Equivalent Fractions Worksheets - Math Monks - Free Printable

Let's solve each of the equivalent fractions step by step. The goal is to find the missing numerator or denominator so that both fractions are equivalent (i.e., they represent the same value).

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1) $\frac{5}{10} = \frac{?}{90}$

We simplify $\frac{5}{10} = \frac{1}{2}$.
Now, we want $\frac{1}{2} = \frac{x}{90}$.
Multiply both sides by 90:
$x = \frac{1}{2} \times 90 = 45$

✔ Answer: 45

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2) $\frac{2}{4} = \frac{?}{20}$

Simplify $\frac{2}{4} = \frac{1}{2}$
So $\frac{1}{2} = \frac{x}{20}$ → $x = 10$

✔ Answer: 10

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3) $\frac{3}{7} = \frac{?}{28}$

We want to scale up from 7 to 28:
$28 ÷ 7 = 4$, so multiply numerator by 4:
$3 × 4 = 12$

✔ Answer: 12

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4) $\frac{?}{15} = \frac{8}{3}$

We can cross-multiply:
Let $x$ be the unknown numerator:
$\frac{x}{15} = \frac{8}{3}$ → $x × 3 = 8 × 15$ → $3x = 120$ → $x = 40$

Alternatively, since $\frac{8}{3} = \frac{40}{15}$, because $8×5=40$, $3×5=15$

✔ Answer: 40

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5) $\frac{9}{2} = \frac{?}{40}$

We need to go from denominator 2 to 40:
$40 ÷ 2 = 20$, so multiply numerator by 20:
$9 × 20 = 180$

✔ Answer: 180

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6) $\frac{6}{?} = \frac{30}{45}$

First, simplify $\frac{30}{45} = \frac{2}{3}$
So $\frac{6}{x} = \frac{2}{3}$

Cross-multiply: $6 × 3 = 2 × x$ → $18 = 2x$ → $x = 9$

✔ Answer: 9

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7) $\frac{?}{27} = \frac{7}{9}$

Scale up from 9 to 27: $27 ÷ 9 = 3$, so multiply numerator by 3:
$7 × 3 = 21$

✔ Answer: 21

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8) $\frac{39}{12} = \frac{13}{?}$

Simplify $\frac{39}{12}$: divide numerator and denominator by 3:
$\frac{39 ÷ 3}{12 ÷ 3} = \frac{13}{4}$

So $\frac{13}{4} = \frac{13}{x}$ → $x = 4$

✔ Answer: 4

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9) $\frac{10}{3} = \frac{?}{27}$

Go from 3 to 27: $27 ÷ 3 = 9$, so multiply numerator by 9:
$10 × 9 = 90$

✔ Answer: 90

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10) $\frac{1}{6} = \frac{?}{54}$

Go from 6 to 54: $54 ÷ 6 = 9$, so multiply numerator by 9:
$1 × 9 = 9$

✔ Answer: 9

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11) $\frac{4}{4} = \frac{?}{12}$

$\frac{4}{4} = 1$, so we want $\frac{x}{12} = 1$ → $x = 12$

✔ Answer: 12

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12) $\frac{1}{2} = \frac{5}{?}$

We have $\frac{1}{2} = \frac{5}{x}$ → Cross-multiply:
$1 × x = 2 × 5$ → $x = 10$

✔ Answer: 10

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13) $\frac{4}{12} = \frac{?}{6}$

Simplify $\frac{4}{12} = \frac{1}{3}$
So $\frac{1}{3} = \frac{x}{6}$ → $x = 2$

Or: Scale down from 12 to 6: divide by 2 → $4 ÷ 2 = 2$

✔ Answer: 2

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14) $\frac{1}{4} = \frac{?}{48}$

From 4 to 48: $48 ÷ 4 = 12$, so multiply numerator by 12:
$1 × 12 = 12$

✔ Answer: 12

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15) $\frac{1}{7} = \frac{?}{28}$

From 7 to 28: $28 ÷ 7 = 4$, so multiply numerator by 4:
$1 × 4 = 4$

✔ Answer: 4

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✔ Final Answers:

1) 45
2) 10
3) 12
4) 40
5) 180
6) 9
7) 21
8) 4
9) 90
10) 9
11) 12
12) 10
13) 2
14) 12
15) 4

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