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Mathematics LibreTexts

Chapter 1 Review Exercises

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    30471
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    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. 1
    2. 2
    3. 9
    4. 5
    5. 6
    Answer
    1. tens
    2. ten thousands
    3. hundreds
    4. ones
    5. thousands

    Exercise \(\PageIndex{2}\)

    359,417

    1. 9
    2. 3
    3. 4
    4. 7
    5. 1

    Exercise \(\PageIndex{3}\)

    58,129,304

    1. 5
    2. 0
    3. 1
    4. 8
    5. 2
    Answer
    1. ten millions
    2. tens
    3. hundred thousands
    4. millions
    5. ten thousands

    Exercise \(\PageIndex{4}\)

    9,430,286,157

    1. 6
    2. 4
    3. 9
    4. 0
    5. 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.

    1. 407
    2. 8,564
    Answer
    1. 410
    2. 8,560

    Exercise \(\PageIndex{14}\)

    Round to the nearest hundred.

    1. 25,846
    2. 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
    1. 865,000865,000
    2. 865,000865,000
    3. 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 \(\PageIndex{81}\)

    1. 6___2
    2. −7___4
    3. −9___−1
    4. 9___−3

    Answer
    1. >
    2. <
    3. <
    4. >

    Exercise \(\PageIndex{82}\)

    1. −5___1
    2. −4___−9
    3. 6___10
    4. 3___−8

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

    Exercise \(\PageIndex{83}\)

    1. −8
    2. 1
    Answer
    1. 8
    2. −1

    Exercise \(\PageIndex{84}\)

    1. −2
    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

    1. m=3
    2. m=−3
    Answer
    1. −3
    2. 3

    Exercise \(\PageIndex{88}\)

    −p when

    1. p=6
    2. p=−6

    Simplify Expressions with Absolute Value

    In the following exercises,, simplify.

    Exercise \(\PageIndex{89}\)

    1. |7|
    2. |−25|
    3. |0|
    Answer
    1. 7
    2. 25
    3. 0

    Exercise \(\PageIndex{90}\)

    1. |5|
    2. |0|
    3. |−19|

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

    Exercise \(\PageIndex{91}\)

    1. −8___|−8|
    2. −|−2|___−2
    Answer
    1. <
    2. =

    Exercise \(\PageIndex{92}\)

    1. |−3|___−|−3|
    2. 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
    1. 28
    2. 15

    Exercise \(\PageIndex{98}\)

    1. ∣y∣ when y=−37
    2. |−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 \(\PageIndex{107}\)

    1. 15−6
    2. 15+(−6)
    Answer
    1. 9
    2. 9

    Exercise \(\PageIndex{108}\)

    1. 12−9
    2. 12+(−9)

    Exercise \(\PageIndex{109}\)

    1. 8−(−9)
    2. 8+9
    Answer
    1. 17
    2. 17

    Exercise \(\PageIndex{110}\)

    1. 4−(−4)
    2. 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

    1. x=−26
    2. x=−95
    Answer
    1. −18
    2. −87

    Exercise \(\PageIndex{140}\)

    y+9 when

    1. y=−29
    2. y=−84

    Exercise \(\PageIndex{141}\)

    When b=−11, evaluate:

    1. b+6
    2. −b+6
    Answer
    1. −5
    2. 17

    Exercise \(\PageIndex{142}\)

    When c=−9, evaluate:

    1. c+(−4)c+(−4)
    2. −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 \(\PageIndex{148}\)

    1. the difference of 15 and −7
    2. 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

    1. \(x=-\frac{1}{8}\)
    2. \(x=-\frac{1}{2}\)
    Answer
    1. \(\frac{3}{8}\)
    2. \(0\)

    Exercise \(\PageIndex{233}\)

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

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

    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

    1. hundredth
    2. tenth
    3. whole number.

    Exercise \(\PageIndex{246}\)

    5.7932

    Answer
    1. 5.79
    2. 5.8
    3. 6

    Exercise \(\PageIndex{247}\)

    3.6284

    Exercise \(\PageIndex{248}\)

    12.4768

    Answer
    1. 12.48
    2. 12.5
    3. 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 \(\PageIndex{302}\)

    1. 9
    2. 8.47
    Answer
    1. \(\frac{9}{1}\)
    2. \(\frac{847}{100}\)

    Exercise \(\PageIndex{303}\)

    1. −15
    2. 3.591

    In the following exercises, list the

    1. rational numbers,
    2. irrational numbers.

    Exercise \(\PageIndex{304}\)

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

    Answer
    1. \(0.84,1.3\)
    2. \(0.79132 \ldots\)

    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 \(\PageIndex{306}\)

    1. \(\sqrt{121}\)
    2. \(\sqrt{48}\)
    Answer
    1. rational
    2. irrational

    Exercise \(\PageIndex{307}\)

    1. \(\sqrt{56}\)
    2. \(\sqrt{16}\)

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

    Exercise \(\PageIndex{308}\)

    1. \(\sqrt{-9}\)
    2. \(-\sqrt{169}\)
    Answer
    1. not a real number
    2. real number

    Exercise \(\PageIndex{309}\)

    1. \(\sqrt{-64}\)
    2. \(-\sqrt{81}\)

    In the following exercises, list the

    1. whole numbers,
    2. integers,
    3. rational numbers,
    4. irrational numbers,
    5. real numbers for each set of numbers.

    Exercise \(\PageIndex{310}\)

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

    Answer
    1. \(0, \sqrt{16}\)
    2. \(-4,0, \sqrt{16}\)
    3. \(-4,0, \frac{5}{6}, \sqrt{16}\)
    4. \(\sqrt{18}, 5.2537 \ldots\)
    5. \(-4,0, \frac{5}{6}, \sqrt{16}, \sqrt{18}, 5.2537 \ldots\)

    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

    This figure is a number line ranging from 0 to 6 with tick marks for each integer. 2 thirds, 5 fourths, and 12 fifths are plotted.

    Exercise \(\PageIndex{313}\)

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

    Exercise \(\PageIndex{314}\)

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

    Answer

    This figure is a number line ranging from negative 4 to 4 with tick marks for each integer. Negative 2 and 1 third, and 2 and 1 third are plotted.

    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

    This figure is a number line ranging from 0 to 1 with tick marks for each tenth of an integer. 0.3 is plotted.

    Exercise \(\PageIndex{321}\)

    −0.2

    Exercise \(\PageIndex{322}\)

    −2.5

    Answer

    This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. Negative 2.5 is plotted.

    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 \(\PageIndex{340}\)

    1. \(\frac{1}{3}\)
    2. 5.1
    3. \(-14\)
    4. \(-\frac{8}{5}\)
    Answer
    1. \(-\frac{1}{3}\)
    2. \(-5.1\)
    3. -14
    4. \(-\frac{8}{5}\)

    Exercise \(\PageIndex{341}\)

    1. \(-\frac{7}{8}\)
    2. \(-0.03\)
    3. 17
    4. \(\frac{12}{5}\)

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

    Exercise \(\PageIndex{342}\)

    1. \(10\)
    2. \(-\frac{4}{9}\)
    3. 0.6
    Answer
    1. \(\frac{1}{10}\)
    2. \(-\frac{9}{4}\)
    3. \(\frac{5}{3}\)

    Exercise \(\PageIndex{343}\)

    1. \(-\frac{9}{2}\)
    2. -7
    3. 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