Chapter 1

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

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

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

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

$\mathrm{2,466,714,051}$

$\mathrm{11,921,830,106}$

$\mathrm{17,900}$

$\mathrm{468,800}$

ⓐ 207,000 ⓑ 207,000 ⓒ 210,000

ⓐ 785,000 ⓑ 785,000 ⓒ 780,000

by 2, 3, and 6

by 3 and 5

$2·2·2·2·5$

$2·2·3·5$

$2·3·3·7$

$2·3·7·7$

36

72

36

72

84

96

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

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

ⓐ equation ⓑ expression

ⓐ expression ⓑ equation

ⓐ 125 ⓑ 1

ⓐ 49 ⓑ 0

ⓐ 2 ⓑ 14

ⓐ 35 ⓑ 99

16

23

86

1

ⓐ 13 ⓑ 5

ⓐ 8 ⓑ 16

ⓐ $9$ ⓑ $64$

ⓐ $216$ ⓑ $64$

40

9

ⓐ 14 ⓑ 41 ⓒ 1

ⓐ 9 ⓑ 13 ⓒ 1

9 and 15, $y^2$ and $11y^2,$ $2x^3$ and $8x^3$

19 and 24, $8x^2$ and $3x^2,$ $4x^3$ and $6x^3$

$4x^2,5x,17$

5x, 2y

$10x^2+16x+17$

$12y^2+9y+7$

ⓐ $14x^2-13$ ⓑ $12x÷2$

ⓐ $17y^2+19$ ⓑ 7y

ⓐ $x+11$ ⓑ $11a-14$

ⓐ $z+13$ ⓑ $8x-18$

ⓐ $4\left(p+q\right)$ ⓑ $4p+q$

ⓐ $2x-8$ ⓑ $2\left(x-8\right)$

$w-7$

$l-6$

$4q-8$

$7n+3$

ⓐ > ⓑ < ⓒ > ⓓ >

ⓐ < ⓑ > ⓒ < ⓓ >

ⓐ $\mathrm{-4}$ ⓑ 3 ⓒ 1

ⓐ $\mathrm{-8}$ ⓑ 5 ⓒ 5

ⓐ $\mathrm{-4}$ ⓑ 4

ⓐ $\mathrm{-11}$ ⓑ 11

ⓐ 4 ⓑ 28 ⓒ 0

ⓐ 13 ⓑ 47 ⓒ 0

ⓐ > ⓑ > ⓒ < ⓓ >

ⓐ > ⓑ > ⓒ > ⓓ <

16

9

ⓐ $17$ ⓑ $39$ ⓒ $\mathrm{-22}$ ⓓ $\mathrm{-11}$

ⓐ $23$ ⓑ $21$ ⓒ $\mathrm{-37}$ ⓓ $\mathrm{-49}$

ⓐ 6 ⓑ $\mathrm{-6}$

ⓐ 7 ⓑ $\mathrm{-7}$

ⓐ 2 ⓑ $\mathrm{-2}$

ⓐ 3 ⓑ $\mathrm{-3}$

ⓐ $\mathrm{-50}$ ⓑ $\mathrm{-17}$

ⓐ $\mathrm{-70}$ ⓑ $\mathrm{-36}$

13

0

ⓐ 2 ⓑ $\mathrm{-2}$

ⓐ 3 ⓑ $\mathrm{-3}$

ⓐ $\mathrm{-10}$ ⓑ 10

ⓐ $\mathrm{-11}$ ⓑ 11

ⓐ 8 ⓑ −18

ⓐ $8$ ⓑ $\mathrm{-22}$

ⓐ $19$ ⓑ $\mathrm{-4}$

ⓐ 23 ⓑ 3

3

13

ⓐ $\mathrm{-48}$ ⓑ 28 ⓒ $\mathrm{-63}$ ⓓ 60

ⓐ $\mathrm{-56}$ ⓑ 54 ⓒ $\mathrm{-28}$ ⓓ 39

ⓐ $\mathrm{-9}$ ⓑ 17

ⓐ $\mathrm{-8}$ ⓑ 16

ⓐ $\mathrm{-7}$ ⓑ 39

ⓐ $\mathrm{-9}$ ⓑ 23

$\mathrm{-63}$

$\mathrm{-84}$

ⓐ 81 ⓑ $\mathrm{-81}$

ⓐ 49 ⓑ $\mathrm{-49}$

29

52

4

9

21

6

ⓐ $\mathrm{-6}$ ⓑ 10

ⓐ $\mathrm{-1}$ ⓑ 17

196

8

ⓐ $\mathrm{-2}$ ⓑ 36

ⓐ $\mathrm{-19}$ ⓑ 9

39

13

$\left(9+\left(\mathrm{-16}\right)\right)+4-3$

$\left(\mathrm{-8}+\left(\mathrm{-12}\right)\right)+7-13$

ⓐ $14-\left(\mathrm{-23}\right);37$ ⓑ $\mathrm{-17}-21;-38$

ⓐ $11-\left(\mathrm{-19}\right);30$ ⓑ $\mathrm{-11}-18;-29$

$\mathrm{-5}\left(12\right);-60$

$\mathrm{-8}\left(13\right);-104$

$\mathrm{-63}÷\left(\mathrm{-9}\right);7$

$\mathrm{-72}÷\left(\mathrm{-9}\right);8$

The difference in temperatures was 45 degrees.

The difference in temperatures was 9 degrees.

The Bears lost 105 yards.

A $16 fee was deducted from his checking account.

$\frac{6}{10},\frac{9}{15},\frac{12}{20};$ answers may vary

$\frac{8}{10},\frac{12}{15},\frac{16}{20};$ answers may vary

$-\frac{7}{9}$

$-\frac{5}{9}$

$-\frac{23}{40}$

$-\frac{5}{8}$

$\frac{x}{y}$

$\frac{a}{b}$

$-\frac{4}{21}$

$-\frac{3}{16}$

$\mathrm{-33}a$

$\mathrm{-2}b$

$-\frac{21}{5p}$

$-\frac{15}{8q}$

$\frac{4}{15}$

$\frac{2}{3}$

$\frac{4}{5}$

$\frac{11}{14}$

$\frac{3}{4b}$

$\frac{4}{2q}$

$-\frac{3}{4}$

$-\frac{2}{3}$

4

2

$\frac{a-b}{cd}$

$\frac{p+q}{r}$

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

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

$-\frac{26}{28}$

$-\frac{7}{8}$

$-\frac{16}{x}$

$-\frac{22}{a}$

$\mathrm{-1}$

$-\frac{2}{3}$

$\frac{79}{60}$

$\frac{103}{60}$

$\frac{1}{96}$

$\frac{75}{224}$

$\frac{9y+42}{54}$

$\frac{15x+42}{135}$

ⓐ $\frac{27a-32}{36}$ ⓑ $\frac{2a}{3}$

ⓐ $\frac{24k-5}{30}$ ⓑ $\frac{2k}{15}$

$\frac{1}{90}$

$272$

2

$\frac{2}{7}$

ⓐ $\mathrm{-1}$ ⓑ $-\frac{1}{2}$

ⓐ $\frac{7}{6}$ ⓑ $-\frac{1}{12}$

$-\frac{1}{4}$

$-\frac{17}{8}$

$-\frac{1}{2}$

$\frac{2}{3}$

$-\frac{5}{2}$

$\frac{3}{2}$

six and seven tenths

five and eight tenths

negative thirteen and four hundred sixty-one thousandths

negative two and fifty-three thousandths

13.68

5.94

1.05

9.17

ⓐ 6.58 ⓑ 6.6 ⓒ 7

ⓐ 15.218 ⓑ 15.22 ⓒ 15.2

16.49

23.593

0.42

12.58

$\mathrm{-27.4815}$

$\mathrm{-87.6148}$

ⓐ 25.8 ⓑ 258 ⓒ 2,580

ⓐ 142 ⓑ 1,420 ⓒ 14,200

687.3

34.25

$0.19

$0.42

$\frac{117}{500}$

$\frac{3}{125}$

$\mathrm{-0.875}$

$\mathrm{-0.375}$

$2.\stackrel{\text{—}}{45}$

$2.3\stackrel{\text{—}}{18}$

5.275

6.35

ⓐ 0.09 ⓑ 0.87 ⓒ 0.039

ⓐ 0.03 ⓑ 0.91 ⓒ 0.083

ⓐ 17% ⓑ 175% ⓒ 8.25%

ⓐ 41% ⓑ 225% ⓒ 9.25%

ⓐ 6 ⓑ 13

ⓐ 4 ⓑ 14

ⓐ $\mathrm{-2}$ ⓑ $\mathrm{-15}$

ⓐ $\mathrm{-9}$ ⓑ $\mathrm{-10}$

ⓐ $\frac{\mathrm{-24}}{1}$ ⓑ $\frac{357}{100}$

ⓐ $\frac{\mathrm{-19}}{1}$ ⓑ $\frac{841}{100}$

ⓐ $0.29,0.81\stackrel{\text{–}}{6}$ ⓑ $2.515115111\text{…}$

ⓐ $2.6\stackrel{\text{–}}{3},0.125$ ⓑ $0.418302\text{…}$

ⓐ rational ⓑ irrational

ⓐ irrational ⓑ rational

ⓐ not a real number ⓑ real number

ⓐ real number ⓑ not a real number

ⓐ $4,\sqrt{49}$ ⓑ $\mathrm{-3},4,\sqrt{49}$ ⓒ $\mathrm{-3},0.\stackrel{\text{–}}{3},\frac{9}{5},4,\sqrt{49}$ ⓓ $\text{−}\sqrt{2}$ ⓔ $\mathrm{-3},\text{−}\sqrt{2},0.\stackrel{\text{–}}{3},\frac{9}{5},4,\sqrt{49}$

ⓐ $6,\sqrt{121}$ ⓑ $\text{−}\sqrt{25},\mathrm{-1},6,\sqrt{121}$ ⓒ $\text{−}\sqrt{25},-\frac{3}{8},\mathrm{-1},6,\sqrt{121}$ ⓓ $2.041975\text{…}$ ⓔ $\text{−}\sqrt{25},-\frac{3}{8},\mathrm{-1},6,\sqrt{121},2.041975\text{…}$

ⓐ > ⓑ > ⓒ < ⓓ <

ⓐ < ⓑ < ⓒ > ⓓ <

>

>

>

<

>

>

$32r+29s$

$41m+6n$

$1\frac{7}{15}$

$1\frac{2}{9}$

32x

$\mathrm{-63}y$

ⓐ $-\frac{7}{9}$ ⓑ $\mathrm{-1.2}$ ⓒ $14$ ⓓ $\frac{9}{4}$

ⓐ $-\frac{7}{13}$ ⓑ $\mathrm{-8.4}$ ⓒ $46$ ⓓ $\frac{5}{2}$

ⓐ $\frac{1}{4}$ ⓑ $\mathrm{-7}$ ⓒ $\frac{10}{3}$

ⓐ $\frac{1}{18}$ ⓑ $-\frac{5}{4}$ ⓒ $\frac{5}{3}$

ⓐ 0 ⓑ 0 ⓒ undefined

ⓐ 0 ⓑ 0 ⓒ undefined

$\mathrm{-48}a$

$\mathrm{-92}x$

$\frac{5}{49}$

$\frac{11}{25}$

ⓐ 0 ⓑ undefined

ⓐ 0 ⓑ undefined

$20y+50$

$12z+16$

$4x+8$

$6x+42$

$5y+3$

$4n+9$

$70+15p$

$4+35d$

$\mathrm{-18}m-15$

$\mathrm{-48}n-66$

$\mathrm{-10}+15a$

$\mathrm{-56}+105y$

$\text{−}z+11$

$\text{−}x+4$

$3-3x$

$2x-20$

$5x-66$

$7x-13$

2.5 feet

54 feet

8,600 pounds

102,000,000 pounds

440,000,000 yards

151,200 minutes

16 cups

48 teaspoons

$\text{9 lbs}.\text{8 oz}$

21 ft. 6 in.

4 lbs. 8 oz.

11 gallons 2 qt.

5,000 meters

250 centimeters

2.8 kilograms

4.5 kilograms

ⓐ 7,250 kiloliters ⓑ 6,300 milliliters

ⓐ 35,000 liters ⓑ 410 centiliters

83 centimeters

1.04 meters

2 liters

2.4 kilograms

2.12 quarts

3.8 liters

19,335.6 feet

8,993.46 km

$15\text{°}\text{C}$

$5\text{°}\text{C}$

$59\text{°}\text{F}$

$50\text{°}\text{F}$

ⓐ thousands ⓑ hundreds ⓒ tens ⓓ ten thousands ⓔ ones

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

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

ⓐ trillions ⓑ billions ⓒ millions ⓓ tens ⓔ thousands

one thousand, seventy-eight

three hundred sixty-four thousand, five hundred ten

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

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

412

35,975

11,044,167

3,226,512,017

ⓐ 390 ⓑ 2,930

ⓐ 13,700 ⓑ 391,800

ⓐ 1,490 ⓑ 1,500

ⓐ 64,000 ⓑ 63,900

ⓐ 392,500 ⓑ 393,000 ⓒ 390,000

ⓐ 2,587,000 ⓑ 2,587,000 ⓒ 2,590,000

divisible by 2, 3, and 6

divisible by 3 and 5

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

divisible by 2

divisible by 2, 5, and 10

divisible by 3 and 5

$2·43$

$2·2·3·11$

$3·3·7·11$

$2·2·2·2·3·3·3$

$2·2·2·2·3·3·3·5$

24

48

60

24

280

440

twenty-four thousand, four hundred ninety-three dollars

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

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

40

Answers may vary.

16 minus 9, the difference of sixteen and nine

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

2 times 7, the product of two and seven

fourteen is less than twenty-one

thirty-six is greater than or equal to nineteen

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

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

equation

expression

expression

125

256

ⓐ 43 ⓑ 55

5

34

58

6

4

35

58

149

50

22

144

32

21

9

73

54

8

5

$x^3\text{and}8x^3,14\text{and}5$

$16\text{and}4,16b^2\text{and}9b^2$

$15x^2,6x,2$

$10y^3,y,2$

13x

7c

$10u+3$

$22a+1$

$17x^2+20x+16$

$14-9$

$9·7$

$36÷9$

$8x+3x$

$\frac{y}{3}$

$8\left(y-9\right)$

$c+3$

$2n-7$

ⓐ $750 ⓑ $1,350

Answers may vary

Answers may vary

ⓐ > ⓑ < ⓒ < ⓓ >

ⓐ $\mathrm{-2}$ ⓑ 6

4

15

ⓐ $\mathrm{-12}$ ⓑ 12

ⓐ 32 ⓑ 0 ⓒ 16

ⓐ < ⓑ $=$

$5,\mathrm{-5}$

56

0

8

ⓐ $\mathrm{-19}$ ⓑ $\mathrm{-33}$

$\mathrm{-80}$

32

$\mathrm{-22}$

108

29

6

$\mathrm{-9}$

12

ⓐ 16 ⓑ 16

ⓐ 45 ⓑ 45

27

$\mathrm{-39}$

$\mathrm{-59}$

$\mathrm{-51}$

9

$\mathrm{-2}$

$\mathrm{-2}$

22

0

4

6

$\mathrm{-8}$

$\mathrm{-11}$

ⓐ 20,329 ⓑ $\mathrm{-282}$

ⓐ $540 million ⓑ $\text{−}\mathrm{\$27}$ billion

$\mathrm{-32}$

Answers may vary

Answers may vary

$\mathrm{-32}$

$\mathrm{-63}$

$\mathrm{-6}$

14

$\mathrm{-4}$

13

$\mathrm{-12}$

$\mathrm{-47}$

64

$\mathrm{-16}$

90

9

41

$\mathrm{-9}$

$\mathrm{-29}$

5

ⓐ $\mathrm{-47}$ ⓑ 16

ⓐ $\mathrm{-4}$ ⓑ 10

$\mathrm{-8}$

$\mathrm{-16}$

121

ⓐ 1 ⓑ 33

ⓐ $\mathrm{-5}$ ⓑ 25

21

$\mathrm{-56}$

$\left(3+\left(\mathrm{-15}\right)\right)+7;-5$

$10-\left(\mathrm{-18}\right);28$

$\mathrm{-5}-\left(\mathrm{-30}\right);25$

$\mathrm{-3}·15;-45$

$\mathrm{-60}÷\left(\mathrm{-20}\right);3$

$\frac{\mathrm{-6}}{a+b}$

$\mathrm{-10}\left(p-q\right)$

$96\text{°}$

21

$\text{−}\mathrm{\$28}$

$187

$\text{−}\mathrm{\$3600}$

Answers may vary

Answers may vary

$\frac{6}{16},\frac{9}{24},\frac{12}{32}$ answers may vary

$\frac{10}{18},\frac{15}{27},\frac{20}{36}$ answers may vary

$-\frac{5}{11}$

$-\frac{12}{7}$

$\frac{10}{21}$

$-\frac{x}{4y}$

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

$\frac{27}{40}$

$\frac{1}{4}$