Grade 3 Math worksheets Fractions | Grade1to6.com - Free Printable

Let's solve each problem step by step, explaining 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 and denominator by the same number.

Example:
$$
\frac{1}{2} = \frac{2}{4} = \frac{3}{6}
$$
We multiplied numerator and denominator by 2, then by 3.

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Now let’s go through each row:

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✔ Problem 1: Already solved!

$$
\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} = \frac{6}{12}
$$
✔️ All correct — these are all multiples of $\frac{1}{2}$.

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✔ Problem 2: $\frac{1}{3} = \ ?$

We need to find fractions equal to $\frac{1}{3}$ with denominators: 6, ?, 12, ?, 18

- $\frac{1}{3} = \frac{?}{6}$ → Multiply top and bottom by 2 → $\frac{2}{6}$
- $\frac{1}{3} = \frac{3}{?}$ → Multiply top and bottom by 3 → $\frac{3}{9}$
- $\frac{1}{3} = \frac{?}{12}$ → Multiply by 4 → $\frac{4}{12}$
- $\frac{1}{3} = \frac{?}{?}$ → Let's use 15 → $\frac{5}{15}$
- $\frac{1}{3} = \frac{?}{18}$ → Multiply by 6 → $\frac{6}{18}$

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

✔ Answer:
$$
\boxed{\frac{2}{6}, \frac{3}{9}, \frac{4}{12}, \frac{5}{15}, \frac{6}{18}}
$$

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✔ Problem 3: $\frac{1}{7} = \ ?$

We’ll multiply numerator and denominator by 2, 3, 4, 5, 6.

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

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

✔ Answer:
$$
\boxed{\frac{2}{14}, \frac{3}{21}, \frac{4}{28}, \frac{5}{35}, \frac{6}{42}}
$$

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✔ Problem 4: $\frac{2}{3} = \ ?$

We want fractions equal to $\frac{2}{3}$

- $ \frac{2}{3} = \frac{?}{?} $ → Try denominator 6 → $ \frac{4}{6} $
- $ = \frac{6}{?} $ → We’re given $ \frac{6}{?} $, so solve: $ \frac{2}{3} = \frac{6}{x} $ → cross-multiply: $2x = 18$ → $x = 9$ → $ \frac{6}{9} $
- $ = \frac{?}{12} $ → $ \frac{2}{3} = \frac{x}{12} $ → $ x = 8 $ → $ \frac{8}{12} $
- $ = \frac{?}{15} $ → $ x = 10 $ → $ \frac{10}{15} $
- $ = \frac{12}{?} $ → $ \frac{2}{3} = \frac{12}{x} $ → $ 2x = 36 $ → $ x = 18 $ → $ \frac{12}{18} $

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

✔ Answer:
$$
\boxed{\frac{4}{6}, \frac{6}{9}, \frac{8}{12}, \frac{10}{15}, \frac{12}{18}}
$$

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✔ Problem 5: $\frac{1}{4} = \ ?$

- $ \frac{1}{4} = \frac{?}{?} $ → Try $ \frac{3}{?} $ → So $ \frac{1}{4} = \frac{3}{x} $ → $ x = 12 $ → $ \frac{3}{12} $
- $ = \frac{?}{20} $ → $ x = 5 $ → $ \frac{5}{20} $
- $ = \frac{?}{?} $ → Try $ \frac{6}{24} $
- $ = \frac{?}{?} $ → Try $ \frac{7}{28} $
- $ = \frac{?}{?} $ → Try $ \frac{8}{32} $

Check: All should be $ \frac{1}{4} $

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

✔ Answer:
$$
\boxed{\frac{3}{12}, \frac{5}{20}, \frac{6}{24}, \frac{7}{28}, \frac{8}{32}}
$$

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✔ Problem 6: $\frac{3}{8} = \ ?$

- $ \frac{3}{8} = \frac{?}{?} $ → Try $ \frac{6}{16} $
- $ = \frac{?}{24} $ → $ \frac{3}{8} = \frac{x}{24} $ → $ x = 9 $ → $ \frac{9}{24} $
- $ = \frac{?}{32} $ → $ x = 12 $ → $ \frac{12}{32} $
- $ = \frac{15}{?} $ → $ \frac{3}{8} = \frac{15}{x} $ → $ 3x = 120 $ → $ x = 40 $ → $ \frac{15}{40} $
- $ = \frac{?}{48} $ → $ x = 18 $ → $ \frac{18}{48} $

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

✔ Answer:
$$
\boxed{\frac{6}{16}, \frac{9}{24}, \frac{12}{32}, \frac{15}{40}, \frac{18}{48}}
$$

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✔ Problem 7: $\frac{1}{5} = \ ?$

- $ \frac{1}{5} = \frac{?}{10} $ → $ \frac{2}{10} $
- $ = \frac{?}{15} $ → $ \frac{3}{15} $
- $ = \frac{?}{?} $ → Try $ \frac{4}{20} $
- $ = \frac{?}{?} $ → Try $ \frac{5}{25} $
- $ = \frac{?}{30} $ → $ \frac{6}{30} $

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

✔ Answer:
$$
\boxed{\frac{2}{10}, \frac{3}{15}, \frac{4}{20}, \frac{5}{25}, \frac{6}{30}}
$$

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✔ Problem 8: $\frac{5}{10} = \ ?$

First simplify: $ \frac{5}{10} = \frac{1}{2} $

So we want equivalent fractions to $ \frac{1}{2} $

Let’s write five equivalent fractions:

- $ \frac{1}{2} = \frac{2}{4} $
- $ = \frac{3}{6} $
- $ = \frac{4}{8} $
- $ = \frac{5}{10} $ (already given)
- $ = \frac{6}{12} $

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

$$
\frac{5}{10} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{6}{12} = \frac{7}{14}
$$

(Or any others like $ \frac{8}{16} $, etc.)

But to keep it simple and consistent with pattern:

$$
\frac{5}{10} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{6}{12} = \frac{7}{14}
$$

✔ Answer:
$$
\boxed{\frac{2}{4}, \frac{3}{6}, \frac{4}{8}, \frac{6}{12}, \frac{7}{14}}
$$

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🟩 Final Answers Summary:

| Problem | Equivalent Fractions |
|--------|----------------------|
| 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 | $\frac{5}{10} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{6}{12} = \frac{7}{14}$ |

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✔ Tips for Students:

- Always multiply both numerator and denominator by the same number.
- Use multiplication facts to help.
- Simplify fractions if needed (like reducing $ \frac{5}{10} $ to $ \frac{1}{2} $).
- Check your work: divide numerator by denominator — they should give the same decimal.

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