Equivalent Fractions Sheet 3 - Practice finding equivalent fractions with this printable math worksheet.

Let's solve each of these equivalent fraction problems step by step. The key idea is that to find an equivalent fraction, you multiply or divide both the numerator and denominator by the same number.

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Problem 1)

$$
\frac{1}{3} = \frac{?}{6}
$$
We need to go from denominator 3 to 6 → multiply by 2.
So, multiply numerator by 2: $1 \times 2 = 2$
Answer: $\boxed{\frac{2}{6}}$

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Problem 2)

$$
\frac{1}{4} = \frac{?}{12}
$$
From 4 to 12 → multiply by 3
Numerator: $1 \times 3 = 3$
Answer: $\boxed{\frac{3}{12}}$

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Problem 3)

$$
\frac{1}{3} = \frac{?}{9}
$$
From 3 to 9 → multiply by 3
Numerator: $1 \times 3 = 3$
Answer: $\boxed{\frac{3}{9}}$

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Problem 4)

$$
\frac{1}{2} = \frac{?}{12}
$$
From 2 to 12 → multiply by 6
Numerator: $1 \times 6 = 6$
Answer: $\boxed{\frac{6}{12}}$

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Problem 5)

$$
\frac{1}{4} = \frac{?}{8}
$$
From 4 to 8 → multiply by 2
Numerator: $1 \times 2 = 2$
Answer: $\boxed{\frac{2}{8}}$

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Problem 6)

$$
\frac{1}{2} = \frac{?}{8}
$$
From 2 to 8 → multiply by 4
Numerator: $1 \times 4 = 4$
Answer: $\boxed{\frac{4}{8}}$

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Problem 7)

$$
\frac{1}{6} = \frac{?}{12}
$$
From 6 to 12 → multiply by 2
Numerator: $1 \times 2 = 2$
Answer: $\boxed{\frac{2}{12}}$

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Problem 8)

$$
\frac{1}{5} = \frac{?}{10}
$$
From 5 to 10 → multiply by 2
Numerator: $1 \times 2 = 2$
Answer: $\boxed{\frac{2}{10}}$

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Problem 9)

$$
\frac{2}{2} = \frac{?}{4}
$$
$\frac{2}{2} = 1$, so we want a fraction equal to 1 with denominator 4 → $\frac{4}{4}$
Alternatively: Multiply numerator and denominator by 2: $2 \times 2 = 4$
Answer: $\boxed{\frac{4}{4}}$

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Problem 10)

$$
\frac{3}{4} = \frac{?}{8}
$$
From 4 to 8 → multiply by 2
Numerator: $3 \times 2 = 6$
Answer: $\boxed{\frac{6}{8}}$

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Problem 11)

$$
\frac{2}{3} = \frac{?}{6}
$$
From 3 to 6 → multiply by 2
Numerator: $2 \times 2 = 4$
Answer: $\boxed{\frac{4}{6}}$

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Problem 12)

$$
\frac{2}{4} = \frac{?}{12}
$$
Simplify $\frac{2}{4} = \frac{1}{2}$, but let’s work directly:
From 4 to 12 → multiply by 3
Numerator: $2 \times 3 = 6$
Answer: $\boxed{\frac{6}{12}}$

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Problem 13)

$$
\frac{2}{3} = \frac{?}{9}
$$
From 3 to 9 → multiply by 3
Numerator: $2 \times 3 = 6$
Answer: $\boxed{\frac{6}{9}}$

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Problem 14)

$$
\frac{4}{6} = \frac{?}{12}
$$
From 6 to 12 → multiply by 2
Numerator: $4 \times 2 = 8$
Answer: $\boxed{\frac{8}{12}}$

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Problem 15)

$$
\frac{3}{5} = \frac{?}{10}
$$
From 5 to 10 → multiply by 2
Numerator: $3 \times 2 = 6$
Answer: $\boxed{\frac{6}{10}}$

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Problem 16)

$$
\frac{3}{4} = \frac{?}{12}
$$
From 4 to 12 → multiply by 3
Numerator: $3 \times 3 = 9$
Answer: $\boxed{\frac{9}{12}}$

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Problem 17)

$$
\frac{4}{5} = \frac{?}{10}
$$
From 5 to 10 → multiply by 2
Numerator: $4 \times 2 = 8$
Answer: $\boxed{\frac{8}{10}}$

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Problem 18)

$$
\frac{3}{6} = \frac{?}{12}
$$
From 6 to 12 → multiply by 2
Numerator: $3 \times 2 = 6$
Answer: $\boxed{\frac{6}{12}}$

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Problem 19)

$$
\frac{2}{5} = \frac{?}{10}
$$
From 5 to 10 → multiply by 2
Numerator: $2 \times 2 = 4$
Answer: $\boxed{\frac{4}{10}}$

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Problem 20)

$$
\frac{4}{4} = \frac{?}{12}
$$
$\frac{4}{4} = 1$, so we want a fraction equal to 1 with denominator 12 → $\frac{12}{12}$
Multiply numerator and denominator by 3: $4 \times 3 = 12$
Answer: $\boxed{\frac{12}{12}}$

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Problem 21)

$$
\frac{1}{2} = \frac{4}{?}
$$
We know $\frac{1}{2} = \frac{4}{x}$
Since numerator went from 1 to 4 → multiplied by 4
So denominator must also be multiplied by 4: $2 \times 4 = 8$
Answer: $\boxed{8}$

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Problem 22)

$$
\frac{1}{4} = \frac{3}{?}
$$
Numerator: 1 → 3 → multiplied by 3
So denominator: $4 \times 3 = 12$
Answer: $\boxed{12}$

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Problem 23)

$$
\frac{1}{3} = \frac{3}{?}
$$
Numerator: 1 → 3 → ×3
Denominator: $3 \times 3 = 9$
Answer: $\boxed{9}$

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Problem 24)

$$
\frac{2}{4} = \frac{4}{?}
$$
Simplify: $\frac{2}{4} = \frac{1}{2}$
Now: $\frac{1}{2} = \frac{4}{x}$ → numerator ×4 → denominator ×4 → $2 \times 4 = 8$
Answer: $\boxed{8}$

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Problem 25)

$$
\frac{1}{2} = \frac{5}{?}
$$
Numerator: 1 → 5 → ×5
Denominator: $2 \times 5 = 10$
Answer: $\boxed{10}$

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Problem 26)

$$
\frac{3}{4} = \frac{6}{?}
$$
Numerator: 3 → 6 → ×2
Denominator: $4 \times 2 = 8$
Answer: $\boxed{8}$

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Problem 27)

$$
\frac{2}{3} = \frac{6}{?}
$$
Numerator: 2 → 6 → ×3
Denominator: $3 \times 3 = 9$
Answer: $\boxed{9}$

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Problem 28)

$$
\frac{3}{4} = \frac{9}{?}
$$
Numerator: 3 → 9 → ×3
Denominator: $4 \times 3 = 12$
Answer: $\boxed{12}$

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✔ Final Answers:

1) $\frac{2}{6}$
2) $\frac{3}{12}$
3) $\frac{3}{9}$
4) $\frac{6}{12}$
5) $\frac{2}{8}$
6) $\frac{4}{8}$
7) $\frac{2}{12}$
8) $\frac{2}{10}$
9) $\frac{4}{4}$
10) $\frac{6}{8}$
11) $\frac{4}{6}$
12) $\frac{6}{12}$
13) $\frac{6}{9}$
14) $\frac{8}{12}$
15) $\frac{6}{10}$
16) $\frac{9}{12}$
17) $\frac{8}{10}$
18) $\frac{6}{12}$
19) $\frac{4}{10}$
20) $\frac{12}{12}$
21) $8$
22) $12$
23) $9$
24) $8$
25) $10$
26) $8$
27) $9$
28) $12$

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💡 Tip: Always check if the multiplication factor is consistent between numerator and denominator. You can cross-multiply to verify:
For example: Is $\frac{1}{2} = \frac{4}{8}$?
$1 \times 8 = 8$, $2 \times 4 = 8$ → Yes! ✔

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