Ratio and Proportion Worksheets | Definitions, Examples, Activities - Free Printable

Let's solve the Equivalent Ratios worksheet step by step. The goal is to find equivalent ratios by scaling up or down using multiplication or division, and then express each ratio as a fraction.

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🔍 Understanding Equivalent Ratios

A ratio like $1:2$ means "1 part to 2 parts". To find an equivalent ratio, we multiply or divide both sides by the same number.

For example:
- $1:2 = 5:10$ because $1 \times 5 = 5$, $2 \times 5 = 10$
- $1:2 = 9:18$ because $1 \times 9 = 9$, $2 \times 9 = 18$

We’ll apply this logic to each problem.

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✔ Solutions with Explanation

#### 1. $1:2 = \_\_ : 10 = 9 : \_\_$
- First blank: $1:2 = ? : 10$
Multiply both sides by 5: $1 \times 5 = 5$, $2 \times 5 = 10$ → $5:10$
- Second blank: $1:2 = 9 : ?$
Multiply both sides by 9: $1 \times 9 = 9$, $2 \times 9 = 18$ → $9:18$

✔ Answer: $1:2 = \boxed{5} : 10 = 9 : \boxed{18}$
Fraction: $\frac{1}{2} = \frac{5}{10} = \frac{9}{18}$

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#### 2. $1:3 = \_\_ : 15 = 2 : \_\_$
- $1:3 = ? : 15$
Multiply by 5: $1 \times 5 = 5$, $3 \times 5 = 15$ → $5:15$
- $1:3 = 2 : ?$
Multiply by 2: $1 \times 2 = 2$, $3 \times 2 = 6$ → $2:6$

✔ Answer: $1:3 = \boxed{5} : 15 = 2 : \boxed{6}$
Fraction: $\frac{1}{3} = \frac{5}{15} = \frac{2}{6}$

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#### 3. $1:4 = \_\_ : 24 = 5 : \_\_$
- $1:4 = ? : 24$
Multiply by 6: $1 \times 6 = 6$, $4 \times 6 = 24$ → $6:24$
- $1:4 = 5 : ?$
Multiply by 5: $1 \times 5 = 5$, $4 \times 5 = 20$ → $5:20$

✔ Answer: $1:4 = \boxed{6} : 24 = 5 : \boxed{20}$
Fraction: $\frac{1}{4} = \frac{6}{24} = \frac{5}{20}$

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#### 4. $1:5 = \_\_ : 35 = 3 : \_\_$
- $1:5 = ? : 35$
Multiply by 7: $1 \times 7 = 7$, $5 \times 7 = 35$ → $7:35$
- $1:5 = 3 : ?$
Multiply by 3: $1 \times 3 = 3$, $5 \times 3 = 15$ → $3:15$

✔ Answer: $1:5 = \boxed{7} : 35 = 3 : \boxed{15}$
Fraction: $\frac{1}{5} = \frac{7}{35} = \frac{3}{15}$

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#### 5. $1:6 = \_\_ : 12 = 4 : \_\_$
- $1:6 = ? : 12$
Multiply by 2: $1 \times 2 = 2$, $6 \times 2 = 12$ → $2:12$
- $1:6 = 4 : ?$
Multiply by 4: $1 \times 4 = 4$, $6 \times 4 = 24$ → $4:24$

✔ Answer: $1:6 = \boxed{2} : 12 = 4 : \boxed{24}$
Fraction: $\frac{1}{6} = \frac{2}{12} = \frac{4}{24}$

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#### 6. $1:7 = \_\_ : 21 = 6 : \_\_$
- $1:7 = ? : 21$
Multiply by 3: $1 \times 3 = 3$, $7 \times 3 = 21$ → $3:21$
- $1:7 = 6 : ?$
Multiply by 6: $1 \times 6 = 6$, $7 \times 6 = 42$ → $6:42$

✔ Answer: $1:7 = \boxed{3} : 21 = 6 : \boxed{42}$
Fraction: $\frac{1}{7} = \frac{3}{21} = \frac{6}{42}$

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#### 7. $1:8 = \_\_ : 16 = 7 : \_\_$
- $1:8 = ? : 16$
Multiply by 2: $1 \times 2 = 2$, $8 \times 2 = 16$ → $2:16$
- $1:8 = 7 : ?$
Multiply by 7: $1 \times 7 = 7$, $8 \times 7 = 56$ → $7:56$

✔ Answer: $1:8 = \boxed{2} : 16 = 7 : \boxed{56}$
Fraction: $\frac{1}{8} = \frac{2}{16} = \frac{7}{56}$

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#### 8. $1:9 = \_\_ : 72 = 6 : \_\_$
- $1:9 = ? : 72$
Multiply by 8: $1 \times 8 = 8$, $9 \times 8 = 72$ → $8:72$
- $1:9 = 6 : ?$
Multiply by 6: $1 \times 6 = 6$, $9 \times 6 = 54$ → $6:54$

✔ Answer: $1:9 = \boxed{8} : 72 = 6 : \boxed{54}$
Fraction: $\frac{1}{9} = \frac{8}{72} = \frac{6}{54}$

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✔ Final Answers:

| Problem | Equivalent Ratios | Fraction |
|--------|-------------------|---------|
| 1. | $1:2 = \boxed{5} : 10 = 9 : \boxed{18}$ | $\frac{1}{2} = \frac{5}{10} = \frac{9}{18}$ |
| 2. | $1:3 = \boxed{5} : 15 = 2 : \boxed{6}$ | $\frac{1}{3} = \frac{5}{15} = \frac{2}{6}$ |
| 3. | $1:4 = \boxed{6} : 24 = 5 : \boxed{20}$ | $\frac{1}{4} = \frac{6}{24} = \frac{5}{20}$ |
| 4. | $1:5 = \boxed{7} : 35 = 3 : \boxed{15}$ | $\frac{1}{5} = \frac{7}{35} = \frac{3}{15}$ |
| 5. | $1:6 = \boxed{2} : 12 = 4 : \boxed{24}$ | $\frac{1}{6} = \frac{2}{12} = \frac{4}{24}$ |
| 6. | $1:7 = \boxed{3} : 21 = 6 : \boxed{42}$ | $\frac{1}{7} = \frac{3}{21} = \frac{6}{42}$ |
| 7. | $1:8 = \boxed{2} : 16 = 7 : \boxed{56}$ | $\frac{1}{8} = \frac{2}{16} = \frac{7}{56}$ |
| 8. | $1:9 = \boxed{8} : 72 = 6 : \boxed{54}$ | $\frac{1}{9} = \frac{8}{72} = \frac{6}{54}$ |

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💡 Tips for Students:

- Always check what number you multiplied (or divided) the first term by.
- Then apply that same multiplier to the second term.
- Think in fractions: $1:2 = \frac{1}{2}$, so any equivalent ratio should simplify to $\frac{1}{2}$.

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