Equivalent Fractions worksheet with 20 problems to solve for X.

Let's solve each of these equivalent fractions problems step by step. The goal is to solve for $ X $ in each equation, where two fractions are set equal to each other.

We use the cross-multiplication method:
> If $ \frac{a}{b} = \frac{c}{d} $, then $ a \cdot d = b \cdot c $

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1) $ \frac{1}{4} = \frac{X}{6} $

Cross multiply:
$ 1 \cdot 6 = 4 \cdot X $ → $ 6 = 4X $
Divide both sides by 4:
$ X = \frac{6}{4} = \frac{3}{2} = 1.5 $

✔ Answer: $ X = \frac{3}{2} $

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2) $ \frac{7}{13} = \frac{X}{26} $

Cross multiply:
$ 7 \cdot 26 = 13 \cdot X $ → $ 182 = 13X $
Divide by 13:
$ X = \frac{182}{13} = 14 $

✔ Answer: $ X = 14 $

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3) $ \frac{8}{26} = \frac{X}{13} $

Simplify $ \frac{8}{26} = \frac{4}{13} $, so:
$ \frac{4}{13} = \frac{X}{13} $ → $ X = 4 $

✔ Answer: $ X = 4 $

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4) $ \frac{X}{12} = \frac{6}{8} $

Simplify $ \frac{6}{8} = \frac{3}{4} $
So: $ \frac{X}{12} = \frac{3}{4} $
Cross multiply:
$ 4X = 3 \cdot 12 = 36 $ → $ X = 9 $

✔ Answer: $ X = 9 $

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5) $ \frac{1}{6} = \frac{2}{X} $

Cross multiply:
$ 1 \cdot X = 6 \cdot 2 $ → $ X = 12 $

✔ Answer: $ X = 12 $

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6) $ \frac{X}{9} = \frac{2}{3} $

Cross multiply:
$ 3X = 2 \cdot 9 = 18 $ → $ X = 6 $

✔ Answer: $ X = 6 $

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7) $ \frac{2}{X} = \frac{4}{11} $

Cross multiply:
$ 2 \cdot 11 = 4 \cdot X $ → $ 22 = 4X $ → $ X = \frac{22}{4} = \frac{11}{2} = 5.5 $

✔ Answer: $ X = \frac{11}{2} $

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8) $ \frac{X}{7} = \frac{8}{14} $

Simplify $ \frac{8}{14} = \frac{4}{7} $
So: $ \frac{X}{7} = \frac{4}{7} $ → $ X = 4 $

✔ Answer: $ X = 4 $

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9) $ \frac{X}{14} = \frac{6}{7} $

Cross multiply:
$ 7X = 6 \cdot 14 = 84 $ → $ X = 12 $

✔ Answer: $ X = 12 $

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10) $ \frac{X}{12} = \frac{4}{6} $

Simplify $ \frac{4}{6} = \frac{2}{3} $
So: $ \frac{X}{12} = \frac{2}{3} $
Cross multiply:
$ 3X = 2 \cdot 12 = 24 $ → $ X = 8 $

✔ Answer: $ X = 8 $

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11) $ \frac{3}{14} = \frac{X}{7} $

Cross multiply:
$ 3 \cdot 7 = 14 \cdot X $ → $ 21 = 14X $ → $ X = \frac{21}{14} = \frac{3}{2} = 1.5 $

✔ Answer: $ X = \frac{3}{2} $

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12) $ \frac{9}{X} = \frac{1}{4} $

Cross multiply:
$ 9 \cdot 4 = 1 \cdot X $ → $ X = 36 $

✔ Answer: $ X = 36 $

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13) $ \frac{5}{X} = \frac{9}{14} $

Cross multiply:
$ 5 \cdot 14 = 9 \cdot X $ → $ 70 = 9X $ → $ X = \frac{70}{9} \approx 7.78 $

✔ Answer: $ X = \frac{70}{9} $

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14) $ \frac{4}{5} = \frac{3}{X} $

Cross multiply:
$ 4 \cdot X = 5 \cdot 3 = 15 $ → $ X = \frac{15}{4} = 3.75 $

✔ Answer: $ X = \frac{15}{4} $

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15) $ \frac{6}{7} = \frac{X}{21} $

Cross multiply:
$ 6 \cdot 21 = 7 \cdot X $ → $ 126 = 7X $ → $ X = 18 $

✔ Answer: $ X = 18 $

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16) $ \frac{7}{9} = \frac{X}{27} $

Cross multiply:
$ 7 \cdot 27 = 9 \cdot X $ → $ 189 = 9X $ → $ X = 21 $

✔ Answer: $ X = 21 $

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17) $ \frac{5}{X} = \frac{2}{9} $

Cross multiply:
$ 5 \cdot 9 = 2 \cdot X $ → $ 45 = 2X $ → $ X = \frac{45}{2} = 22.5 $

✔ Answer: $ X = \frac{45}{2} $

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18) $ \frac{1}{6} = \frac{X}{24} $

Cross multiply:
$ 1 \cdot 24 = 6 \cdot X $ → $ 24 = 6X $ → $ X = 4 $

✔ Answer: $ X = 4 $

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19) $ \frac{8}{11} = \frac{10}{X} $

Cross multiply:
$ 8 \cdot X = 11 \cdot 10 = 110 $ → $ X = \frac{110}{8} = \frac{55}{4} = 13.75 $

✔ Answer: $ X = \frac{55}{4} $

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20) $ \frac{6}{8} = \frac{X}{16} $

Simplify $ \frac{6}{8} = \frac{3}{4} $
So: $ \frac{3}{4} = \frac{X}{16} $
Cross multiply:
$ 3 \cdot 16 = 4 \cdot X $ → $ 48 = 4X $ → $ X = 12 $

✔ Answer: $ X = 12 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | $ \frac{3}{2} $ |
| 2) | 14 |
| 3) | 4 |
| 4) | 9 |
| 5) | 12 |
| 6) | 6 |
| 7) | $ \frac{11}{2} $ |
| 8) | 4 |
| 9) | 12 |
| 10) | 8 |
| 11) | $ \frac{3}{2} $ |
| 12) | 36 |
| 13) | $ \frac{70}{9} $ |
| 14) | $ \frac{15}{4} $ |
| 15) | 18 |
| 16) | 21 |
| 17) | $ \frac{45}{2} $ |
| 18) | 4 |
| 19) | $ \frac{55}{4} $ |
| 20) | 12 |

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📝 Explanation Summary:

To solve equivalent fractions:
- Use cross multiplication: $ \frac{a}{b} = \frac{c}{d} \Rightarrow a \cdot d = b \cdot c $
- Solve for $ X $
- Simplify fractions when possible
- Reduce answers to lowest terms

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