Equivalent Fractions - Worksheet Digital - Free Printable

Let's solve each of these equivalent fractions problems step by step.

The goal is to find the missing number in the fraction so that both sides are equivalent. We do this by using cross-multiplication or by finding a common multiplier between the numerators and denominators.

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1) $\frac{5}{9} = \frac{45}{?}$

We know $5 \times 9 = 45$, so we multiply numerator and denominator by 9:
- $5 \times 9 = 45$
- $9 \times 9 = 81$

✔ So, $\frac{5}{9} = \frac{45}{81}$

> Answer: 81

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2) $\frac{3}{7} = \frac{15}{?}$

$3 \times 5 = 15$, so multiply denominator by 5:
- $7 \times 5 = 35$

✔ $\frac{3}{7} = \frac{15}{35}$

> Answer: 35

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3) $\frac{6}{9} = \frac{60}{?}$

Simplify $\frac{6}{9} = \frac{2}{3}$, but let’s work directly:

$6 \times 10 = 60$, so multiply denominator by 10:
- $9 \times 10 = 90$

✔ $\frac{6}{9} = \frac{60}{90}$

> Answer: 90

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4) $\frac{4}{5} = \frac{32}{?}$

$4 \times 8 = 32$, so multiply denominator by 8:
- $5 \times 8 = 40$

✔ $\frac{4}{5} = \frac{32}{40}$

> Answer: 40

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5) $\frac{1}{6} = \frac{7}{?}$

$1 \times 7 = 7$, so multiply denominator by 7:
- $6 \times 7 = 42$

✔ $\frac{1}{6} = \frac{7}{42}$

> Answer: 42

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6) $\frac{3}{8} = \frac{18}{?}$

$3 \times 6 = 18$, so multiply denominator by 6:
- $8 \times 6 = 48$

✔ $\frac{3}{8} = \frac{18}{48}$

> Answer: 48

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7) $\frac{4}{5} = \frac{32}{?}$

Same as #4: $4 \times 8 = 32$, so $5 \times 8 = 40$

✔ $\frac{4}{5} = \frac{32}{40}$

> Answer: 40

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8) $\frac{4}{7} = \frac{20}{?}$

$4 \times 5 = 20$, so $7 \times 5 = 35$

✔ $\frac{4}{7} = \frac{20}{35}$

> Answer: 35

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9) $\frac{2}{3} = \frac{18}{?}$

$2 \times 9 = 18$, so $3 \times 9 = 27$

✔ $\frac{2}{3} = \frac{18}{27}$

> Answer: 27

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10) $\frac{5}{9} = \frac{35}{?}$

$5 \times 7 = 35$, so $9 \times 7 = 63$

✔ $\frac{5}{9} = \frac{35}{63}$

> Answer: 63

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11) $\frac{3}{8} = \frac{27}{?}$

$3 \times 9 = 27$, so $8 \times 9 = 72$

✔ $\frac{3}{8} = \frac{27}{72}$

> Answer: 72

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12) $\frac{5}{9} = \frac{30}{?}$

$5 \times 6 = 30$, so $9 \times 6 = 54$

✔ $\frac{5}{9} = \frac{30}{54}$

> Answer: 54

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13) $\frac{7}{11} = \frac{21}{?}$

$7 \times 3 = 21$, so $11 \times 3 = 33$

✔ $\frac{7}{11} = \frac{21}{33}$

> Answer: 33

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14) $\frac{8}{10} = \frac{16}{?}$

$8 \times 2 = 16$, so $10 \times 2 = 20$

✔ $\frac{8}{10} = \frac{16}{20}$

> Answer: 20

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15) $\frac{5}{6} = \frac{40}{?}$

$5 \times 8 = 40$, so $6 \times 8 = 48$

✔ $\frac{5}{6} = \frac{40}{48}$

> Answer: 48

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | 81 |
| 2) | 35 |
| 3) | 90 |
| 4) | 40 |
| 5) | 42 |
| 6) | 48 |
| 7) | 40 |
| 8) | 35 |
| 9) | 27 |
| 10) | 63 |
| 11) | 72 |
| 12) | 54 |
| 13) | 33 |
| 14) | 20 |
| 15) | 48 |

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🔍 Summary of Strategy:

To find an equivalent fraction:
1. Identify how the numerator changed (multiplied by what?).
2. Multiply the denominator by the same factor.
3. Or use cross-multiplication:
If $\frac{a}{b} = \frac{c}{x}$, then $a \cdot x = b \cdot c$, so $x = \frac{b \cdot c}{a}$

This method ensures the fractions remain equivalent.

Let me know if you'd like a printable version or explanation for any specific problem!