Question

1–9, write three ratios that are equivalent to the given ratio.

1. \\(\frac{3}{5}\\) \t\t\t\t2. \\(\frac{4}{8}\\) \t\t\t\t3. \\(\frac{6}{18}\\)

1. 8:10 \t\t\t\t5. 6:8 \t\t\t\t6. 10:12

1. 12 to 18 \t\t\t\t8. 16 to 18 \t\t\t\t9. 5 to 25

10–15, use = or \\(\
eq\\) to show whether the ratios are equivalent.

1. 3:12 \\(\bigcirc\\) 6:24 \t\t\t11. \\(\frac{28}{16}\\) \\(\bigcirc\\) \\(\frac{7}{4}\\) \t\t\t12. 4 to 20 \\(\bigcirc\\) 1 to

1. \\(\frac{4}{6}\\) \\(\bigcirc\\) \\(\frac{6}{9}\\) \t\t\t14. 27 to 9 \\(\bigcirc\\) 24 to 4 \t\t\t15. 6:10 \\(\bigcirc\\) 8:15

16 and 17, complete the tables with equivalent ratios.

1. a wildlife conservancy maintains a ratio of 2 squirrels for every 8 birds. how many birds would there be if there were 15 squirrels?

animals
birds	8	\\(\square\\)	20	40	\\(\square\\)

1. at rolling hills middle school, the ratio of the total number of students to the number of students with pets is 3 to 1. if there are 243 students at the school, how many students have pets?

number of students with pets	1	3	9	\\(\square\\)	81

Explanation:

1-9: Equivalent Ratios

Step1: Multiply/divide numerator/denominator by same non-zero number.

For each ratio, scale by 2, 3, 4 (or simplify first then scale).
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1. $\frac{3}{5}$

Step1: Scale by 2

$\frac{3\times2}{5\times2}=\frac{6}{10}$

Step2: Scale by 3

$\frac{3\times3}{5\times3}=\frac{9}{15}$

Step3: Scale by 4

$\frac{3\times4}{5\times4}=\frac{12}{20}$

2. $\frac{4}{8}$

Step1: Simplify first

$\frac{4\div4}{8\div4}=\frac{1}{2}$

Step2: Scale simplified by 3

$\frac{1\times3}{2\times3}=\frac{3}{6}$

Step3: Scale simplified by 5

$\frac{1\times5}{2\times5}=\frac{5}{10}$

3. $\frac{6}{18}$

Step1: Simplify first

$\frac{6\div6}{18\div6}=\frac{1}{3}$

Step2: Scale simplified by 2

$\frac{1\times2}{3\times2}=\frac{2}{6}$

Step3: Scale simplified by 4

$\frac{1\times4}{3\times4}=\frac{4}{12}$

4. $8:10$

Step1: Simplify first

$8\div2:10\div2=4:5$

Step2: Scale by 2

$8\times2:10\times2=16:20$

Step3: Scale by 3

$8\times3:10\times3=24:30$

5. $6:8$

Step1: Simplify first

$6\div2:8\div2=3:4$

Step2: Scale by 2

$6\times2:8\times2=12:16$

Step3: Scale by 3

$6\times3:8\times3=18:24$

6. $10:12$

Step1: Simplify first

$10\div2:12\div2=5:6$

Step2: Scale by 2

$10\times2:12\times2=20:24$

Step3: Scale by 3

$10\times3:12\times3=30:36$

7. $12$ to $18$

Step1: Simplify first

$12\div6:18\div6=2$ to $3$

Step2: Scale by 2

$12\times2:18\times2=24$ to $36$

Step3: Scale by 3

$12\times3:18\times3=36$ to $54$

8. $16$ to $18$

Step1: Simplify first

$16\div2:18\div2=8$ to $9$

Step2: Scale by 2

$16\times2:18\times2=32$ to $36$

Step3: Scale by 3

$16\times3:18\times3=48$ to $54$

9. $5$ to $25$

Step1: Simplify first

$5\div5:25\div5=1$ to $5$

Step2: Scale by 2

$5\times2:25\times2=10$ to $50$

Step3: Scale by 3

$5\times3:25\times3=15$ to $75$

Step1: Simplify both ratios to lowest terms.

Step2: Compare simplified forms; mark $=$ if equal, $

eq$ if not.
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10. $3:12$ $\bigcirc$ $6:24$

Step1: Simplify $3:12$

$3\div3:12\div3=1:4$

Step2: Simplify $6:24$

$6\div6:24\div6=1:4$

Step3: Compare

$1:4 = 1:4$

11. $\frac{28}{16}$ $\bigcirc$ $\frac{7}{4}$

Step1: Simplify $\frac{28}{16}$

$\frac{28\div4}{16\div4}=\frac{7}{4}$

Step2: Compare

$\frac{7}{4} = \frac{7}{4}$

12. $4$ to $20$ $\bigcirc$ $1$ to $4$

Step1: Simplify $4$ to $20$

$4\div4:20\div4=1$ to $5$

Step2: Compare

$1$ to $5
eq 1$ to $4$

13. $\frac{4}{6}$ $\bigcirc$ $\frac{6}{9}$

Step1: Simplify $\frac{4}{6}$

$\frac{4\div2}{6\div2}=\frac{2}{3}$

Step2: Simplify $\frac{6}{9}$

$\frac{6\div3}{9\div3}=\frac{2}{3}$

Step3: Compare

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

14. $27$ to $9$ $\bigcirc$ $24$ to $4$

Step1: Simplify $27$ to $9$

$27\div9:9\div9=3$ to $1$

Step2: Simplify $24$ to $4$

$24\div4:4\div4=6$ to $1$

Step3: Compare

$3$ to $1
eq 6$ to $1$

15. $6:10$ $\bigcirc$ $8:15$

Step1: Simplify $6:10$

$6\div2:10\div2=3:5$

Step2: Simplify $8:15$

$8:15$ (already simplest)

Step3: Compare

$3:5
eq 8:15$

Step1: Find ratio: $\frac{\text{Squirrels}}{\text{Birds}}=\frac{2}{8}=\frac{1}{4}$, so $\text{Birds}=4\times\text{Squirrels}$

Step2: Calculate missing birds for 4 squirrels

$4\times4=16$

Step3: Calculate missing squirrels for 40 birds

$\frac{40}{4}=10$

Step4: Calculate birds for 15 squirrels

$15\times4=60$

Answer:

(1-9):

1. $\frac{6}{10}$, $\frac{9}{15}$, $\frac{12}{20}$
2. $\frac{1}{2}$, $\frac{3}{6}$, $\frac{5}{10}$
3. $\frac{1}{3}$, $\frac{2}{6}$, $\frac{4}{12}$
4. $4:5$, $16:20$, $24:30$
5. $3:4$, $12:16$, $18:24$
6. $5:6$, $20:24$, $30:36$
7. $2$ to $3$, $24$ to $36$, $36$ to $54$
8. $8$ to $9$, $32$ to $36$, $48$ to $54$
9. $1$ to $5$, $10$ to $50$, $15$ to $75$

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10-15: Equivalent Ratio Check