Comparing and Ordering Fractions - Worksheet | Maths Year 3 - Free Printable

Let's solve each of the fraction comparison problems step by step, using reasoning and visual shading as suggested. We'll compare the fractions and fill in the correct inequality sign (either > or <) between them.

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1. Compare: $ \frac{1}{4} $ ___ $ \frac{3}{4} $

- Both fractions have the same denominator (4).
- Since 1 < 3, then $ \frac{1}{4} < \frac{3}{4} $
- Answer: $ \frac{1}{4} < \frac{3}{4} $

✔ Shading:
- First bar (for $ \frac{1}{4} $): Shade 1 out of 4 boxes.
- Second bar (for $ \frac{3}{4} $): Shade 3 out of 4 boxes.
→ Clearly, the second is larger.

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2. Compare: $ \frac{4}{5} $ ___ $ \frac{2}{5} $

- Same denominator (5).
- 4 > 2 → So $ \frac{4}{5} > \frac{2}{5} $
- Answer: $ \frac{4}{5} > \frac{2}{5} $

✔ Shading:
- First bar: shade 4 out of 5 boxes.
- Second bar: shade 2 out of 5 boxes.
→ First is clearly larger.

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3. Compare: $ \frac{7}{8} $ ___ $ \frac{5}{8} $

- Same denominator (8).
- 7 > 5 → So $ \frac{7}{8} > \frac{5}{8} $
- Answer: $ \frac{7}{8} > \frac{5}{8} $

✔ Shading:
- First bar: shade 7 out of 8 boxes.
- Second bar: shade 5 out of 8 boxes.
→ First is larger.

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4. Compare: $ \frac{1}{6} $ ___ $ \frac{3}{6} $

- Same denominator (6).
- 1 < 3 → So $ \frac{1}{6} < \frac{3}{6} $
- Answer: $ \frac{1}{6} < \frac{3}{6} $

✔ Shading:
- First bar: shade 1 out of 6 boxes.
- Second bar: shade 3 out of 6 boxes.
→ Second is larger.

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5. Compare: $ \frac{5}{10} $ ___ $ \frac{8}{10} $

- Same denominator (10).
- 5 < 8 → So $ \frac{5}{10} < \frac{8}{10} $
- Answer: $ \frac{5}{10} < \frac{8}{10} $

✔ Shading:
- First bar: shade 5 out of 10 boxes.
- Second bar: shade 8 out of 10 boxes.
→ Second is larger.

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6. Compare: $ \frac{9}{12} $ ___ $ \frac{3}{12} $

- Same denominator (12).
- 9 > 3 → So $ \frac{9}{12} > \frac{3}{12} $
- Answer: $ \frac{9}{12} > \frac{3}{12} $

✔ Shading:
- First bar: shade 9 out of 12 boxes.
- Second bar: shade 3 out of 12 boxes.
→ First is much larger.

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✔ Final Answers:

1. $ \frac{1}{4} < \frac{3}{4} $
2. $ \frac{4}{5} > \frac{2}{5} $
3. $ \frac{7}{8} > \frac{5}{8} $
4. $ \frac{1}{6} < \frac{3}{6} $
5. $ \frac{5}{10} < \frac{8}{10} $
6. $ \frac{9}{12} > \frac{3}{12} $

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🔍 Explanation:

All these comparisons involve fractions with the same denominators, which makes it easy to compare just by looking at the numerators:
- The fraction with the larger numerator is greater.
- The fraction with the smaller numerator is smaller.

The diagrams help visualize this: when you shade the appropriate number of parts in equal-sized bars, you can see which one takes up more space.

Let me know if you'd like a printable version or visual sketches!