Math worksheet for comparing fractions, including visual and numerical exercises for students.

Let's go through each part of the worksheet "Comparing Fractions" step by step and solve the problems.

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a. Color and compare.

We are given two circles:
- One is divided into 4 equal parts, with 3 shaded → $\frac{3}{4}$
- The other is divided into 6 equal parts, with 5 shaded → $\frac{5}{6}$

We need to color them (as per instruction), but since we can't color here, we’ll compare the fractions.

To compare $\frac{3}{4}$ and $\frac{5}{6}$:

Find a common denominator:
LCM of 4 and 6 is 12.

Convert:
- $\frac{3}{4} = \frac{9}{12}$
- $\frac{5}{6} = \frac{10}{12}$

So, $\frac{5}{6} > \frac{3}{4}$

✔ Answer: $\frac{5}{6}$ is greater than $\frac{3}{4}$

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b. Write any fraction that is less than $\frac{1}{4}$

We need a fraction smaller than $\frac{1}{4}$.

Examples:
- $\frac{1}{8}$, $\frac{1}{5}$, $\frac{1}{6}$, $\frac{1}{10}$, etc.

✔ Answer: $\frac{1}{8}$ (or any fraction less than $\frac{1}{4}$)

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c. Olivia and Hudson each have an apple...

- Olivia cuts her apple into halves and eats one piece → $\frac{1}{2}$
- Hudson cuts his into quarters and eats one piece → $\frac{1}{4}$

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

$\frac{1}{2} = \frac{2}{4}$, so $\frac{1}{2} > \frac{1}{4}$

✔ Answer: Olivia ate more of her apple.

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d. Color and compare.

Given:
- First rectangle: $\frac{1}{2}$
- Second rectangle: $\frac{1}{2}$

They are equal.

So, $\frac{1}{2} = \frac{1}{2}$

But then it shows: $\frac{1}{2}$ ___ $\frac{2}{3}$

Wait — the problem says "Color and compare" with:
- $\frac{1}{2}$ and $\frac{2}{3}$

Let’s compare $\frac{1}{2}$ and $\frac{2}{3}$

Common denominator: 6
- $\frac{1}{2} = \frac{3}{6}$
- $\frac{2}{3} = \frac{4}{6}$

So, $\frac{2}{3} > \frac{1}{2}$

✔ Answer: $\frac{1}{2} < \frac{2}{3}$

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e. Color and compare.

Two triangles:
- First: divided into 2 parts, 1 shaded → $\frac{1}{2}$
- Second: divided into 6 parts, 4 shaded → $\frac{4}{6}$

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

Compare $\frac{1}{2}$ and $\frac{2}{3}$

As above: $\frac{1}{2} = \frac{3}{6}$, $\frac{2}{3} = \frac{4}{6}$ → $\frac{2}{3} > \frac{1}{2}$

✔ So, $\frac{4}{6} > \frac{1}{2}$

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f. Use the number line to compare the fractions below.

Number line from 0 to 1, marked in eighths:
0, $\frac{1}{8}$, $\frac{2}{8}$, $\frac{3}{8}$, $\frac{4}{8}$, $\frac{5}{8}$, $\frac{6}{8}$, $\frac{7}{8}$, 1

Compare: $\frac{3}{4}$ and $\frac{3}{8}$

Convert:
- $\frac{3}{4} = \frac{6}{8}$
- $\frac{3}{8} = \frac{3}{8}$

On the number line, $\frac{6}{8}$ is farther right than $\frac{3}{8}$

So, $\frac{3}{4} > \frac{3}{8}$

✔ Answer: $\frac{3}{4} > \frac{3}{8}$

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g. Sal and Jen ordered pizzas...

- Sal ate $\frac{1}{4}$ of his pizza
- Jen ate $\frac{1}{2}$ of her pizza

Compare $\frac{1}{4}$ and $\frac{1}{2}$

$\frac{1}{2} = \frac{2}{4}$ → $\frac{1}{2} > \frac{1}{4}$

✔ Answer: Jen ate more pizza.

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h. Write any fraction that is greater than $\frac{1}{2}$

Examples:
- $\frac{3}{4}$, $\frac{2}{3}$, $\frac{5}{8}$, $\frac{3}{5}$, etc.

✔ Answer: $\frac{3}{4}$ (or any fraction greater than $\frac{1}{2}$)

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✔ Final Answers Summary:

| Question | Answer |
|--------|--------|
| a | $\frac{5}{6} > \frac{3}{4}$ |
| b | Any fraction less than $\frac{1}{4}$, e.g., $\frac{1}{8}$ |
| c | Olivia |
| d | $\frac{1}{2} < \frac{2}{3}$ |
| e | $\frac{1}{2} < \frac{4}{6}$ |
| f | $\frac{3}{4} > \frac{3}{8}$ |
| g | Jen |
| h | Any fraction greater than $\frac{1}{2}$, e.g., $\frac{3}{4}$ |

Let me know if you'd like this formatted as a printable answer sheet!