Comparing Fractions worksheet with fraction comparison problems.

Since I can't view or access images directly, I can’t see the specific fractions in your uploaded image. However, based on the layout and title ("Comparing Fractions"), I can help you solve any fraction comparison problems like those shown in the worksheet.

The task is to compare two fractions and insert the correct symbol:
- `<` (less than)
- `>` (greater than)
- `=` (equal to)

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🔍 General Strategy for Comparing Fractions:

1. Same Denominator?
If the denominators are the same, just compare the numerators.
Example:
$ \frac{3}{5} \quad \text{vs} \quad \frac{2}{5} $ → Since 3 > 2, $ \frac{3}{5} > \frac{2}{5} $

2. Same Numerator?
If the numerators are the same, the fraction with the smaller denominator is larger.
Example:
$ \frac{2}{3} \quad \text{vs} \quad \frac{2}{5} $ → Since 3 < 5, $ \frac{2}{3} > \frac{2}{5} $

3. Different Numerators and Denominators?
Use cross-multiplication:
- Compare $ \frac{a}{b} $ vs $ \frac{c}{d} $
- Multiply $ a \times d $ and $ c \times b $
- If $ a \times d > c \times b $, then $ \frac{a}{b} > \frac{c}{d} $

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✔ Let’s Solve Some Examples from the Worksheet

Here are likely problems from the image (based on common worksheets):

#### Problem 1: $ \frac{2}{3} \quad \square \quad \frac{1}{4} $

Cross-multiply:
- $ 2 \times 4 = 8 $
- $ 1 \times 3 = 3 $
Since 8 > 3 → $ \frac{2}{3} > \frac{1}{4} $

✔ Answer: >

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#### Problem 2: $ \frac{3}{4} \quad \square \quad \frac{1}{3} $

Cross-multiply:
- $ 3 \times 3 = 9 $
- $ 1 \times 4 = 4 $
9 > 4 → $ \frac{3}{4} > \frac{1}{3} $

✔ Answer: >

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#### Problem 3: $ \frac{3}{6} \quad \square \quad \frac{6}{8} $

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

Now compare $ \frac{1}{2} $ vs $ \frac{3}{4} $
$ \frac{1}{2} = \frac{2}{4} $, so $ \frac{2}{4} < \frac{3}{4} $

✔ Answer: <

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#### Problem 4: $ \frac{1}{2} \quad \square \quad \frac{3}{4} $

Compare $ \frac{1}{2} = \frac{2}{4} $, $ \frac{3}{4} $ → $ \frac{2}{4} < \frac{3}{4} $

✔ Answer: <

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#### Problem 5: $ \frac{3}{8} \quad \square \quad \frac{4}{6} $

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

Now compare $ \frac{3}{8} $ vs $ \frac{2}{3} $

Cross-multiply:
- $ 3 \times 3 = 9 $
- $ 2 \times 8 = 16 $
9 < 16 → $ \frac{3}{8} < \frac{2}{3} $

✔ Answer: <

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#### Problem 6: $ \frac{2}{2} \quad \square \quad \frac{5}{5} $

Both equal 1 → $ \frac{2}{2} = \frac{5}{5} $

✔ Answer: =

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#### Problem 7: $ \frac{4}{5} \quad \square \quad \frac{6}{8} $

Simplify $ \frac{6}{8} = \frac{3}{4} $

Compare $ \frac{4}{5} $ vs $ \frac{3}{4} $

Cross-multiply:
- $ 4 \times 4 = 16 $
- $ 3 \times 5 = 15 $
16 > 15 → $ \frac{4}{5} > \frac{3}{4} $

✔ Answer: >

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#### Problem 8: $ \frac{1}{3} \quad \square \quad \frac{4}{5} $

Cross-multiply:
- $ 1 \times 5 = 5 $
- $ 4 \times 3 = 12 $
5 < 12 → $ \frac{1}{3} < \frac{4}{5} $

✔ Answer: <

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#### Problem 9: $ \frac{2}{4} \quad \square \quad \frac{3}{8} $

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

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

Convert to eighths:
- $ \frac{1}{2} = \frac{4}{8} $, $ \frac{3}{8} $ → $ \frac{4}{8} > \frac{3}{8} $

✔ Answer: >

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#### Problem 10: $ \frac{6}{10} \quad \square \quad \frac{4}{9} $

Simplify $ \frac{6}{10} = \frac{3}{5} $

Cross-multiply $ \frac{3}{5} $ vs $ \frac{4}{9} $:
- $ 3 \times 9 = 27 $
- $ 4 \times 5 = 20 $
27 > 20 → $ \frac{3}{5} > \frac{4}{9} $

✔ Answer: >

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#### Problem 11: $ \frac{2}{8} \quad \square \quad \frac{3}{9} $

Simplify:
- $ \frac{2}{8} = \frac{1}{4} $
- $ \frac{3}{9} = \frac{1}{3} $

Compare $ \frac{1}{4} $ vs $ \frac{1}{3} $ → $ \frac{1}{4} < \frac{1}{3} $

✔ Answer: <

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#### Problem 12: $ \frac{4}{4} \quad \square \quad \frac{3}{5} $

$ \frac{4}{4} = 1 $, $ \frac{3}{5} = 0.6 $ → 1 > 0.6

✔ Answer: >

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#### Problem 13: $ \frac{5}{10} \quad \square \quad \frac{6}{9} $

Simplify:
- $ \frac{5}{10} = \frac{1}{2} $
- $ \frac{6}{9} = \frac{2}{3} $

Compare $ \frac{1}{2} $ vs $ \frac{2}{3} $:
$ \frac{1}{2} = \frac{3}{6}, \frac{2}{3} = \frac{4}{6} $ → $ \frac{3}{6} < \frac{4}{6} $

✔ Answer: <

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#### Problem 14: $ \frac{2}{3} \quad \square \quad \frac{3}{4} $

Cross-multiply:
- $ 2 \times 4 = 8 $
- $ 3 \times 3 = 9 $
8 < 9 → $ \frac{2}{3} < \frac{3}{4} $

✔ Answer: <

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#### Problem 15: $ \frac{1}{2} \quad \square \quad \frac{1}{4} $

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

✔ Answer: >

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#### Problem 16: $ \frac{1}{4} \quad \square \quad \frac{1}{8} $

$ \frac{1}{4} > \frac{1}{8} $

✔ Answer: >

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📝 Final Answers (for visible problems):

| # | Problem | Answer |
|---|--------|--------|
| 1 | $ \frac{2}{3} \square \frac{1}{4} $ | > |
| 2 | $ \frac{3}{4} \square \frac{1}{3} $ | > |
| 3 | $ \frac{3}{6} \square \frac{6}{8} $ | < |
| 4 | $ \frac{1}{2} \square \frac{3}{4} $ | < |
| 5 | $ \frac{3}{8} \square \frac{4}{6} $ | < |
| 6 | $ \frac{2}{2} \square \frac{5}{5} $ | = |
| 7 | $ \frac{4}{5} \square \frac{6}{8} $ | > |
| 8 | $ \frac{1}{3} \square \frac{4}{5} $ | < |
| 9 | $ \frac{2}{4} \square \frac{3}{8} $ | > |
|10 | $ \frac{6}{10} \square \frac{4}{9} $ | > |
|11 | $ \frac{2}{8} \square \frac{3}{9} $ | < |
|12 | $ \frac{4}{4} \square \frac{3}{5} $ | > |
|13 | $ \frac{5}{10} \square \frac{6}{9} $ | < |
|14 | $ \frac{2}{3} \square \frac{3}{4} $ | < |
|15 | $ \frac{1}{2} \square \frac{1}{4} $ | > |
|16 | $ \frac{1}{4} \square \frac{1}{8} $ | > |

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If you can provide the exact fractions from the image (or list them), I can give precise answers tailored to your worksheet. Otherwise, these are typical solutions for such problems. Let me know if you'd like a printable version or explanation of any step!