Equivalent Ratios worksheet for math practice, helping students understand ratios and fractions through fill-in-the-blank exercises.

Let's solve the Equivalent Ratios worksheet step by step. The goal is to find equivalent ratios for each given ratio and express them in fraction form.

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🔍 Understanding Equivalent Ratios

A ratio like 1:2 means "1 part to 2 parts." To find an equivalent ratio, you multiply or divide both numbers by the same value.

For example:
- 1:2 = 2:4 = 3:6 = 5:10 → all are equivalent because they represent the same fraction: $ \frac{1}{2} $

We’ll use this idea to complete each row.

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✔ Solving Each Problem

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#### 1. 1 : 2 = __ : 10 = 9 : ____
- First: $1:2 = ? : 10$
Multiply both sides by 5:
$1×5 = 5$, $2×5 = 10$ → So, 5:10

- Second: $1:2 = 9 : ?$
Multiply both sides by 9:
$1×9 = 9$, $2×9 = 18$ → So, 9:18

- Fraction: $ \frac{1}{2} $

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

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#### 2. 1 : 3 = __ : 15 = 2 : ____
- First: $1:3 = ? : 15$
Multiply by 5: $1×5=5$, $3×5=15$ → 5:15

- Second: $1:3 = 2 : ?$
Multiply by 2: $1×2=2$, $3×2=6$ → 2:6

- Fraction: $ \frac{1}{3} $

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

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#### 3. 1 : 4 = __ : 24 = 5 : ____
- First: $1:4 = ? : 24$
Multiply by 6: $1×6=6$, $4×6=24$ → 6:24

- Second: $1:4 = 5 : ?$
Multiply by 5: $1×5=5$, $4×5=20$ → 5:20

- Fraction: $ \frac{1}{4} $

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

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#### 4. 1 : 5 = __ : 35 = 3 : ____
- First: $1:5 = ? : 35$
Multiply by 7: $1×7=7$, $5×7=35$ → 7:35

- Second: $1:5 = 3 : ?$
Multiply by 3: $1×3=3$, $5×3=15$ → 3:15

- Fraction: $ \frac{1}{5} $

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

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#### 5. 1 : 6 = __ : 12 = 4 : ____
- First: $1:6 = ? : 12$
Multiply by 2: $1×2=2$, $6×2=12$ → 2:12

- Second: $1:6 = 4 : ?$
Multiply by 4: $1×4=4$, $6×4=24$ → 4:24

- Fraction: $ \frac{1}{6} $

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

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#### 6. 1 : 7 = __ : 21 = 6 : ____
- First: $1:7 = ? : 21$
Multiply by 3: $1×3=3$, $7×3=21$ → 3:21

- Second: $1:7 = 6 : ?$
Multiply by 6: $1×6=6$, $7×6=42$ → 6:42

- Fraction: $ \frac{1}{7} $

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

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#### 7. 1 : 8 = __ : 16 = 7 : ____
- First: $1:8 = ? : 16$
Multiply by 2: $1×2=2$, $8×2=16$ → 2:16

- Second: $1:8 = 7 : ?$
Multiply by 7: $1×7=7$, $8×7=56$ → 7:56

- Fraction: $ \frac{1}{8} $

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

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#### 8. 1 : 9 = __ : 72 = 6 : ____
- First: $1:9 = ? : 72$
Multiply by 8: $1×8=8$, $9×8=72$ → 8:72

- Second: $1:9 = 6 : ?$
Multiply by 6: $1×6=6$, $9×6=54$ → 6:54

- Fraction: $ \frac{1}{9} $

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

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✔ Final Answers:

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

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📝 Tips for Students:

- Think of the fraction form first (e.g., 1:2 = $ \frac{1}{2} $).
- Then scale up or down using multiplication/division.
- Always keep the same multiplier on both sides.

Let me know if you'd like a printable version or visual explanation! 😊