Comparing Fractions Worksheets - Math Monks - Free Printable

Let's solve each fraction comparison step by step using the visual models provided. We'll shade the appropriate parts and then use <, >, or = to compare the fractions.

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

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

✔ Visually, half of a circle is larger than one-third.

➡️ So:
$$
\frac{1}{2} > \frac{1}{3}
$$

✔️ Already filled in correctly.

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2. Compare: $\frac{2}{3}$ vs. $\frac{2}{6}$

- Left triangle: Divided into 3 parts, 2 shaded → $\frac{2}{3}$
- Right triangle: Divided into 6 parts, 2 shaded → $\frac{2}{6}$

Now simplify $\frac{2}{6} = \frac{1}{3}$

We know:
$$
\frac{2}{3} > \frac{1}{3}
$$

So:
$$
\frac{2}{3} > \frac{2}{6}
$$

✔ Shade 2 out of 3 on the left triangle, 2 out of 6 (i.e., 1/3) on the right.

Answer:
$$
\frac{2}{3} > \frac{2}{6}
$$

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

- Left square: Divided into 4 parts, 2 shaded → $\frac{2}{4}$
- Right square: Divided into 2 parts, 1 shaded → $\frac{1}{2}$

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

So both are equal.

✔ Shade 2 out of 4 on the left, 1 out of 2 on the right.

Answer:
$$
\frac{2}{4} = \frac{1}{2}
$$

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4. Compare: $\frac{4}{5}$ vs. $\frac{8}{10}$

- Left pentagon: 5 parts, 4 shaded → $\frac{4}{5}$
- Right decagon (10 sides): 10 parts, 8 shaded → $\frac{8}{10}$

Simplify $\frac{8}{10} = \frac{4}{5}$

So they are equal.

✔ Shade 4 out of 5 on the left, 8 out of 10 on the right.

Answer:
$$
\frac{4}{5} = \frac{8}{10}
$$

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5. Compare: $\frac{5}{6}$ vs. $\frac{2}{6}$

- Left hexagon: 6 parts, 5 shaded → $\frac{5}{6}$
- Right hexagon: 6 parts, 2 shaded → $\frac{2}{6}$

Same denominator → compare numerators: 5 > 2

So:
$$
\frac{5}{6} > \frac{2}{6}
$$

✔ Shade 5 out of 6 on the left, 2 out of 6 on the right.

Answer:
$$
\frac{5}{6} > \frac{2}{6}
$$

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6. Compare: $\frac{3}{8}$ vs. $\frac{3}{4}$

- Left octagon: 8 parts, 3 shaded → $\frac{3}{8}$
- Right octagon: 4 parts, 3 shaded → $\frac{3}{4}$

But wait — the second shape is divided into 4 parts? Actually, it's an octagon divided into 4 parts? That’s unusual.

Wait — let’s look closely:

- The left octagon has 8 equal parts → $\frac{3}{8}$
- The right octagon has 4 equal parts? But it looks like it's divided into 4 sectors → so it's actually a circle-like division?

Wait — no: both shapes are octagons, but the right one is divided into 4 parts, meaning each part is 1/4 of the whole.

But that means the whole is split into 4 equal parts, so if 3 are shaded, it's $\frac{3}{4}$.

Now compare:
- $\frac{3}{8}$ vs. $\frac{3}{4}$

We can write $\frac{3}{4} = \frac{6}{8}$

So:
$$
\frac{3}{8} < \frac{6}{8} \Rightarrow \frac{3}{8} < \frac{3}{4}
$$

✔ Shade 3 out of 8 on the left, 3 out of 4 on the right.

Answer:
$$
\frac{3}{8} < \frac{3}{4}
$$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| $\frac{1}{2}$ ___ $\frac{1}{3}$ | $>$ |
| $\frac{2}{3}$ ___ $\frac{2}{6}$ | $>$ |
| $\frac{2}{4}$ ___ $\frac{1}{2}$ | $=$ |
| $\frac{4}{5}$ ___ $\frac{8}{10}$ | $=$ |
| $\frac{5}{6}$ ___ $\frac{2}{6}$ | $>$ |
| $\frac{3}{8}$ ___ $\frac{3}{4}$ | $<$ |

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🔍 Explanation Summary:

- When comparing fractions:
- If denominators are same → compare numerators.
- If not, simplify or convert to common denominators.
- Visual models help see which shaded area is larger.

For example:
- $\frac{2}{4} = \frac{1}{2}$ → same amount
- $\frac{8}{10} = \frac{4}{5}$ → same as left
- $\frac{3}{8}$ is less than $\frac{3}{4}$ because even though both have 3 shaded parts, the parts in $\frac{3}{4}$ are larger (since the whole is divided into fewer pieces).

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🎯 Final Answer Sheet:

```
1/2 > 1/3
2/3 > 2/6
2/4 = 1/2
4/5 = 8/10
5/6 > 2/6
3/8 < 3/4
```

✔ All comparisons are correct based on shading and fraction equivalence.