Chapter 1

ⓐ yes ⓑ yes ⓒ no ⓓ yes
ⓔ no

ⓐ no ⓑ yes ⓒ yes ⓓ no
ⓔ no

$2·2·2·2·5$

$2·2·3·5$

$36$

$72$

16

23

86

1

ⓐ 9 ⓑ 64 ⓒ 40

ⓐ 216 ⓑ 64 ⓒ 185

$10x^2+16x+17$

$12y^2+9y+7$

ⓐ $14x^2-13$ ⓑ $12x÷2$
ⓒ $z+13$ ⓓ $8x-18$

ⓐ $17y^2+19$ ⓑ $7y$
ⓒ $x+11$ ⓓ $11a-14$

ⓐ $4\left(p+q\right)$ ⓑ $4p+q$

ⓐ $2x-8$ ⓑ $2\left(x-8\right)$

$w-7$

$l-6$

$4q-8$

$7n+3$

ⓐ $=$ ⓑ $>$ ⓒ $<$
ⓓ $=$

ⓐ $>$ ⓑ $=$ ⓒ $>$
ⓓ $<$

16

9

ⓐ $\mathrm{-6}$ ⓑ 2 ⓒ $\mathrm{-2}$

ⓐ $\mathrm{-7}$ ⓑ 3 ⓒ $\mathrm{-3}$

ⓐ 2 ⓑ $\mathrm{-2}$ ⓒ $\mathrm{-10}$ ⓓ 10

ⓐ 3 ⓑ $\mathrm{-3}$ ⓒ $\mathrm{-11}$ ⓓ 11

ⓐ $8,8$ ⓑ $\mathrm{-18},$ $\mathrm{-18}$
ⓒ $19,19$ ⓓ $\mathrm{-4},$ $\mathrm{-4}$

ⓐ $8,8$ ⓑ $\mathrm{-22},$ $\mathrm{-22}$
ⓒ $23,23$ ⓓ $3,3$

3

13

ⓐ 23 ⓑ 60 ⓒ $\mathrm{-63}$ ⓓ $\mathrm{-9}$

ⓐ 39 ⓑ 39 ⓒ −28 ⓓ −7

ⓐ 81 ⓑ $\mathrm{-81}$

ⓐ 49 ⓑ $\mathrm{-49}$

ⓐ 4 ⓑ 21

ⓐ 9 ⓑ 6

31

67

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

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

The difference in temperatures was 45 degrees.

The difference in temperatures was 9 degrees.

$-\frac{23}{40}$

$-\frac{5}{8}$

$\mathrm{-33}a$

$\mathrm{-26}b$

$\frac{4}{15}$

$\frac{2}{3}$

$\frac{3}{4b}$

$\frac{4}{q}$

$\frac{79}{60}$

$\frac{103}{60}$

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

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

4

2

$\frac{1}{90}$

272

2

$\frac{2}{7}$

$-\frac{1}{2}$

$\frac{2}{3}$

ⓐ $6.58$ ⓑ $6.6$ ⓒ 7

ⓐ $15.218$ ⓑ $15.22$
ⓒ $15.2$

ⓐ $\mathrm{-16.49}$ ⓑ $\mathrm{-0.42}$

ⓐ $\mathrm{-23.593}$ ⓑ $\mathrm{-12.58}$

$\mathrm{-27.4815}$

$\mathrm{-87.6148}$

ⓐ 25.8 ⓑ 258 ⓒ 2,580

ⓐ 142 ⓑ 1,420 ⓒ 14,200

$587.3$

$34.25$

ⓐ $\frac{117}{500}$ ⓑ $\mathrm{-0.875}$

ⓐ $\frac{3}{125}$ ⓑ $\mathrm{-0.375}$

ⓐ 0.09, 0.87, 0.039 ⓑ 17%, 175%, 8.25%

ⓐ 0.03, 0.91, 0.083 ⓑ 41%, 225%, 9.25%

ⓐ 6 ⓑ 13 ⓒ $\mathrm{-15}$

ⓐ 4 ⓑ 14 ⓒ $\mathrm{-10}$

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

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

ⓐ

ⓑ

ⓐ

ⓑ

$32r+29s$

$41m+6n$

$1\frac{7}{15}$

$1\frac{2}{9}$

$\mathrm{-48}a$

$\mathrm{-92}x$

$\frac{5}{49}$

$\frac{11}{25}$

ⓐ 0 ⓑ undefined

ⓐ 0 ⓑ undefined

$4x+8$

$6x+42$

$5y+3$

$4n+9$

$70+15p$

$4+35d$

$\mathrm{-10}+15a$

$\mathrm{-56}+105y$

$\text{−}z+11$

$\text{−}x+4$

$3-3x$

$2x-20$

$5x-66$

$7x-13$

Divisible by 2, 3, 6

Divisible by 2

Divisible by 3, 5

$2·43$

$5·7·13$

$2·2·2·2·3·3·3$

24

280

440

5

58

29

149

50

5

ⓐ 64 ⓑ 16 ⓒ 7

21

9

$10x+6$

$22a+1$

$17x^2+20x+16$

ⓐ $5x^2-6xy$ ⓑ $\frac{6y^2}{5x}$
ⓒ $y^2+21$ ⓓ $81x^2-6x$

ⓐ $4a{b}^2+3a^{2}b$ ⓑ $20x{y}^2$
ⓒ $m+15$ ⓓ $121x^2-9x$

ⓐ $8\left(y-9\right)$ ⓑ $8y-9$

ⓐ $5\left(3x+y\right)$ ⓑ $15x+y$

$2c+14$

$3n-7$

Answers will vary.

Answers will vary.

ⓐ $>$ ⓑ $>$ ⓒ $>$ ⓓ $>$

ⓐ $=$ ⓑ $=$ ⓒ $>$ ⓓ $=$

0

8

15

1

ⓐ $\mathrm{-11}$ ⓑ $\mathrm{-3}$ ⓒ $3$

32

$\mathrm{-22}$

$29$

ⓐ 6 ⓑ $\mathrm{-6}$ ⓒ $\mathrm{-20}$ ⓓ $20$

$\mathrm{-59}$

22

ⓐ 16 ⓑ 16

ⓐ 45 ⓑ 45

0

4

6

ⓐ $\mathrm{-32}$ ⓑ $\mathrm{-65}$ ⓒ $\mathrm{-4}$
ⓓ $13$

ⓐ $\mathrm{-4}$ ⓑ $\mathrm{-12}$ ⓒ $\mathrm{-39}$
ⓓ $14$

ⓐ $64$ ⓑ $\mathrm{-64}$

$\mathrm{-47}$

$90$

$9$

$41$

$\mathrm{-9}$

$\mathrm{-29}$

$1$

$\mathrm{-3}$

$5$

ⓐ $\mathrm{-47}$ ⓑ $16$

$121$

$\mathrm{-56}$

$6$

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

ⓐ $10-\left(\mathrm{-18}\right);28$
ⓑ $\mathrm{-25}-11;-36$

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

$96\text{°}$

21 yards

$\text{−}\text{\$}28$

Answers will vary.

Answers will vary.

$-\frac{12}{7}$

$\frac{10}{21}$

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

$-\frac{21a^2}{11b^2}$

$\frac{1}{3}$

$-\frac{21}{50}$

$\frac{11}{30}$

$9n$

$\frac{33}{4x}$

$-\frac{4}{9}$

$\frac{10u}{9v}$

$-\frac{1}{16}$

$-\frac{10}{9}$

$-\frac{2}{5}$

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

$\frac{29}{24}$

$\frac{1}{48}$

$\frac{17}{105}$

$-\frac{53}{40}$

$\frac{1}{12}$

$\frac{4x+3}{12}$

ⓐ $\frac{5}{6}$ ⓑ $4$

ⓐ $\frac{25n}{16}$ ⓑ $\frac{25n-16}{30}$

ⓐ $\frac{\mathrm{-8}x-15}{18}$ ⓑ $-\frac{10k}{27}$

ⓐ $\frac{\mathrm{-5}\left(a+1\right)}{3}$ ⓑ $a$

$\frac{9}{7}$

$\mathrm{-8}$

$\frac{11}{6}$

$\frac{5}{2}$

$54$

$\frac{49}{25}$

$\frac{15}{4}$

$\frac{5}{21}$

$\frac{5}{4}$

$\frac{1}{24}$

$\frac{\mathrm{-28}-15y}{60}$

$\frac{33}{64}$

$\frac{7}{9}$

$\mathrm{-5}$

$\frac{23}{24}$

$\frac{11}{5}$

$1$

$\frac{13}{3}$

ⓐ $\frac{1}{5}$ ⓑ $\frac{6}{5}$

$-\frac{1}{9}$

$-\frac{5}{11}$

Answers will vary.

Answers will vary.

ⓐ 5.78 ⓑ 5.8 ⓒ 6

ⓐ 0.30 ⓑ 0.3 ⓒ 0

ⓐ 63.48 ⓑ 63.5 ⓒ 63

$\mathrm{-40.91}$

$\mathrm{-7.22}$

$\mathrm{-27.5}$

$102.212$

$51.31$

$\mathrm{-4.89}$

$\mathrm{-1200.47982}$

$337.8914$

$1.305$

$92.4$

2.5

55200

$\text{\$}2.44$

$\mathrm{-4.8}$

$2.08$

$\frac{1}{25}$

$\frac{19}{200}$

$0.85$

$\mathrm{-12.4}$

$0.71$

$0.393$

$156\%$

$6.25\%$

8

12

$\mathrm{-10}$

ⓐ $0,\sqrt{36},9$ ⓑ $\mathrm{-8},0,\sqrt{36},9$ ⓒ $\mathrm{-8},0,\frac{12}{5},\sqrt{36},9$ ⓓ $\mathrm{1.95286...},$ ⓔ $\mathrm{-8},0,\mathrm{1.95286...},\frac{12}{5},\sqrt{36},9$

ⓐ none ⓑ $\text{−}\sqrt{100},\mathrm{-7},\mathrm{-1}$
ⓒ $\text{−}\sqrt{100},\mathrm{-7},-\frac{8}{3},\mathrm{-1},0.77,3\frac{1}{4}$
ⓓ none
ⓔ $\text{−}\sqrt{100},\mathrm{-7},-\frac{8}{3},\mathrm{-1},0.77,3\frac{1}{4}$

Answers will vary.

Answers will vary.

$27m+\left(\mathrm{-21}n\right)$

$\frac{5}{4}g+\frac{1}{2}h$

$2.43p+8.26q$

$\mathrm{-63}$

$1\frac{5}{6}$

$17$

$14.88$

$10p$

$44$

$\frac{7}{8}$

$d$

$\frac{49}{11}$

0

undefined

undefined

$32y+72$

$6c-78$

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

$5y-3$

$3+8r$

$36d+90$

$rs-18r$

$yp+4p$

$\mathrm{-28}p-7$

$\mathrm{-3}x+18$

$\mathrm{-3}x+7$

$\mathrm{-3}y-8$

$\mathrm{-33}c+26$

$\text{−}a+19$

$4m-10$

$72x-25$

$22n+9$

$6c+34$

$12y+63$

Answers will vary.

Answers will vary.

Divisible by $2,3,5,6,10$

120

4

3

$6x^2-x+5$

ⓐ $11\left(y-2\right)$ ⓑ $11y-2$

ⓐ $=$ ⓑ $=$ ⓒ $>$ ⓓ $=$

$\mathrm{-9}$

ⓐ 8 ⓑ $\mathrm{-8}$ ⓒ $\mathrm{-22}$ ⓓ 22

ⓐ 40 ⓑ 40

ⓐ $\mathrm{-3}$ ⓑ $\mathrm{-15}$ ⓒ $\mathrm{-56}$ ⓓ 17

28

$\mathrm{-12}$

9

$\left(\mathrm{-4}+\left(\mathrm{-9}\right)\right)+23;10$

${46}^{\text{°}}$

$-\frac{15x^3}{11y^2}$

$\frac{8x}{15y}$

$\frac{31}{36}$

ⓐ $\frac{11}{8}$ ⓑ $\frac{5}{6}$

$-\frac{1}{6}$

75

$-\frac{1}{5}$

$6.17$

$96.978$

488.1813

$56.3$

$\mathrm{-2.3}$

$-\frac{48}{5}$

$1.\overline{27}$

$4.75\%$

no real number

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

$1\frac{11}{15}$

$\frac{9}{17}$

undefined

$8b+10$

$xp-5p$

$\mathrm{-6}x-6$

$6y+16$

$7n+7$

$\mathrm{-8}-11;-19$

$\left(\mathrm{-8}-\left(\mathrm{-3}\right)\right)+5;0$

ⓐ $28.15$ ⓑ $28.146$

1

$\mathrm{-8}$

$\frac{15}{17}$

$-\frac{5}{3}$

$3$

$-\frac{7}{6}$

$\mathrm{-65.4}$

−160

$1\frac{8}{13}$

ⓐ 0 ⓑ undefined

$13y-3$