Free worksheet · Australian Curriculum

Fraction worksheets with answers

Every fraction skill a secondary student needs, from simplifying to dividing mixed numbers. Learn each one with a worked example, then make a free worksheet with full solutions.

Make a worksheet ↓How to do it and a quick check ↓

Topic guide

Fractions, explained

Six skills cover almost every fraction question in Years 7 to 10. Here they are, one at a time.

1. Equivalent fractions

Multiplying or dividing the top and bottom by the same number gives an equal fraction:

$\frac{3}{4} = \frac{6}{8} = \frac{9}{12}$

This is the idea behind simplifying and behind adding fractions with different denominators.

2. Simplifying

Divide the numerator and denominator by their highest common factor (HCF). For $\frac{18}{24}$ the HCF is $6$ :

$\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}$

3. Adding and subtracting

Fractions need the same denominator before you add or subtract. Use the lowest common denominator, then add the numerators only:

$\frac{2}{3} + \frac{1}{4} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}$

4. Multiplying

Multiply the numerators, multiply the denominators, then simplify:

$\frac{3}{5} \times \frac{10}{9} = \frac{30}{45} = \frac{2}{3}$

No common denominator is needed when multiplying.

5. Dividing

Keep the first fraction, change $\div$ to $\times$ , and flip the second fraction:

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

6. Mixed numbers and improper fractions

To change $2\frac{1}{3}$ to an improper fraction, multiply the whole number by the denominator and add the numerator: $2 \times 3 + 1 = 7$ , so $2\frac{1}{3} = \frac{7}{3}$ .

To go back, divide: $17 \div 5 = 3$ remainder $2$ , so $\frac{17}{5} = 3\frac{2}{5}$ . Change mixed numbers to improper fractions before multiplying or dividing.

Quick check: 10 questions

Try each one, then open the answer.

Simplify $\frac{12}{16}$ .
Answer
$\frac{3}{4}$
Write $2\frac{3}{5}$ as an improper fraction.
Answer
$\frac{13}{5}$
Calculate $\frac{1}{5} + \frac{2}{5}$ .
Answer
$\frac{3}{5}$
Calculate $\frac{5}{6} - \frac{1}{3}$ .
Answer
$\frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$
Calculate $\frac{2}{3} \times \frac{3}{8}$ .
Answer
$\frac{6}{24} = \frac{1}{4}$
Calculate $\frac{4}{5} \div \frac{2}{3}$ .
Answer
$\frac{4}{5} \times \frac{3}{2} = \frac{12}{10} = 1\frac{1}{5}$
Calculate $\frac{1}{2} + \frac{2}{3}$ .
Answer
$\frac{3}{6} + \frac{4}{6} = \frac{7}{6} = 1\frac{1}{6}$
Calculate $1\frac{1}{2} \times 2\frac{2}{3}$ .
Answer
$\frac{3}{2} \times \frac{8}{3} = \frac{24}{6} = 4$
What fraction of $60$ is $45$ ? Give it in simplest form.
Answer
$\frac{45}{60} = \frac{3}{4}$
In a class of $32$ students, $\frac{3}{4}$ walk to school. How many students walk?
Answer
$\frac{3}{4} \times 32 = 24$ students

Generate a free maths worksheet

Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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

Year 7 worksheetFraction operations Year 7 worksheetFractions and decimals Year 7 worksheetPercentages Year 7 worksheetRatios

Questions

What fraction skills do Year 7 students need?

Year 7 students simplify fractions, find equivalent fractions, convert between mixed numbers and improper fractions, and add, subtract, multiply and divide fractions, including mixed numbers. These skills are used again in algebra, ratios and probability.

Do the fraction worksheets come with answers?

Yes. Every question on a generated worksheet has a fully worked solution, and every example on this page shows each step.

Why do students find fractions hard?

Most errors come from mixing up the rules: adding the denominators, or looking for a common denominator when multiplying. Practising each operation separately, then mixing them, fixes this.

More skill worksheets

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