Equivalent fractions practice worksheet for Grade 3 students.

Let's solve each problem step by step and explain how to find equivalent fractions.

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🔷 What are Equivalent Fractions?

Equivalent fractions are different fractions that represent the same value. You can create equivalent fractions by multiplying or dividing both the numerator (top number) and denominator (bottom number) by the same number.

For example:
- $ \frac{1}{2} = \frac{2}{4} $ because we multiplied both 1 and 2 by 2.
- $ \frac{3}{6} = \frac{1}{2} $ because we divided both 3 and 6 by 3.

We’ll use this idea to fill in the blanks.

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Now, let’s go through each row:

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1. $ \frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} = \frac{6}{12} $

✔ This one is already filled in correctly!
All these fractions simplify to $ \frac{1}{2} $.

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2. $ \frac{1}{3} = \frac{?}{6} = \frac{3}{?} = \frac{?}{12} = \frac{5}{?} = \frac{?}{18} $

We need to find equivalent fractions of $ \frac{1}{3} $.

- $ \frac{1}{3} = \frac{2}{6} $ → Multiply numerator and denominator by 2
- $ \frac{1}{3} = \frac{3}{9} $ → Multiply by 3
- $ \frac{1}{3} = \frac{4}{12} $ → Multiply by 4
- $ \frac{1}{3} = \frac{5}{15} $ → Multiply by 5
- $ \frac{1}{3} = \frac{6}{18} $ → Multiply by 6

✔ So:
$ \frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12} = \frac{5}{15} = \frac{6}{18} $

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3. $ \frac{1}{7} = \frac{?}{?} = \frac{?}{?} = \frac{?}{?} = \frac{?}{?} = \frac{?}{?} $

Let’s multiply $ \frac{1}{7} $ by 2, 3, 4, 5, 6:

- $ \frac{1}{7} = \frac{2}{14} $
- $ \frac{1}{7} = \frac{3}{21} $
- $ \frac{1}{7} = \frac{4}{28} $
- $ \frac{1}{7} = \frac{5}{35} $
- $ \frac{1}{7} = \frac{6}{42} $

✔ So:
$ \frac{1}{7} = \frac{2}{14} = \frac{3}{21} = \frac{4}{28} = \frac{5}{35} = \frac{6}{42} $

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4. $ \frac{2}{3} = \frac{?}{?} = \frac{6}{?} = \frac{?}{12} = \frac{?}{15} = \frac{12}{?} $

We know $ \frac{2}{3} $. Let’s find missing numerators/denominators.

- First blank: $ \frac{2}{3} = \frac{4}{6} $ → multiply by 2
- $ \frac{6}{?} $: Since numerator is 6, which is $ 2 \times 3 $, so denominator must be $ 3 \times 3 = 9 $ → $ \frac{6}{9} $
- $ \frac{?}{12} $: Denominator is 12, $ 3 \times 4 = 12 $, so numerator = $ 2 \times 4 = 8 $ → $ \frac{8}{12} $
- $ \frac{?}{15} $: $ 3 \times 5 = 15 $, so numerator = $ 2 \times 5 = 10 $ → $ \frac{10}{15} $
- $ \frac{12}{?} $: Numerator is 12, $ 2 \times 6 = 12 $, so denominator = $ 3 \times 6 = 18 $ → $ \frac{12}{18} $

✔ So:
$ \frac{2}{3} = \frac{4}{6} = \frac{6}{9} = \frac{8}{12} = \frac{10}{15} = \frac{12}{18} $

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5. $ \frac{1}{4} = \frac{3}{?} = \frac{?}{20} = \frac{?}{?} = \frac{?}{?} = \frac{?}{?} $

- $ \frac{3}{?} $: $ \frac{1}{4} = \frac{3}{x} $ → $ x = 4 \times 3 = 12 $ → $ \frac{3}{12} $
- $ \frac{?}{20} $: $ 4 \times 5 = 20 $, so numerator = $ 1 \times 5 = 5 $ → $ \frac{5}{20} $
- Next: $ \frac{6}{24} $ → $ 1 \times 6 = 6 $, $ 4 \times 6 = 24 $
- $ \frac{7}{28} $
- $ \frac{8}{32} $

✔ So:
$ \frac{1}{4} = \frac{3}{12} = \frac{5}{20} = \frac{6}{24} = \frac{7}{28} = \frac{8}{32} $

(You could also write $ \frac{2}{8}, \frac{4}{16} $, etc., but since the pattern continues with increasing numbers, this works.)

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6. $ \frac{3}{8} = \frac{?}{?} = \frac{?}{24} = \frac{?}{32} = \frac{15}{?} = \frac{?}{48} $

Let’s go step by step:

- $ \frac{?}{?} $: Let's do $ \frac{6}{16} $ → multiply by 2
- $ \frac{?}{24} $: $ 8 \times 3 = 24 $, so numerator = $ 3 \times 3 = 9 $ → $ \frac{9}{24} $
- $ \frac{?}{32} $: $ 8 \times 4 = 32 $, so $ 3 \times 4 = 12 $ → $ \frac{12}{32} $
- $ \frac{15}{?} $: $ 3 \times 5 = 15 $, so denominator = $ 8 \times 5 = 40 $ → $ \frac{15}{40} $
- $ \frac{?}{48} $: $ 8 \times 6 = 48 $, so numerator = $ 3 \times 6 = 18 $ → $ \frac{18}{48} $

✔ So:
$ \frac{3}{8} = \frac{6}{16} = \frac{9}{24} = \frac{12}{32} = \frac{15}{40} = \frac{18}{48} $

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7. $ \frac{1}{5} = \frac{?}{10} = \frac{?}{15} = \frac{?}{?} = \frac{?}{?} = \frac{?}{30} $

- $ \frac{?}{10} $: $ 5 \times 2 = 10 $, so numerator = $ 1 \times 2 = 2 $ → $ \frac{2}{10} $
- $ \frac{?}{15} $: $ 5 \times 3 = 15 $, so $ 1 \times 3 = 3 $ → $ \frac{3}{15} $
- $ \frac{?}{?} $: $ \frac{4}{20} $
- $ \frac{5}{25} $
- $ \frac{6}{30} $

✔ So:
$ \frac{1}{5} = \frac{2}{10} = \frac{3}{15} = \frac{4}{20} = \frac{5}{25} = \frac{6}{30} $

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8. $ \frac{5}{10} = \frac{?}{?} = \frac{?}{?} = \frac{?}{?} = \frac{?}{?} = \frac{?}{?} $

First, simplify $ \frac{5}{10} = \frac{1}{2} $. So all answers should be equivalent to $ \frac{1}{2} $.

Let’s make equivalent fractions:

- $ \frac{2}{4} $
- $ \frac{3}{6} $
- $ \frac{4}{8} $
- $ \frac{5}{10} $ (already given)
- $ \frac{6}{12} $

But since $ \frac{5}{10} $ is the first, we can continue:

- $ \frac{5}{10} = \frac{6}{12} = \frac{7}{14} = \frac{8}{16} = \frac{9}{18} = \frac{10}{20} $

Alternatively, keep it simple and use multiples:

✔ So:
$ \frac{5}{10} = \frac{6}{12} = \frac{7}{14} = \frac{8}{16} = \frac{9}{18} = \frac{10}{20} $

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✔ Final Answers:

1. $ \frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} = \frac{6}{12} $
2. $ \frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12} = \frac{5}{15} = \frac{6}{18} $
3. $ \frac{1}{7} = \frac{2}{14} = \frac{3}{21} = \frac{4}{28} = \frac{5}{35} = \frac{6}{42} $
4. $ \frac{2}{3} = \frac{4}{6} = \frac{6}{9} = \frac{8}{12} = \frac{10}{15} = \frac{12}{18} $
5. $ \frac{1}{4} = \frac{3}{12} = \frac{5}{20} = \frac{6}{24} = \frac{7}{28} = \frac{8}{32} $
6. $ \frac{3}{8} = \frac{6}{16} = \frac{9}{24} = \frac{12}{32} = \frac{15}{40} = \frac{18}{48} $
7. $ \frac{1}{5} = \frac{2}{10} = \frac{3}{15} = \frac{4}{20} = \frac{5}{25} = \frac{6}{30} $
8. $ \frac{5}{10} = \frac{6}{12} = \frac{7}{14} = \frac{8}{16} = \frac{9}{18} = \frac{10}{20} $

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🎯 How to Check Your Work:

Always check if the simplified form of each fraction equals the original. For example, $ \frac{6}{12} $ simplifies to $ \frac{1}{2} $, same as $ \frac{5}{10} $ — correct!

Let me know if you’d like a printable version or visual help!