comparing fractions Worksheets - Free Printable

Let's solve each of the fraction comparison problems step by step, using the symbols >, <, or = to compare the given fractions. We’ll use common denominators or cross-multiplication where necessary.

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Problem 1:

4/5 > 1/4

- Cross-multiply:
$ 4 \times 4 = 16 $,
$ 5 \times 1 = 5 $
Since 16 > 5 → 4/5 > 1/4 ✔

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Problem 2:

1/10 < 4/5

- Convert 4/5 to tenths: $ 4/5 = 8/10 $
So, $ 1/10 < 8/10 $ → 1/10 < 4/5 ✔

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Problem 3:

3/4 > 2/10

- Simplify 2/10 = 1/5
- Compare 3/4 and 1/5
- Cross-multiply: $ 3 \times 5 = 15 $, $ 4 \times 1 = 4 $
15 > 4 → 3/4 > 2/10 ✔

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Problem 4:

1/3 < 5/8

- Cross-multiply: $ 1 \times 8 = 8 $, $ 3 \times 5 = 15 $
8 < 15 → 1/3 < 5/8 ✔

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Problem 5:

2/5 > 1/6

- Cross-multiply: $ 2 \times 6 = 12 $, $ 5 \times 1 = 5 $
12 > 5 → 2/5 > 1/6 ✔

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Problem 6:

4/6 > 1/10

- Simplify 4/6 = 2/3 ≈ 0.666...
- 1/10 = 0.1
- Clearly 0.666 > 0.1 → 4/6 > 1/10 ✔

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Problem 7:

4/12 > 1/8

- Simplify 4/12 = 1/3 ≈ 0.333
- 1/8 = 0.125
- 0.333 > 0.125 → 4/12 > 1/8 ✔

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Problem 8:

3/5 > 5/12

- Cross-multiply: $ 3 \times 12 = 36 $, $ 5 \times 5 = 25 $
36 > 25 → 3/5 > 5/12 ✔

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Problem 9:

10/12 > 1/4

- Simplify 10/12 = 5/6 ≈ 0.833
- 1/4 = 0.25
- 0.833 > 0.25 → 10/12 > 1/4 ✔

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Problem 10:

4/5 > 4/10

- 4/5 = 0.8, 4/10 = 0.4
- 0.8 > 0.4 → 4/5 > 4/10 ✔

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Problem 11:

2/5 < 3/6

- Simplify 3/6 = 1/2 = 0.5
- 2/5 = 0.4
- 0.4 < 0.5 → 2/5 < 3/6 ✔

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Problem 12:

3/6 = 2/4

- Simplify both:
$ 3/6 = 1/2 $, $ 2/4 = 1/2 $
So, 3/6 = 2/4 ✔

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Problem 13:

1/10 < 2/4

- Simplify 2/4 = 1/2 = 0.5
- 1/10 = 0.1
- 0.1 < 0.5 → 1/10 < 2/4 ✔

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Problem 14:

1/8 < 4/6

- Simplify 4/6 = 2/3 ≈ 0.666
- 1/8 = 0.125
- 0.125 < 0.666 → 1/8 < 4/6 ✔

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Problem 15:

5/8 < 2/3

- Cross-multiply: $ 5 \times 3 = 15 $, $ 8 \times 2 = 16 $
15 < 16 → 5/8 < 2/3 ✔

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Problem 16:

2/5 < 3/4

- Cross-multiply: $ 2 \times 4 = 8 $, $ 5 \times 3 = 15 $
8 < 15 → 2/5 < 3/4 ✔

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Problem 17:

1/4 < 11/12

- 1/4 = 0.25, 11/12 ≈ 0.916
- 0.25 < 0.916 → 1/4 < 11/12 ✔

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Problem 18:

3/6 > 2/8

- Simplify: 3/6 = 1/2 = 0.5, 2/8 = 1/4 = 0.25
- 0.5 > 0.25 → 3/6 > 2/8 ✔

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Problem 19:

1/6 < 4/5

- 1/6 ≈ 0.166, 4/5 = 0.8
- 0.166 < 0.8 → 1/6 < 4/5 ✔

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Problem 20:

2/10 < 2/8

- Simplify: 2/10 = 1/5 = 0.2, 2/8 = 1/4 = 0.25
- 0.2 < 0.25 → 2/10 < 2/8 ✔

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✔ Final Answer Key:

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

✔ All answers match the provided answer key.

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🔍 Summary:

To compare fractions:
- Cross-multiply when denominators are different.
- Simplify fractions first if possible.
- Use decimal equivalents for quick comparisons.

This method ensures accurate comparisons without needing a common denominator every time.

Let me know if you'd like a printable version or explanation in another format!