Comparing Fractions with Diagrams Worksheet - Students use fraction circles to compare values and fill in missing fractions and comparison symbols.

Let's solve each problem on the "Comparing Fractions with Diagrams Sheet 3" worksheet step by step.

We are given pairs of circles divided into equal parts, with some parts shaded. We need to:

1. Determine the fraction represented by each shaded portion.
2. Compare the two fractions using >, <, or =.

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🔍 How to read the diagrams:

- Count the total number of equal parts in the circle → this is the denominator.
- Count the number of shaded parts → this is the numerator.
- Write the fraction and compare.

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✔ Problem 1 (Already done for us):

- Left circle: 4 parts, 3 shaded → $ \frac{3}{4} $
- Right circle: 3 parts, 2 shaded → $ \frac{2}{3} $
- Comparison: $ \frac{3}{4} > \frac{2}{3} $

Let’s go through the rest.

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2)

- Left circle: 5 parts, 3 shaded → $ \frac{3}{5} $
- Right circle: 4 parts, 3 shaded → $ \frac{3}{4} $
- Compare: $ \frac{3}{5} < \frac{3}{4} $

✔ Answer: $ \frac{3}{5} < \frac{3}{4} $

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3)

- Left circle: 8 parts, 1 shaded → $ \frac{1}{8} $
- Right circle: 3 parts, 1 shaded → $ \frac{1}{3} $
- Compare: $ \frac{1}{8} < \frac{1}{3} $

✔ Answer: $ \frac{1}{8} < \frac{1}{3} $

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4)

- Left circle: 6 parts, 4 shaded → $ \frac{4}{6} = \frac{2}{3} $
- Right circle: 3 parts, 2 shaded → $ \frac{2}{3} $
- Compare: $ \frac{4}{6} = \frac{2}{3} $

✔ Answer: $ \frac{4}{6} = \frac{2}{3} $

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5)

- Left circle: 5 parts, 4 shaded → $ \frac{4}{5} $
- Right circle: 8 parts, 6 shaded → $ \frac{6}{8} = \frac{3}{4} $
- Compare: $ \frac{4}{5} = 0.8 $, $ \frac{3}{4} = 0.75 $ → $ \frac{4}{5} > \frac{3}{4} $

✔ Answer: $ \frac{4}{5} > \frac{6}{8} $

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6)

- Left circle: 10 parts, 7 shaded → $ \frac{7}{10} $
- Right circle: 4 parts, 3 shaded → $ \frac{3}{4} $
- Compare: $ \frac{7}{10} = 0.7 $, $ \frac{3}{4} = 0.75 $ → $ \frac{7}{10} < \frac{3}{4} $

✔ Answer: $ \frac{7}{10} < \frac{3}{4} $

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7)

- Left circle: 10 parts, 2 shaded → $ \frac{2}{10} = \frac{1}{5} $
- Right circle: 5 parts, 2 shaded → $ \frac{2}{5} $
- Compare: $ \frac{1}{5} < \frac{2}{5} $

✔ Answer: $ \frac{2}{10} < \frac{2}{5} $

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8)

- Left circle: 8 parts, 5 shaded → $ \frac{5}{8} $
- Right circle: 10 parts, 6 shaded → $ \frac{6}{10} = \frac{3}{5} $
- Compare: $ \frac{5}{8} = 0.625 $, $ \frac{3}{5} = 0.6 $ → $ \frac{5}{8} > \frac{6}{10} $

✔ Answer: $ \frac{5}{8} > \frac{6}{10} $

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9)

- Left circle: 5 parts, 1 shaded → $ \frac{1}{5} $
- Right circle: 12 parts, 5 shaded → $ \frac{5}{12} $
- Compare: $ \frac{1}{5} = 0.2 $, $ \frac{5}{12} \approx 0.4167 $ → $ \frac{1}{5} < \frac{5}{12} $

✔ Answer: $ \frac{1}{5} < \frac{5}{12} $

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10)

- Left circle: 8 parts, 6 shaded → $ \frac{6}{8} = \frac{3}{4} $
- Right circle: 6 parts, 4 shaded → $ \frac{4}{6} = \frac{2}{3} $
- Compare: $ \frac{3}{4} = 0.75 $, $ \frac{2}{3} \approx 0.666... $ → $ \frac{3}{4} > \frac{2}{3} $

✔ Answer: $ \frac{6}{8} > \frac{4}{6} $

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✔ Final Answers:

| # | Fraction 1 | Symbol | Fraction 2 |
|---|------------|--------|------------|
| 1 | $ \frac{3}{4} $ | > | $ \frac{2}{3} $ |
| 2 | $ \frac{3}{5} $ | < | $ \frac{3}{4} $ |
| 3 | $ \frac{1}{8} $ | < | $ \frac{1}{3} $ |
| 4 | $ \frac{4}{6} $ | = | $ \frac{2}{3} $ |
| 5 | $ \frac{4}{5} $ | > | $ \frac{6}{8} $ |
| 6 | $ \frac{7}{10} $ | < | $ \frac{3}{4} $ |
| 7 | $ \frac{2}{10} $ | < | $ \frac{2}{5} $ |
| 8 | $ \frac{5}{8} $ | > | $ \frac{6}{10} $ |
| 9 | $ \frac{1}{5} $ | < | $ \frac{5}{12} $ |
|10 | $ \frac{6}{8} $ | > | $ \frac{4}{6} $ |

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📝 Explanation Summary:

- Always count total parts (denominator) and shaded parts (numerator).
- Simplify fractions when possible.
- Use decimals or common denominators to compare if needed.
- The symbol shows which fraction is larger or if they’re equal.

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