Equivalent fractions practice worksheet with shaded circles and fill-in-the-blank problems.

Let's solve the Equivalent Fractions worksheet step by step. The goal is to fill in the missing numerators or denominators so that the fractions on both sides of the equation are equivalent.

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🔍 Understanding Equivalent Fractions

Two fractions are equivalent if they represent the same value, even if their numerators and denominators are different.
To find an equivalent fraction, you can:
- Multiply or divide both the numerator and denominator by the same number.

For example:
- $ \frac{1}{2} = \frac{2}{4} $ because $ 1 \times 2 = 2 $ and $ 2 \times 2 = 4 $

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✔ Let’s solve each row:

#### Row 1:
1. $ \frac{1}{2} = \frac{?}{4} $
→ Multiply numerator and denominator by 2: $ \frac{1 \times 2}{2 \times 2} = \frac{2}{4} $
✔ Answer: 2

2. $ \frac{1}{3} = \frac{?}{6} $
→ Multiply by 2: $ \frac{1 \times 2}{3 \times 2} = \frac{2}{6} $
✔ Answer: 2

3. $ \frac{2}{6} = \frac{?}{12} $
→ Multiply by 2: $ \frac{2 \times 2}{6 \times 2} = \frac{4}{12} $
✔ Answer: 4

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#### Row 2:
4. $ \frac{1}{2} = \frac{?}{8} $
→ Multiply by 4: $ \frac{1 \times 4}{2 \times 4} = \frac{4}{8} $
✔ Answer: 4

5. $ \frac{1}{3} = \frac{?}{12} $
→ Multiply by 4: $ \frac{1 \times 4}{3 \times 4} = \frac{4}{12} $
✔ Answer: 4

6. $ \frac{2}{6} = \frac{?}{3} $
→ Simplify $ \frac{2}{6} = \frac{1}{3} $, so $ \frac{1}{3} = \frac{1}{3} $ → numerator is 1
✔ Answer: 1

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#### Row 3:
7. $ \frac{2}{4} = \frac{?}{8} $
→ Multiply by 2: $ \frac{2 \times 2}{4 \times 2} = \frac{4}{8} $
✔ Answer: 4

8. $ \frac{4}{8} = \frac{?}{2} $
→ Simplify $ \frac{4}{8} = \frac{1}{2} $, so $ \frac{1}{2} = \frac{1}{2} $ → numerator is 1
✔ Answer: 1

9. $ \frac{4}{12} = \frac{?}{3} $
→ Simplify $ \frac{4}{12} = \frac{1}{3} $, so $ \frac{1}{3} = \frac{1}{3} $ → numerator is 1
✔ Answer: 1

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#### Row 4:
10. $ \frac{2}{4} = \frac{?}{2} $
→ Simplify $ \frac{2}{4} = \frac{1}{2} $, so $ \frac{1}{2} = \frac{1}{2} $ → numerator is 1
✔ Answer: 1

11. $ \frac{4}{8} = \frac{?}{4} $
→ Simplify $ \frac{4}{8} = \frac{1}{2} $, so $ \frac{1}{2} = \frac{2}{4} $ → numerator is 2
✔ Answer: 2

12. $ \frac{4}{12} = \frac{?}{6} $
→ Simplify $ \frac{4}{12} = \frac{1}{3} $, and $ \frac{1}{3} = \frac{2}{6} $ → numerator is 2
✔ Answer: 2

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✔ Final Answers (in order):

| Problem | Answer |
|--------|--------|
| $ \frac{1}{2} = \frac{?}{4} $ | 2 |
| $ \frac{1}{3} = \frac{?}{6} $ | 2 |
| $ \frac{2}{6} = \frac{?}{12} $ | 4 |
| $ \frac{1}{2} = \frac{?}{8} $ | 4 |
| $ \frac{1}{3} = \frac{?}{12} $ | 4 |
| $ \frac{2}{6} = \frac{?}{3} $ | 1 |
| $ \frac{2}{4} = \frac{?}{8} $ | 4 |
| $ \frac{4}{8} = \frac{?}{2} $ | 1 |
| $ \frac{4}{12} = \frac{?}{3} $ | 1 |
| $ \frac{2}{4} = \frac{?}{2} $ | 1 |
| $ \frac{4}{8} = \frac{?}{4} $ | 2 |
| $ \frac{4}{12} = \frac{?}{6} $ | 2 |

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🧠 Summary Tips:

- Use multiplication/division to scale up/down.
- Always check if the fraction can be simplified.
- Remember: "What you do to the bottom, you must do to the top."

Let me know if you'd like this as a printable answer key!