Chapter 4

$11$

$-2>-5$

$2\cdot 2\cdot 2\cdot 2\cdot 3$

Answers may vary. Acceptable answers include $\frac{10}{12},\frac{15}{18},\frac{50}{60},$ etc.

$3$

$\frac{1}{12}$

$\frac{13}{5}$

$5x+5$

$\frac{5}{6}$

$\frac{10}{12},\frac{15}{18}$

$2$

$2\frac{3}{4}$

$\frac{7}{2}$

$1$

$y=6$

$-6$

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

$\frac{13}{8}=1\frac{5}{8}$

$1\frac{2}{7}$

$1\frac{3}{4}$

$\frac{11}{8}$

$\frac{11}{6}$

$1\frac{6}{7}.$

$1\frac{5}{9}$

$3\frac{2}{7}$

$4\frac{4}{11}$

$\frac{26}{7}$

$\frac{23}{8}$

$\frac{50}{11}$

$\frac{34}{3}$

2

3

Correct answers include $\frac{6}{10},\frac{9}{15},$ and $\frac{12}{20}.$

Correct answers include $\frac{8}{10},\frac{12}{15},$ and $\frac{16}{20}.$

$\frac{18}{21}$

$\frac{30}{100}$

$\frac{2}{3}$

$\frac{3}{4}$

$-\frac{3}{4}$

$-\frac{2}{3}$

$-\frac{9}{7}$

$-\frac{9}{5}$

$\frac{23}{40}$

$\frac{5}{8}$

$\frac{x}{y}$

$\frac{a}{b}$

$\frac{3}{10}$

$\frac{5}{12}$

$\frac{2}{15}$

$\frac{21}{40}$

$\frac{5}{14}$

$\frac{14}{27}$

$-\frac{4}{21}$

$-\frac{3}{16}$

2

2

6

6

$-\frac{9}{14}$

$-\frac{10}{21}$

$\frac{21}{5p}$

$\frac{15}{8q}$

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{4}{15}$

$\frac{2}{3}$

2

$\frac{9}{4}$

−15

$-\frac{85}{6}$

$\frac{5}{8}$

$\frac{7}{8}$

2

$\frac{5}{2}$

$\frac{9s}{14}$

$\frac{5y}{6}$

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

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

$\frac{4}{5}$

$\frac{11}{14}$

$-\frac{2}{7}$

$-\frac{10}{3}$

$\frac{3}{4b}$

$\frac{4}{q}$

$\frac{25}{49}.$

$\frac{1}{2}$

$-\frac{3}{5},\frac{3}{\mathrm{-5}}$

$\frac{\mathrm{-2}}{7},\frac{2}{\mathrm{-7}}$

$\frac{10}{9}$

$\frac{1}{2}$

$\frac{\mathrm{-3}}{4}$

$-\frac{2}{3}$

$\frac{2}{9}$

$\frac{8}{5}$

4

2

$\frac{5}{8}$

$\frac{5}{6}$

$\frac{5}{6}$

1

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

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

$\frac{1}{d}$

$\frac{3}{m}$

$\frac{9p}{8}$

$\frac{9q}{5}$

$-\frac{2}{3}$

$-\frac{2}{3}$

$\frac{3}{8}$, models may differ.

$\frac{1}{6}$, models may differ

$\frac{3}{7}$

$\frac{1}{2}$

$\frac{x-2}{7}$

$\frac{y-13}{14}$

$-\frac{16}{x}$

$-\frac{22}{a}$

−1

$-\frac{2}{3}$

60

15

96

224

$\frac{9}{12},\frac{10}{12}$

$-\frac{35}{60},\frac{44}{60}$

$\frac{52}{96},\frac{51}{96}$

$\frac{72}{224},\frac{189}{224}$

$\frac{7}{12}$

$\frac{7}{10}$

$\frac{5}{8}$

$\frac{1}{2}$

$\frac{79}{60}$

$\frac{103}{60}$

$\frac{1}{96}$

$\frac{75}{224}$

$\frac{37}{210}$

$-\frac{25}{96}$

$\frac{3y+14}{18}$

$\frac{5x+14}{30}$

$\frac{1}{90}$

272

2

$\frac{2}{7}$

$-\frac{3}{4}$

$-\frac{23}{8}$

$-\frac{1}{2}$

$\frac{2}{3}$

$-\frac{5}{2}$

$\frac{3}{2}$

5

5

$4\frac{2}{3}$

$3\frac{1}{2}$

$5\frac{6}{7}$

$7\frac{9}{11}$

$16\frac{1}{2}$

$15\frac{1}{3}$

$9\frac{1}{3}$

$6\frac{3}{5}$

$\frac{3}{4}$

$\frac{4}{5}$

$\frac{9}{5}$

$\frac{5}{3}$

$\frac{2}{3}$

$\frac{3}{4}$

$\frac{2}{3}$

$\frac{2}{5}$

$2\frac{2}{3}$

$1\frac{5}{7}$

$2\frac{2}{3}$

$1\frac{5}{7}$

$6\frac{7}{12}$

$12\frac{3}{10}$

$4\frac{7}{10}$

$2\frac{11}{12}$

$-\frac{41}{8}$

$-\frac{757}{63}$

$-\frac{1}{2}$

$-\frac{4}{15}$

−1

$-\frac{6}{7}$

$-\frac{19}{3}$

$\frac{23}{2}$

−125

−243

245

132

−48

23

35

18

−91

−108

$\frac{n}{7}=\mathrm{-21};n=\mathrm{-147}$

$\frac{n}{8}=\mathrm{-56};n=\mathrm{-448}$

$\frac{q}{\mathrm{-8}}=72;q=\mathrm{-576}$

$\frac{p}{\mathrm{-9}}=81;p=\mathrm{-729}$

$\frac{2}{5}f=16;f=40$

$\frac{3}{4}f=21;f=28$

$\frac{n}{\frac{2}{3}}=\frac{5}{12};n=\frac{5}{18}$

$\frac{c}{\frac{3}{8}}=\frac{4}{9};c=\frac{1}{6}$

$\frac{5}{8}+x=\frac{1}{4};x=-\frac{3}{8}$

$1\frac{3}{4}-x=\frac{5}{6};x=\frac{11}{12}$

$1\frac{2}{3}$

$2\frac{3}{5}$

$3\frac{1}{9}$

$3\frac{2}{15}$

$\frac{7}{5}$

$\frac{17}{6}$

$\frac{19}{7}$

$\frac{32}{9}$

4

9

9

Answers may vary. Correct answers include $\frac{2}{6},\frac{3}{9},\frac{4}{12}.$

Answers may vary. Correct answers include $\frac{10}{12},\frac{15}{18},\frac{20}{24}.$

Answers may vary. Correct answers include $\frac{10}{18},\frac{15}{27},\frac{20}{36}.$

<

>

<

<

Answers will vary.

$\frac{1}{3}$

$\frac{3}{4}$

$-\frac{5}{11}$

$-\frac{12}{7}$

$\frac{10}{21}$

$-\frac{7}{8}$

$\frac{x}{y}$

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

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

$\frac{1}{3}$

$\frac{5}{18}$

$\frac{2}{15}$

$\frac{27}{40}$

$\frac{1}{4}$

$-\frac{1}{6}$

$-\frac{2}{9}$

$-\frac{21}{50}$

$\frac{11}{30}$

$\frac{20}{11}$

9n

7p

−34

$\frac{3}{8}$

$\frac{8}{27}$

$\frac{1296}{625}$

$\frac{4}{3}$

$-\frac{17}{5}$

$\frac{8}{11}$

$-\frac{1}{19}$

1

4

12

4

$\frac{16}{15}$

$-\frac{5}{4}$

1

$\frac{18}{5y}$

$\frac{25}{2c}$

$-\frac{3}{4}$

$\frac{2}{9}$

$\frac{14r}{15s}$

−12

$-\frac{1}{25}$

9

$\frac{8}{7}$

• ⓐ $4·\frac{2}{3}$ cups$=\frac{8}{3}$ cups$=2\frac{2}{3}$ cups$$
• ⓑ Answers will vary.

$\frac{1}{8}$ yard

Answers will vary.

Answers will vary.

$\frac{44}{21}$

$\frac{35}{8}$

$-\frac{16}{3}$

$-\frac{63}{16}$

$\frac{3}{2}$

$-\frac{4}{3}$

2

5

$\frac{7v}{13}$

$\frac{a}{b}$

$\frac{A}{3-B}$

$\frac{3}{2}$

$-\frac{15}{22}$

$-\frac{3}{10}$

$\frac{1}{6}$

$\frac{3r}{5s}$

$\frac{9}{2y}$

28

$-\frac{1}{18}$

$\frac{\mathrm{-4}}{9},-\frac{4}{9}$

$\frac{13}{\mathrm{-6}},\frac{\mathrm{-13}}{6}$

$\frac{12}{7}$

$\frac{5}{2}$

$\frac{23}{4}$

$-\frac{1}{3}$

$\frac{4}{5}$

$-\frac{1}{2}$

2

$\frac{5}{6}$

$\frac{26}{25}$

$\frac{11}{6}$

$\frac{5}{2}$

−10

−2

$\frac{51}{20}$

$\frac{18}{7}$

Answers will vary.

Answers will vary.

$\frac{7}{10}$

$\frac{3}{4}$

$\frac{7}{9}$

$\frac{16}{15}$

$\frac{y+2}{3}$

$\frac{14}{q}$

$\frac{9a}{7}$

$\frac{\mathrm{-4}x}{5}$

$-\frac{3}{4}$

$-\frac{7}{8}$

$\frac{8}{19}$

$-\frac{13}{12}$

$\frac{1}{2}$

$\frac{1}{5}$

$\frac{5}{13}$

$\frac{1}{6}$

$-\frac{8}{3}$

$\frac{x-8}{19}$

$\frac{11z-8}{13}$

$-\frac{14}{c}$

$-\frac{55}{v}$

$\frac{3d}{11}$

$-\frac{14s}{3}$

$\frac{2}{7}$

$-\frac{3}{11}$

$-\frac{1}{8}$

$\frac{6-s}{11}$

$-\frac{2}{9}$

$\frac{49}{27}$

$\frac{1}{4}$ cup

No, adding up the number of pieces gives $\frac{13}{12}$, which is greater than 1. (Answers may vary.)

20

48

240

245

60

$\frac{5}{20},\frac{4}{20}$

$\frac{14}{24},\frac{15}{24}$

$\frac{33}{48},-\frac{20}{48}$

$\frac{20}{60},\frac{45}{60},\frac{36}{60}$

$\frac{9}{20}$

$\frac{11}{24}$