Equivalent fractions practice worksheet for students to solve missing values in fraction pairs.

Let's solve each of these equivalent fraction problems 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 want to find what number over 4 is equivalent to $ \frac{2}{8} $.

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

So:
$$
\frac{\square}{4} = \frac{1}{4} \Rightarrow \square = 1
$$

✔ Answer: 1

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

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

So:
$$
\frac{1}{\square} = \frac{1}{3} \Rightarrow \square = 3
$$

✔ Answer: 3

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

We need to scale $ \frac{2}{3} $ to have denominator 9.

Since $ 3 \times 3 = 9 $, multiply numerator and denominator by 3:

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

✔ Answer: 6

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

We want to scale $ \frac{1}{3} $ to denominator 15.

Since $ 3 \times 5 = 15 $, multiply numerator and denominator by 5:

$$
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
$$

✔ Answer: 5

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

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

So:
$$
\frac{1}{\square} = \frac{1}{2} \Rightarrow \square = 2
$$

✔ 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 \div 7}{21 \div 7} = \frac{2}{3} $

So:
$$
\frac{2}{\square} = \frac{2}{3} \Rightarrow \square = 3
$$

✔ Answer: 3

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

Simplify $ \frac{11}{66} $:
$ \frac{11}{66} = \frac{1}{6} $ (since $ 66 \div 11 = 6 $)

So:
$$
\frac{1}{\square} = \frac{1}{6} \Rightarrow \square = 6
$$

✔ Answer: 6

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

Scale $ \frac{3}{4} $ to denominator 24.

Since $ 4 \times 6 = 24 $, multiply numerator and denominator by 6:

$$
\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}
$$

✔ Answer: 18

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

We know $ \frac{1}{5} = \frac{2}{x} $. Multiply both sides by 5x to eliminate denominators:

$$
\frac{1}{5} = \frac{2}{x} \Rightarrow x = 5 \times 2 = 10
$$

Or think: if numerator doubles from 1 to 2, denominator must also double: $ 5 \times 2 = 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:
$$
\frac{1}{\square} = \frac{1}{8} \Rightarrow \square = 8
$$

✔ 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 can:
- Simplify the given fraction.
- Scale up or down using multiplication/division so that numerators or denominators match.
- Use cross-multiplication when needed.

For example, in problem 8:
$ \frac{3}{4} = \frac{x}{24} $ → $ 3 \times 24 = 4x $ → $ 72 = 4x $ → $ x = 18 $

But simpler: $ 4 \times 6 = 24 $, so $ 3 \times 6 = 18 $

This method works consistently!

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