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Multiplying fractions worksheets with answers

Multiplying is the friendliest fraction operation: no common denominator needed. Learn each question type, including mixed numerals and cancelling, then make a free worksheet with full solutions.

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Multiplying fractions at each year level, matched to the textbook chapters most Victorian schools use: a free printable worksheet with answers, sample questions, and an auto-marked test teachers can share.

Free Year 7 multiplying fractions worksheet

10 questions, then the answers with worked solutions. Printable PDF, no sign-up.

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Year 7 topics covered

Multiplying fractions

Sample Year 7 multiplying fractions questions

Multiplying fractions
Calculate $\dfrac{3}{4} \times \dfrac{2}{5}$ .
Show the answer
Key idea: Multiply the numerators together and the denominators together, then simplify.
1. Multiply the numerators: $3 \times 2 = 6$
2. Multiply the denominators: $4 \times 5 = 20$
3. Write the result: $\dfrac{6}{20}$
4. Simplify by dividing numerator and denominator by the highest common factor of 2: $\frac{6}{20} = \frac{3}{10}$
Answer: $\dfrac{3}{10}$
Multiplying fractions
Calculate, giving each answer in simplest form.

(a) $\frac{2}{3} \times \frac{4}{5}$

(b) $\frac{3}{4} \times \frac{2}{9}$

(c) $\frac{1}{2} \times 5$ (give your answer as a mixed number)
Show the answer
Answer: (a) $\frac{8}{15}$ (b) $\frac{1}{6}$ (c) $2\frac{1}{2}$
Multiplying fractions
Calculate:

(a) $1\frac{1}{2} \times 2\frac{2}{3}$

(b) $2\frac{1}{4} \times 1\frac{1}{3}$
Show the answer
Answer: (a) $4$ ( $\frac{3}{2} \times \frac{8}{3}$ ) (b) $3$ ( $\frac{9}{4} \times \frac{4}{3}$ )
Multiplying fractions
Find:

(a) $\frac{3}{8}$ of 72 km

(b) $\frac{2}{5}$ of $45
Show the answer
Answer: (a) $27 \text{ km}$ (b) $18

Free Year 8 multiplying fractions worksheet

10 questions, then the answers with worked solutions. Printable PDF, no sign-up.

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Year 8 topics covered

Operations with fractions

Sample Year 8 multiplying fractions questions

Operations with fractions
Find $\dfrac{2}{3} + \dfrac{3}{4}$ . Give your answer as a mixed number.
Show the answer
Key idea: To add fractions, first write them with a common denominator.
1. The LCD of $3$ and $4$ is $12$
2. $\dfrac{8}{12} + \dfrac{9}{12} = \dfrac{17}{12}$
3. $\dfrac{17}{12} = 1\frac{5}{12}$
Answer: $1\frac{5}{12}$
Operations with fractions
Find $3\frac{1}{2} - 1\frac{4}{5}$ .
Show the answer
Key idea: Convert mixed numbers to improper fractions, then use a common denominator.
1. $3\frac{1}{2} = \dfrac{7}{2}$ and $1\frac{4}{5} = \dfrac{9}{5}$
2. $\dfrac{35}{10} - \dfrac{18}{10} = \dfrac{17}{10}$
3. $\dfrac{17}{10} = 1\frac{7}{10}$
Answer: $1\frac{7}{10}$
Operations with fractions
Find $2\frac{2}{3} \times 1\frac{1}{8}$ .
Show the answer
Key idea: Convert to improper fractions, cancel common factors, then multiply numerators and denominators.
1. $2\frac{2}{3} = \dfrac{8}{3}$ and $1\frac{1}{8} = \dfrac{9}{8}$
2. $\dfrac{8}{3} \times \dfrac{9}{8} = \dfrac{1}{1} \times \dfrac{3}{1}$ (cancel $8$ , and $9$ with $3$ )
3. $= 3$
Answer: $3$
Operations with fractions
Find $4\frac{1}{2} \div 1\frac{1}{5}$ .
Show the answer
Key idea: To divide by a fraction, multiply by its reciprocal.
1. $4\frac{1}{2} = \dfrac{9}{2}$ and $1\frac{1}{5} = \dfrac{6}{5}$
2. $\dfrac{9}{2} \div \dfrac{6}{5} = \dfrac{9}{2} \times \dfrac{5}{6} = \dfrac{45}{12} = \dfrac{15}{4}$
3. $\dfrac{15}{4} = 3\frac{3}{4}$
Answer: $3\frac{3}{4}$

Free Year 9 multiplying fractions worksheet

10 questions, then the answers with worked solutions. Printable PDF, no sign-up.

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Year 9 topics covered

Operations with fractions

Sample Year 9 multiplying fractions questions

Operations with fractions
Evaluate, giving each answer as a mixed number:

(a) $2\frac{1}{3} + 1\frac{3}{4}$

(b) $3\frac{1}{5} - 1\frac{2}{3}$
Show the answer
Key idea: Change mixed numbers to improper fractions, then use a common denominator to add or subtract.
1. (a) $\frac{7}{3} + \frac{7}{4} = \frac{28}{12} + \frac{21}{12} = \frac{49}{12} = 4\frac{1}{12}$
2. (b) $\frac{16}{5} - \frac{5}{3} = \frac{48}{15} - \frac{25}{15} = \frac{23}{15} = 1\frac{8}{15}$
Answer: (a) $4\frac{1}{12}$ (b) $1\frac{8}{15}$
Operations with fractions
Evaluate, giving each answer in simplest form:

(a) $2\frac{2}{5} \times 1\frac{7}{8}$

(b) $3\frac{3}{4} \div 1\frac{1}{2}$
Show the answer
Key idea: Change mixed numbers to improper fractions. To divide, multiply by the reciprocal of the second fraction. Cancel common factors before multiplying.
1. (a) $\frac{12}{5} \times \frac{15}{8}$ ; cancel $5$ into $15$ and $4$ into $12$ and $8$ : $\frac{3}{1} \times \frac{3}{2} = \frac{9}{2} = 4\frac{1}{2}$
2. (b) $\frac{15}{4} \div \frac{3}{2} = \frac{15}{4} \times \frac{2}{3} = \frac{30}{12} = \frac{5}{2} = 2\frac{1}{2}$
Answer: (a) $4\frac{1}{2}$ (b) $2\frac{1}{2}$
Operations with fractions
Evaluate $-\frac{3}{4} + \frac{5}{6} \times \left(-\frac{2}{5}\right)$ , giving your answer as a mixed number.
Show the answer
Key idea: Multiply before adding. A positive times a negative is negative.
1. $\frac{5}{6} \times \left(-\frac{2}{5}\right) = -\frac{10}{30} = -\frac{1}{3}$
2. $-\frac{3}{4} - \frac{1}{3} = -\frac{9}{12} - \frac{4}{12} = -\frac{13}{12}$
3. $-\frac{13}{12} = -1\frac{1}{12}$
Answer: $-1\frac{1}{12}$
Operations with fractions
Evaluate $\frac{5}{6} - \frac{3}{4} \times \frac{2}{9}$ , giving your answer in simplest form.
Show the answer
Key idea: Multiply before subtracting.
1. $\frac{3}{4} \times \frac{2}{9} = \frac{6}{36} = \frac{1}{6}$
2. $\frac{5}{6} - \frac{1}{6} = \frac{4}{6} = \frac{2}{3}$
Answer: $\frac{2}{3}$

Topic guide

Multiplying fractions, explained

Multiply the tops, multiply the bottoms, simplify. Everything else is a variation on that rule.

1. A fraction times a whole number

Write the whole number over $1$ , then multiply. Only the numerator is multiplied by the whole number:

$\frac{2}{5} \times 3 = \frac{2}{5} \times \frac{3}{1} = \frac{6}{5} = 1\frac{1}{5}$

2. A fraction times a fraction

Multiply the numerators together and the denominators together:

$\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$

There is no need for a common denominator. That rule is only for adding and subtracting.

3. Cancel before you multiply

Divide any numerator and any denominator by a common factor first. It keeps the numbers small and the answer comes out in simplest form:

$\frac{4}{9} \times \frac{3}{8} = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$

Here $4$ and $8$ share a factor of $4$ , and $3$ and $9$ share a factor of $3$ . Multiplying first gives $\frac{12}{72}$ , which also simplifies to $\frac{1}{6}$ .

4. Mixed numerals

Change each mixed numeral to an improper fraction first, then multiply and cancel:

$1\frac{1}{2} \times 2\frac{2}{5} = \frac{3}{2} \times \frac{12}{5} = \frac{3}{1} \times \frac{6}{5} = \frac{18}{5} = 3\frac{3}{5}$

Multiplying the whole numbers and the fractions separately gives the wrong answer.

5. "Of" means multiply

A fraction of an amount is a multiplication:

$\frac{3}{4} \text{ of } 20 = \frac{3}{4} \times 20 = 15 \frac{2}{3} \text{ of } \frac{3}{5} = \frac{2}{3} \times \frac{3}{5} = \frac{2}{5}$

For a whole number, you can divide by the denominator and multiply by the numerator: $20 \div 4 \times 3 = 15$ .

6. Word problems

A recipe needs $\frac{3}{4}$ cup of sugar. How much sugar is needed for $2\frac{1}{2}$ batches?

$\frac{3}{4} \times 2\frac{1}{2} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} = 1\frac{7}{8} \text{ cups}$

Scaling a recipe, finding part of a part, and "fraction of" questions are all multiplication.

Quick check: 10 questions

Try each one, then open the answer.

Calculate $\frac{1}{3} \times 6$ .
Answer
$2$
Calculate $\frac{3}{4} \times 5$ .
Answer
$\frac{15}{4} = 3\frac{3}{4}$
Calculate $\frac{1}{2} \times \frac{3}{5}$ .
Answer
$\frac{3}{10}$
Calculate $\frac{2}{3} \times \frac{5}{7}$ .
Answer
$\frac{10}{21}$
Calculate $\frac{5}{6} \times \frac{3}{10}$ .
Answer
$\frac{15}{60} = \frac{1}{4}$
Find $\frac{3}{4}$ of $36$ .
Answer
$27$
Calculate $\frac{7}{12} \times \frac{8}{21}$ , cancelling first.
Answer
$\frac{1}{3} \times \frac{2}{3} = \frac{2}{9}$
Calculate $2\frac{1}{4} \times 1\frac{1}{3}$ .
Answer
$\frac{9}{4} \times \frac{4}{3} = 3$
Calculate $1\frac{2}{3} \times 2\frac{1}{10}$ .
Answer
$\frac{5}{3} \times \frac{21}{10} = \frac{7}{2} = 3\frac{1}{2}$
A garden has an area of $60$ m². $\frac{3}{5}$ of it is lawn, and $\frac{1}{4}$ of the lawn is in shade. What area of lawn is in shade?
Answer
$\frac{1}{4} \times \frac{3}{5} \times 60 = 9$ m²

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These topic pages cover this skill, with worked examples, common mistakes and a question to try.

Year 7 worksheetFractions and decimals Year 7 worksheetFraction operations Year 7 worksheetPercentages Year 10 worksheetAlgebraic fractions

Questions

How do you multiply fractions?

Multiply the numerators together and the denominators together, then simplify. Cancelling common factors before you multiply makes the numbers smaller and saves simplifying at the end.

Do you need a common denominator to multiply fractions?

No. A common denominator is only needed for adding and subtracting. When multiplying, you can multiply straight across.

How do you multiply mixed numerals?

Change each mixed numeral to an improper fraction, multiply, then change the answer back to a mixed numeral if needed. Do not multiply the whole numbers and fractions separately.

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Choose your year level

Multiplying fractions, explained

1. A fraction times a whole number

2. A fraction times a fraction

3. Cancel before you multiply

4. Mixed numerals

5. "Of" means multiply

6. Word problems

Quick check: 10 questions

Generate a free maths worksheet

Practice built from mistakes.

Topic worksheets with worked examples

Questions

How do you multiply fractions?

Do you need a common denominator to multiply fractions?

How do you multiply mixed numerals?

More skill worksheets

Better maths marks start with the next wrong answer.