(\PageIndex{340}\)

- \(\frac{1}{3}\)
- 5.1
- \(-14\)
- \(-\frac{8}{5}\)

**Answer**-
- \(-\frac{1}{3}\)
- \(-5.1\)
- -14
- \(-\frac{8}{5}\)

Exercise \(\PageIndex{341}\)

- \(-\frac{7}{8}\)
- \(-0.03\)
- 17
- \(\frac{12}{5}\)

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

Exercise \(\PageIndex{342}\)

- \(10\)
- \(-\frac{4}{9}\)
- 0.6

**Answer**-
- \(\frac{1}{10}\)
- \(-\frac{9}{4}\)
- \(\frac{5}{3}\)

Exercise \(\PageIndex{343}\)

- \(-\frac{9}{2}\)
- -7
- 2.1

**Use the Properties of Zero**

In the following exercises, simplify.

Exercise \(\PageIndex{344}\)

83\(\cdot 0\)

**Answer**-
0

Exercise \(\PageIndex{345}\)

\(\frac{0}{9}\)

Exercise \(\PageIndex{346}\)

\(\frac{5}{0}\)

**Answer**-
undefined

Exercise \(\PageIndex{347}\)

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

In the following exercises, simplify.

Exercise \(\PageIndex{348}\)

43+39+(−43)

**Answer**-
39

Exercise \(\PageIndex{349}\)

(n+6.75)+0.25

Exercise \(\PageIndex{350}\)

\(\frac{5}{13} \cdot 57 \cdot \frac{13}{5}\)

**Answer**-
57

Exercise \(\PageIndex{351}\)

\(\frac{1}{6} \cdot 17 \cdot 12\)

Exercise \(\PageIndex{352}\)

\(\frac{2}{3} \cdot 28 \cdot \frac{3}{7}\)

**Answer**-
8

Exercise \(\PageIndex{353}\)

\(9(6 x-11)+15\)

**Simplify Expressions Using the Distributive Property**

In the following exercises, simplify using the Distributive Property.

Exercise \(\PageIndex{354}\)

7(x+9)

**Answer**-
7x+63

Exercise \(\PageIndex{355}\)

9(u−4)

Exercise \(\PageIndex{356}\)

−3(6m−1)

**Answer**-
−18m+3

Exercise \(\PageIndex{357}\)

−8(−7a−12)

Exercise \(\PageIndex{358}\)

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

**Answer**-
5n−2

Exercise \(\PageIndex{359}\)

\((y+10) \cdot p\)

Exercise \(\PageIndex{360}\)

(a−4)−(6a+9)

**Answer**-
−5a−13

Exercise \(\PageIndex{361}\)

4(x+3)−8(x−7)

__Systems of Measurement__

**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.

Exercise \(\PageIndex{362}\)

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

**Answer**-
84 inches

Exercise \(\PageIndex{363}\)

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

Exercise \(\PageIndex{364}\)

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

**Answer**-
64 inches

Exercise \(\PageIndex{365}\)

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

Exercise \(\PageIndex{366}\)

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

**Answer**-
2.7 miles

Exercise \(\PageIndex{367}\)

Shamu weights 4.5 tons. Convert the weight to pounds.

Exercise \(\PageIndex{368}\)

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

**Answer**-
105 minutes

Exercise \(\PageIndex{369}\)

How many tablespoons are in a quart?

Exercise \(\PageIndex{370}\)

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

**Answer**-
94 ounces

Exercise \(\PageIndex{371}\)

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

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

In the following exercises, solve.

Exercise \(\PageIndex{372}\)

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.

Exercise \(\PageIndex{373}\)

Every day last week Pedro recorded the number of minutes he spent reading. The number of minutes were 50, 25, 83, 45, 32, 60, 135. How many hours did Pedro spend reading?

Exercise \(\PageIndex{374}\)

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

Exercise \(\PageIndex{375}\)

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

**Make Unit Conversions in the Metric System**

In the following exercises, convert the units.

Exercise \(\PageIndex{376}\)

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

**Answer**-
170 centimeters

Exercise \(\PageIndex{377}\)

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

Exercise \(\PageIndex{378}\)

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

**Answer**-
0.488 grams

Exercise \(\PageIndex{379}\)

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

Exercise \(\PageIndex{380}\)

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

**Answer**-
2,900 grams

Exercise \(\PageIndex{381}\)

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

**Use Mixed Units of Measurement in the Metric System**

In the following exerices, solve.

Exercise \(\PageIndex{382}\)

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

**Answer**-
1.12 meter

Exercise \(\PageIndex{383}\)

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

Exercise \(\PageIndex{384}\)

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

Exercise \(\PageIndex{385}\)

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

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

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

Exercise \(\PageIndex{386}\)

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

**Answer**-
175.3 centimeters

Exercise \(\PageIndex{387}\)

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

Exercise \(\PageIndex{388}\)

Caroline walked 2.5 kilometers. Convert this length to miles.

**Answer**-
1.6 miles

Exercise \(\PageIndex{389}\)

Lucas weighs 78 kilograms. Convert his weight to pounds.

Exercise \(\PageIndex{390}\)

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

**Answer**-
14.6 gallons

Exercise \(\PageIndex{391}\)

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

**Convert between Fahrenheit and Celsius Temperatures**

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

Exercise \(\PageIndex{392}\)

95° Fahrenheit

**Answer**-
35° C

Exercise \(\PageIndex{393}\)

23° Fahrenheit

Exercise \(\PageIndex{394}\)

20° Fahrenheit

**Answer**-
–6.7° C

Exercise \(\PageIndex{395}\)

64° Fahrenheit

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

Exercise \(\PageIndex{396}\)

30° Celsius

**Answer**-
86° F

Exercise \(\PageIndex{397}\)

–5° Celsius

Exercise \(\PageIndex{398}\)

–12° Celsius

**Answer**-
10.4° F

Exercise \(\PageIndex{399}\)

24° Celsius

## Chapter Practice Test

Exercise \(\PageIndex{1}\)

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

**Answer**-
205,617

Exercise \(\PageIndex{2}\)

Find the prime factorization of 504.

Exercise \(\PageIndex{3}\)

Find the Least Common Multiple of 18 and 24.

**Answer**-
72

Exercise \(\PageIndex{4}\)

Combine like terms: 5n+8+2n−1.

In the following exercises, evaluate.

Exercise \(\PageIndex{5}\)

\(-|x|\) when \(x=-2\)

**Answer**-
−2

Exercise \(\PageIndex{6}\)

11−a when a=−3

Exercise \(\PageIndex{7}\)

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

**Answer**-
−7−20;−27

Exercise \(\PageIndex{8}\)

Monique has a balance of −$18 in her checking account. She deposits $152 to the account. What is the new balance?

Exercise \(\PageIndex{9}\)

Round 677.1348 to the nearest hundredth.

**Answer**-
677.13

Exercise \(\PageIndex{10}\)

Convert \(\frac{4}{5}\) to a decimal.

Exercise \(\PageIndex{11}\)

Convert 1.85 to a percent.

**Answer**-
185%

Exercise \(\PageIndex{12}\)

Locate \(\frac{2}{3},-1.5,\) and \(\frac{9}{4}\) on a number line.

In the following exercises, simplify each expression.

Exercise \(\PageIndex{13}\)

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

**Answer**-
99

Exercise \(\PageIndex{14}\)

−85+42

Exercise \(\PageIndex{15}\)

−19−25

**Answer**-
−44

Exercise \(\PageIndex{16}\)

\((-2)^{4}\)

Exercise \(\PageIndex{17}\)

\(-5(-9) \div 15\)

**Answer**-
3

Exercise \(\PageIndex{18}\)

\(\frac{3}{8} \cdot \frac{11}{12}\)

Exercise \(\PageIndex{19}\)

\(\frac{4}{5} \div \frac{9}{20}\)

**Answer**-
\(\frac{16}{9}\)

Exercise \(\PageIndex{20}\)

\(\frac{12+3 \cdot 5}{15-6}\)

Exercise \(\PageIndex{21}\)

\(\frac{m}{7}+\frac{10}{7}\)

**Answer**-
\(\frac{m+10}{7}\)

Exercise \(\PageIndex{22}\)

\(\frac{7}{12}-\frac{3}{8}\)

Exercise \(\PageIndex{23}\)

\(-5.8+(-4.7)\)

**Answer**-
−10.5

Exercise \(\PageIndex{24}\)

100−64.25

Exercise \(\PageIndex{25}\)

(0.07)(31.95)

**Answer**-
2.2365

Exercise \(\PageIndex{26}\)

\(9 \div 0.05\)

Exercise \(\PageIndex{27}\)

\(-14\left(\frac{5}{7} p\right)\)

**Answer**-
−10p

Exercise \(\PageIndex{28}\)

(u+8)−9

Exercise \(\PageIndex{29}\)

6x+(−4y)+9x+8y

**Answer**-
15x+4y

Exercise \(\PageIndex{30}\)

\(\frac{0}{23}\)

Exercise \(\PageIndex{31}\)

\(\frac{75}{0}\)

**Answer**-
undefined

Exercise \(\PageIndex{32}\)

−2(13q−5)

Exercise \(\PageIndex{33}\)

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

**Answer**-
100 minutes

Exercise \(\PageIndex{34}\)

Mike’s SUV is 5 feet 11 inches tall. He wants to put a rooftop cargo bag on the the SUV. The cargo bag is 1 foot 6 inches tall. What will the total height be of the SUV with the cargo bag on the roof? *(1 foot = 12 inches)*

Exercise \(\PageIndex{35}\)

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

**Answer**-
4.508 km