Ace 6th Grade math with interactive games and free worksheets - Free Printable

Let's solve each of these equivalent fraction problems step by step. The goal is to complete each pair of equivalent fractions by finding the missing numerator or denominator.

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🔹 Key Concept: Equivalent Fractions

Two fractions are equivalent if they represent the same value. We can find equivalent fractions by multiplying or dividing both the numerator and denominator by the same number.

We’ll use cross-multiplication or scaling to find the missing part.

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1. $ \frac{2}{?} = \frac{20}{50} $

We know $ \frac{20}{50} $ simplifies:
$$
\frac{20 \div 10}{50 \div 10} = \frac{2}{5}
$$
So, $ \frac{2}{5} = \frac{20}{50} $

✔ Answer: 5

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2. $ \frac{2}{7} = \frac{?}{49} $

We want to scale $ \frac{2}{7} $ so that the denominator becomes 49.

Since $ 7 \times 7 = 49 $, multiply numerator and denominator by 7:
$$
\frac{2 \times 7}{7 \times 7} = \frac{14}{49}
$$

✔ Answer: 14

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3. $ \frac{?}{13} = \frac{12}{39} $

Simplify $ \frac{12}{39} $:
$$
\frac{12 \div 3}{39 \div 3} = \frac{4}{13}
$$

So $ \frac{4}{13} = \frac{12}{39} $

✔ Answer: 4

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4. $ \frac{?}{18} = \frac{1}{6} $

We want a fraction with denominator 18 equal to $ \frac{1}{6} $

Since $ 6 \times 3 = 18 $, multiply numerator and denominator by 3:
$$
\frac{1 \times 3}{6 \times 3} = \frac{3}{18}
$$

✔ Answer: 3

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5. $ \frac{3}{5} = \frac{15}{?} $

We have $ \frac{3}{5} = \frac{15}{x} $

We see $ 3 \times 5 = 15 $, so we must multiply denominator by 5 too:
$$
5 \times 5 = 25
$$

✔ Answer: 25

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6. $ \frac{?}{16} = \frac{3}{8} $

We want to scale $ \frac{3}{8} $ to denominator 16.

$ 8 \times 2 = 16 $, so multiply numerator by 2:
$$
\frac{3 \times 2}{8 \times 2} = \frac{6}{16}
$$

✔ Answer: 6

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7. $ \frac{64}{72} = \frac{?}{9} $

Simplify $ \frac{64}{72} $:

Divide numerator and denominator by 8:
$$
\frac{64 \div 8}{72 \div 8} = \frac{8}{9}
$$

So $ \frac{8}{9} = \frac{64}{72} $

✔ Answer: 8

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8. $ \frac{1}{3} = \frac{?}{12} $

$ 3 \times 4 = 12 $, so multiply numerator by 4:
$$
\frac{1 \times 4}{3 \times 4} = \frac{4}{12}
$$

✔ Answer: 4

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9. $ \frac{9}{24} = \frac{?}{8} $

Simplify $ \frac{9}{24} $: divide numerator and denominator by 3:
$$
\frac{9 \div 3}{24 \div 3} = \frac{3}{8}
$$

So $ \frac{3}{8} = \frac{9}{24} $

✔ Answer: 3

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10. $ \frac{?}{21} = \frac{2}{3} $

$ 3 \times 7 = 21 $, so multiply numerator by 7:
$$
\frac{2 \times 7}{3 \times 7} = \frac{14}{21}
$$

✔ Answer: 14

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11. $ \frac{18}{42} = \frac{3}{?} $

Simplify $ \frac{18}{42} $: divide by 6:
$$
\frac{18 \div 6}{42 \div 6} = \frac{3}{7}
$$

So $ \frac{3}{7} = \frac{18}{42} $

✔ Answer: 7

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12. $ \frac{8}{7} = \frac{16}{?} $

We see $ 8 \times 2 = 16 $, so we must also multiply denominator by 2:
$$
7 \times 2 = 14
$$

✔ Answer: 14

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | 5 |
| 2 | 14 |
| 3 | 4 |
| 4 | 3 |
| 5 | 25 |
| 6 | 6 |
| 7 | 8 |
| 8 | 4 |
| 9 | 3 |
| 10 | 14 |
| 11 | 7 |
| 12 | 14 |

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📝 Summary:

To solve these, you either:
- Simplify the known fraction,
- Or scale it up/down using multiplication/division to match the other fraction.

All answers are based on equivalent fractions using scaling (multiplying or dividing numerator and denominator by the same number).

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