Comparing Fractions Worksheet Download - Free Printable

Let's solve each of these fraction comparison problems step by step. We will use >, <, or = to compare the fractions.

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How to Compare Fractions:

To compare two fractions, you can:
1. Find a common denominator and compare numerators.
2. Convert to decimals (if easy).
3. Use cross-multiplication: For $\frac{a}{b}$ vs $\frac{c}{d}$, compare $a \times d$ vs $c \times b$.

We'll use cross-multiplication for most cases.

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Problem 1: $\frac{4}{5} \quad \text{vs} \quad \frac{1}{4}$

Cross-multiply:
- $4 \times 4 = 16$
- $1 \times 5 = 5$

Since $16 > 5$, then $\frac{4}{5} > \frac{1}{4}$

✔ Answer: >

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Problem 2: $\frac{1}{10} \quad \text{vs} \quad \frac{4}{5}$

Cross-multiply:
- $1 \times 5 = 5$
- $4 \times 10 = 40$

$5 < 40$, so $\frac{1}{10} < \frac{4}{5}$

✔ Answer: <

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Problem 3: $\frac{3}{4} \quad \text{vs} \quad \frac{2}{10}$

Simplify $\frac{2}{10} = \frac{1}{5}$

Compare $\frac{3}{4}$ and $\frac{1}{5}$

Cross-multiply:
- $3 \times 5 = 15$
- $1 \times 4 = 4$

$15 > 4$, so $\frac{3}{4} > \frac{2}{10}$

✔ Answer: >

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Problem 4: $\frac{1}{3} \quad \text{vs} \quad \frac{5}{8}$

Cross-multiply:
- $1 \times 8 = 8$
- $5 \times 3 = 15$

$8 < 15$, so $\frac{1}{3} < \frac{5}{8}$

✔ Answer: <

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Problem 5: $\frac{2}{5} \quad \text{vs} \quad \frac{1}{6}$

Cross-multiply:
- $2 \times 6 = 12$
- $1 \times 5 = 5$

$12 > 5$, so $\frac{2}{5} > \frac{1}{6}$

✔ Answer: >

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Problem 6: $\frac{4}{6} \quad \text{vs} \quad \frac{1}{10}$

Simplify $\frac{4}{6} = \frac{2}{3}$

Compare $\frac{2}{3}$ and $\frac{1}{10}$

Cross-multiply:
- $2 \times 10 = 20$
- $1 \times 3 = 3$

$20 > 3$, so $\frac{4}{6} > \frac{1}{10}$

✔ Answer: >

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Problem 7: $\frac{4}{12} \quad \text{vs} \quad \frac{1}{8}$

Simplify $\frac{4}{12} = \frac{1}{3}$

Compare $\frac{1}{3}$ and $\frac{1}{8}$

Cross-multiply:
- $1 \times 8 = 8$
- $1 \times 3 = 3$

$8 > 3$, so $\frac{1}{3} > \frac{1}{8}$ → $\frac{4}{12} > \frac{1}{8}$

✔ Answer: >

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Problem 8: $\frac{3}{5} \quad \text{vs} \quad \frac{5}{12}$

Cross-multiply:
- $3 \times 12 = 36$
- $5 \times 5 = 25$

$36 > 25$, so $\frac{3}{5} > \frac{5}{12}$

✔ Answer: >

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Problem 9: $\frac{10}{12} \quad \text{vs} \quad \frac{1}{4}$

Simplify $\frac{10}{12} = \frac{5}{6}$

Compare $\frac{5}{6}$ and $\frac{1}{4}$

Cross-multiply:
- $5 \times 4 = 20$
- $1 \times 6 = 6$

$20 > 6$, so $\frac{10}{12} > \frac{1}{4}$

✔ Answer: >

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Problem 10: $\frac{4}{5} \quad \text{vs} \quad \frac{4}{10}$

Same numerator, compare denominators.

Smaller denominator → larger fraction.

$\frac{4}{5} > \frac{4}{10}$

✔ Answer: >

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Problem 11: $\frac{2}{5} \quad \text{vs} \quad \frac{3}{6}$

Simplify $\frac{3}{6} = \frac{1}{2}$

Compare $\frac{2}{5}$ and $\frac{1}{2}$

Cross-multiply:
- $2 \times 2 = 4$
- $1 \times 5 = 5$

$4 < 5$, so $\frac{2}{5} < \frac{3}{6}$

✔ Answer: <

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Problem 12: $\frac{3}{6} \quad \text{vs} \quad \frac{2}{4}$

Simplify both:
- $\frac{3}{6} = \frac{1}{2}$
- $\frac{2}{4} = \frac{1}{2}$

So they are equal.

✔ Answer: =

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Problem 13: $\frac{1}{10} \quad \text{vs} \quad \frac{2}{4}$

Simplify $\frac{2}{4} = \frac{1}{2}$

Clearly $\frac{1}{10} < \frac{1}{2}$

✔ Answer: <

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Problem 14: $\frac{1}{8} \quad \text{vs} \quad \frac{4}{6}$

Simplify $\frac{4}{6} = \frac{2}{3}$

Compare $\frac{1}{8}$ and $\frac{2}{3}$

Cross-multiply:
- $1 \times 3 = 3$
- $2 \times 8 = 16$

$3 < 16$, so $\frac{1}{8} < \frac{4}{6}$

✔ Answer: <

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Problem 15: $\frac{5}{8} \quad \text{vs} \quad \frac{2}{3}$

Cross-multiply:
- $5 \times 3 = 15$
- $2 \times 8 = 16$

$15 < 16$, so $\frac{5}{8} < \frac{2}{3}$

✔ Answer: <

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Problem 16: $\frac{2}{5} \quad \text{vs} \quad \frac{3}{4}$

Cross-multiply:
- $2 \times 4 = 8$
- $3 \times 5 = 15$

$8 < 15$, so $\frac{2}{5} < \frac{3}{4}$

✔ Answer: <

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Problem 17: $\frac{1}{4} \quad \text{vs} \quad \frac{11}{12}$

Cross-multiply:
- $1 \times 12 = 12$
- $11 \times 4 = 44$

$12 < 44$, so $\frac{1}{4} < \frac{11}{12}$

✔ Answer: <

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Problem 18: $\frac{3}{6} \quad \text{vs} \quad \frac{2}{8}$

Simplify:
- $\frac{3}{6} = \frac{1}{2}$
- $\frac{2}{8} = \frac{1}{4}$

$\frac{1}{2} > \frac{1}{4}$

✔ Answer: >

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Problem 19: $\frac{1}{6} \quad \text{vs} \quad \frac{4}{5}$

Clearly $\frac{1}{6} < \frac{4}{5}$

Cross-multiply:
- $1 \times 5 = 5$
- $4 \times 6 = 24$

$5 < 24$, so $\frac{1}{6} < \frac{4}{5}$

✔ Answer: <

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Problem 20: $\frac{2}{10} \quad \text{vs} \quad \frac{2}{8}$

Same numerator, compare denominators.

Smaller denominator → larger fraction.

$\frac{2}{8} > \frac{2}{10}$, so $\frac{2}{10} < \frac{2}{8}$

✔ Answer: <

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| Ex. | < |
| 1 | > |
| 2 | < |
| 3 | > |
| 4 | < |
| 5 | > |
| 6 | > |
| 7 | > |
| 8 | > |
| 9 | > |
| 10 | > |
| 11 | < |
| 12 | = |
| 13 | < |
| 14 | < |
| 15 | < |
| 16 | < |
| 17 | < |
| 18 | > |
| 19 | < |
| 20 | < |

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You can now fill in the answer sheet accordingly.

Let me know if you'd like this printed out or formatted as a worksheet!