Equivalent Fractions worksheet for students to practice finding missing values in fraction equations.

Let's solve each of these equivalent fractions step by step. The goal is to find the missing number (represented by a box) that makes the two fractions equal.

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1. $ \frac{\square}{4} = \frac{2}{8} $

We simplify $ \frac{2}{8} $:
$ \frac{2}{8} = \frac{1}{4} $

So, $ \frac{\square}{4} = \frac{1}{4} $ → $ \square = 1 $

✔ Answer: 1

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2. $ \frac{1}{\square} = \frac{3}{9} $

Simplify $ \frac{3}{9} $:
$ \frac{3}{9} = \frac{1}{3} $

So, $ \frac{1}{\square} = \frac{1}{3} $ → $ \square = 3 $

✔ Answer: 3

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3. $ \frac{2}{3} = \frac{\square}{9} $

We want to scale $ \frac{2}{3} $ to have denominator 9.
Multiply numerator and denominator by 3:
$ \frac{2 \times 3}{3 \times 3} = \frac{6}{9} $

So, $ \square = 6 $

✔ Answer: 6

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4. $ \frac{1}{3} = \frac{\square}{15} $

Scale $ \frac{1}{3} $ to denominator 15:
$ 3 \times 5 = 15 $, so multiply numerator by 5:
$ \frac{1 \times 5}{3 \times 5} = \frac{5}{15} $

So, $ \square = 5 $

✔ Answer: 5

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5. $ \frac{1}{\square} = \frac{10}{20} $

Simplify $ \frac{10}{20} $:
$ \frac{10}{20} = \frac{1}{2} $

So, $ \frac{1}{\square} = \frac{1}{2} $ → $ \square = 2 $

✔ Answer: 2

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6. $ \frac{2}{\square} = \frac{14}{21} $

Simplify $ \frac{14}{21} $:
Divide numerator and denominator by 7:
$ \frac{14 ÷ 7}{21 ÷ 7} = \frac{2}{3} $

So, $ \frac{2}{\square} = \frac{2}{3} $ → $ \square = 3 $

✔ Answer: 3

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7. $ \frac{1}{\square} = \frac{11}{66} $

Simplify $ \frac{11}{66} $:
Divide numerator and denominator by 11:
$ \frac{11 ÷ 11}{66 ÷ 11} = \frac{1}{6} $

So, $ \frac{1}{\square} = \frac{1}{6} $ → $ \square = 6 $

✔ Answer: 6

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8. $ \frac{3}{4} = \frac{\square}{24} $

Scale $ \frac{3}{4} $ to denominator 24:
$ 4 \times 6 = 24 $, so multiply numerator by 6:
$ \frac{3 \times 6}{4 \times 6} = \frac{18}{24} $

So, $ \square = 18 $

✔ Answer: 18

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9. $ \frac{1}{5} = \frac{2}{\square} $

We see that numerator went from 1 to 2 → multiplied by 2.
So denominator must also be multiplied by 2:
$ 5 \times 2 = 10 $

So, $ \square = 10 $

✔ Answer: 10

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10. $ \frac{1}{\square} = \frac{2}{16} $

Simplify $ \frac{2}{16} $:
$ \frac{2}{16} = \frac{1}{8} $

So, $ \frac{1}{\square} = \frac{1}{8} $ → $ \square = 8 $

✔ Answer: 8

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✔ Final Answers:

1. 1
2. 3
3. 6
4. 5
5. 2
6. 3
7. 6
8. 18
9. 10
10. 8

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🔍 Explanation Summary:

To find equivalent fractions, you either:
- Simplify both sides to lowest terms,
- Or scale up/down by multiplying/dividing numerator and denominator by the same number.

This ensures the value of the fraction stays the same.