Fraction Worksheet - 9+ Examples, Format, Pdf - Free Printable

Let's solve each problem step by step and explain the solutions.

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Understanding the Concept:

When we are asked to find "what is $\frac{a}{b}$ of $\frac{c}{d}$?", it means we need to multiply the two fractions:
$$
\frac{a}{b} \times \frac{c}{d}
$$
To multiply fractions:
1. Multiply the numerators.
2. Multiply the denominators.
3. Simplify the result if possible.

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Solving Each Problem

#### a. What is $\frac{1}{3}$ of $\frac{1}{4}$?
$$
\frac{1}{3} \times \frac{1}{4} = \frac{1 \times 1}{3 \times 4} = \frac{1}{12}
$$
✔ Answer: $\boxed{\frac{1}{12}}$

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#### b. What is $\frac{1}{3}$ of $\frac{7}{8}$?
$$
\frac{1}{3} \times \frac{7}{8} = \frac{1 \times 7}{3 \times 8} = \frac{7}{24}
$$
✔ Answer: $\boxed{\frac{7}{24}}$

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#### c. What is $\frac{3}{4}$ of $\frac{3}{7}$?
$$
\frac{3}{4} \times \frac{3}{7} = \frac{3 \times 3}{4 \times 7} = \frac{9}{28}
$$
✔ Answer: $\boxed{\frac{9}{28}}$

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#### d. $\frac{1}{2} \times \frac{2}{8}$
First, simplify $\frac{2}{8} = \frac{1}{4}$, then:
$$
\frac{1}{2} \times \frac{1}{4} = \frac{1 \times 1}{2 \times 4} = \frac{1}{8}
$$
✔ Answer: $\boxed{\frac{1}{8}}$

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#### e. $\frac{1}{3} \times \frac{2}{7} = \frac{2}{21}$
✔ Answer: $\boxed{\frac{2}{21}}$

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#### f. $\frac{5}{5} \times \frac{1}{5}$
Note: $\frac{5}{5} = 1$, so:
$$
1 \times \frac{1}{5} = \frac{1}{5}
$$
✔ Answer: $\boxed{\frac{1}{5}}$

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#### g. $\frac{3}{9} \times \frac{3}{4}$
Simplify $\frac{3}{9} = \frac{1}{3}$, then:
$$
\frac{1}{3} \times \frac{3}{4} = \frac{1 \times 3}{3 \times 4} = \frac{3}{12} = \frac{1}{4}
$$
✔ Answer: $\boxed{\frac{1}{4}}$

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#### h. $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$
✔ Answer: $\boxed{\frac{1}{16}}$

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#### i. $\frac{5}{10} \times \frac{6}{10}$
Simplify both fractions:
- $\frac{5}{10} = \frac{1}{2}$
- $\frac{6}{10} = \frac{3}{5}$

Now:
$$
\frac{1}{2} \times \frac{3}{5} = \frac{3}{10}
$$
✔ Answer: $\boxed{\frac{3}{10}}$

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#### j. $\frac{2}{12} \times \frac{1}{2}$
Simplify $\frac{2}{12} = \frac{1}{6}$, then:
$$
\frac{1}{6} \times \frac{1}{2} = \frac{1}{12}
$$
✔ Answer: $\boxed{\frac{1}{12}}$

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#### k. $\frac{2}{6} \times \frac{1}{2}$
Simplify $\frac{2}{6} = \frac{1}{3}$, then:
$$
\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}
$$
✔ Answer: $\boxed{\frac{1}{6}}$

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#### l. $\frac{1}{4} \times \frac{4}{7}$
$$
\frac{1 \times 4}{4 \times 7} = \frac{4}{28} = \frac{1}{7}
$$
✔ Answer: $\boxed{\frac{1}{7}}$

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#### k. Jacob is baking cookies. The recipe uses $\frac{3}{4}$ cup of sugar. He wants to make half a batch. How much sugar does he need?

This means: $\frac{1}{2}$ of $\frac{3}{4}$

$$
\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}
$$
✔ Answer: $\boxed{\frac{3}{8}}$ cups of sugar

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#### m. Hannah had $\frac{2}{3}$ of a quart of milk. She used half of this for breakfast. How much did she use?

So: $\frac{1}{2}$ of $\frac{2}{3}$

$$
\frac{1}{2} \times \frac{2}{3} = \frac{2}{6} = \frac{1}{3}
$$
✔ Answer: $\boxed{\frac{1}{3}}$ quart of milk

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| a | $\frac{1}{12}$ |
| b | $\frac{7}{24}$ |
| c | $\frac{9}{28}$ |
| d | $\frac{1}{8}$ |
| e | $\frac{2}{21}$ |
| f | $\frac{1}{5}$ |
| g | $\frac{1}{4}$ |
| h | $\frac{1}{16}$ |
| i | $\frac{3}{10}$ |
| j | $\frac{1}{12}$ |
| k | $\frac{1}{6}$ |
| l | $\frac{1}{7}$ |
| k (word problem) | $\frac{3}{8}$ cups |
| m (word problem) | $\frac{1}{3}$ quart |

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