Comparing fractions worksheet with visual representations and inequality symbols.

Let's solve each of the fraction comparison problems step by step. The task is to shade the circles (as shown in the image) and then use >, <, or = to compare the fractions.

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🔹 Problem 1:

Compare:
$$
\frac{1}{2} \quad \text{vs.} \quad \frac{1}{3}
$$

- Visuals:
- Left circle: divided into 2 parts, 1 shaded → $\frac{1}{2}$
- Right circle: divided into 3 parts, 1 shaded → $\frac{1}{3}$

- Analysis:
$\frac{1}{2} = 0.5$, $\frac{1}{3} \approx 0.333$ → So, $\frac{1}{2} > \frac{1}{3}$

✔ Answer: $ \frac{1}{2} > \frac{1}{3} $ ✔ (already filled)

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🔹 Problem 2:

Compare:
$$
\frac{4}{12} \quad \text{vs.} \quad \frac{2}{4}
$$

- Simplify both:
- $\frac{4}{12} = \frac{1}{3} \approx 0.333$
- $\frac{2}{4} = \frac{1}{2} = 0.5$

- So, $\frac{4}{12} < \frac{2}{4}$

✔ Answer: $ \frac{4}{12} < \frac{2}{4} $

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🔹 Problem 3:

Compare:
$$
\frac{3}{4} \quad \text{vs.} \quad \frac{2}{3}
$$

- Convert to common denominator (LCM of 4 and 3 is 12):
- $\frac{3}{4} = \frac{9}{12}$
- $\frac{2}{3} = \frac{8}{12}$

- So, $\frac{3}{4} > \frac{2}{3}$

✔ Answer: $ \frac{3}{4} > \frac{2}{3} $

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🔹 Problem 4:

Compare:
$$
\frac{6}{12} \quad \text{vs.} \quad \frac{3}{8}
$$

- Simplify:
- $\frac{6}{12} = \frac{1}{2} = 0.5$
- $\frac{3}{8} = 0.375$

- So, $\frac{6}{12} > \frac{3}{8}$

✔ Answer: $ \frac{6}{12} > \frac{3}{8} $

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🔹 Problem 5:

Compare:
$$
\frac{1}{2} \quad \text{vs.} \quad \frac{3}{4}
$$

- $\frac{1}{2} = 0.5$, $\frac{3}{4} = 0.75$

- So, $\frac{1}{2} < \frac{3}{4}$

✔ Answer: $ \frac{1}{2} < \frac{3}{4} $

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🔹 Problem 6:

Compare:
$$
\frac{2}{4} \quad \text{vs.} \quad \frac{2}{5}
$$

- Simplify:
- $\frac{2}{4} = \frac{1}{2} = 0.5$
- $\frac{2}{5} = 0.4$

- So, $\frac{2}{4} > \frac{2}{5}$

✔ Answer: $ \frac{2}{4} > \frac{2}{5} $

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✔ Final Answers:

| Problem | Comparison |
|--------|------------|
| 1 | $ \frac{1}{2} > \frac{1}{3} $ |
| 2 | $ \frac{4}{12} < \frac{2}{4} $ |
| 3 | $ \frac{3}{4} > \frac{2}{3} $ |
| 4 | $ \frac{6}{12} > \frac{3}{8} $ |
| 5 | $ \frac{1}{2} < \frac{3}{4} $ |
| 6 | $ \frac{2}{4} > \frac{2}{5} $ |

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📝 How to Shade:

For each pair, shade the number of parts equal to the numerator:

- For $\frac{1}{2}$: shade 1 out of 2 parts.
- For $\frac{1}{3}$: shade 1 out of 3 parts.
- For $\frac{4}{12}$: shade 4 out of 12 parts (i.e., 1/3).
- For $\frac{2}{4}$: shade 2 out of 4 parts.
- And so on...

The visual representation helps students see which fraction takes up more area.

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✔ All comparisons are now solved!