Year 7 - Fraction operations - Free practice

Year 7 Adding, Subtracting, Multiplying and Dividing Fractions Worksheets & Practice

All four operations with fractions, clear steps, and worked solutions every time, free.

Quick answer

How do you add, subtract, multiply and divide fractions?

Find a common denominator to add or subtract fractions, multiply numerators and denominators straight across to multiply, and use keep-change-flip (multiply by the reciprocal) to divide. For example, 1/2 + 2/3 = 3/6 + 4/6 = 7/6 = 1 1/6, and 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2 = 1 1/2.

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

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Worked examples

Year 7 fraction operations: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Adding fractions with different denominators
Calculate $\dfrac{2}{3} + \dfrac{3}{4}$ .
Show worked solution
Key idea: To add fractions with different denominators, first find a common denominator, then add the numerators.
1. Find the lowest common denominator (LCD) of 3 and 4: $\text{LCD} = 12$
2. Rewrite each fraction with denominator 12:
  $\frac{2}{3} = \frac{8}{12}, \frac{3}{4} = \frac{9}{12}$
3. Add the numerators:
  $\frac{8}{12} + \frac{9}{12} = \frac{17}{12}$
4. Convert to a mixed number:
  $\frac{17}{12} = 1\frac{5}{12}$
Answer: $1\dfrac{5}{12}$
Example 2 · Dividing fractions using keep, change, flip
Calculate $\dfrac{5}{6} \div \dfrac{2}{3}$ .
Show worked solution
Key idea: To divide by a fraction, keep the first fraction, change the division sign to multiplication, and flip the second fraction (use its reciprocal).
1. Keep $\dfrac{5}{6}$ , change $\div$ to $\times$ , flip $\dfrac{2}{3}$ to $\dfrac{3}{2}$ :
  $\frac{5}{6} \times \frac{3}{2}$
2. Simplify before multiplying: the 6 and the 3 share a common factor of 3:
  $\frac{5}{\cancel{6}^{\,2}} \times \frac{\cancel{3}^{\,1}}{2} = \frac{5}{2} \times \frac{1}{2} = \frac{5 \times 1}{2 \times 2}$
3. Multiply numerators and denominators:
  $\frac{5}{4}$
4. Convert to a mixed number:
  $\frac{5}{4} = 1\frac{1}{4}$
Answer: $1\dfrac{1}{4}$
Example 3 · Solving a real-life problem with fractions
Mia is making friendship bracelets. She has $2\dfrac{1}{2}$ metres of ribbon. Each bracelet needs $\dfrac{3}{8}$ of a metre of ribbon. How many complete bracelets can she make?
Show worked solution
Key idea: Finding how many times a fraction fits into an amount means dividing the total by the amount per bracelet.
1. Write the mixed number as an improper fraction:
  $2\frac{1}{2} = \frac{5}{2}$
2. Set up the division:
  $\frac{5}{2} \div \frac{3}{8}$
3. Apply keep, change, flip:
  $\frac{5}{2} \times \frac{8}{3}$
4. Simplify before multiplying: the 2 and the 8 share a common factor of 2:
  $\frac{5}{\cancel{2}^{\,1}} \times \frac{\cancel{8}^{\,4}}{3} = \frac{5 \times 4}{1 \times 3} = \frac{20}{3}$
5. Convert to a mixed number: $\dfrac{20}{3} = 6\dfrac{2}{3}$ , so Mia can make 6 complete bracelets.
Answer: 6 complete bracelets

Common mistakes

Where students usually lose marks

Adding numerators AND denominators

$\dfrac{1}{3} + \dfrac{1}{4} = \dfrac{2}{7}$

Only the numerators are added after finding a common denominator. The denominator stays as the common denominator, it never gets added. Always find the LCD first, then add the numerators only.

Forgetting to convert mixed numbers before multiplying or dividing

$1\dfrac{1}{2} \times \dfrac{2}{3} = \dfrac{1 \times 2}{2 \times 3} = \dfrac{2}{6}$

A mixed number must be converted to an improper fraction before multiplying or dividing. Here, $1\dfrac{1}{2} = \dfrac{3}{2}$ , so the calculation becomes $\dfrac{3}{2} \times \dfrac{2}{3}$ .

Flipping the wrong fraction when dividing

$\dfrac{3}{4} \div \dfrac{2}{5} = \dfrac{4}{3} \times \dfrac{2}{5}$

It is always the second fraction (the divisor) that gets flipped, not the first. Keep the first fraction exactly as it is, change the sign to multiplication, then flip the second fraction.

Not simplifying the final answer

$\dfrac{3}{5} \times \dfrac{5}{6} = \dfrac{15}{30}$ (left as is)

Always check whether the final answer can be simplified. Divide the numerator and denominator by their highest common factor. Here, $\dfrac{15}{30} = \dfrac{1}{2}$ .

Try one yourself

Your turn

Calculate $\dfrac{5}{6} \div \dfrac{1}{4}$ . Give your answer as a decimal correct to 2 decimal places.

Got a different fraction operations question wrong? Upload it to Tuterly and get the worked solution and a fresh one to practise, free.

About this worksheet

Why we built it

Fraction operations are a big focus in Year 7, bringing together adding, subtracting, multiplying and dividing both simple fractions and mixed numbers. These worksheets build the key skills from finding common denominators right through to dividing by a fraction, with worked solutions for every question so students can check their method, not just their answer.

What's covered

Sub-skills your student will practise

✓Adding fractions with different denominators using a common denominator
✓Subtracting fractions and mixed numbers
✓Multiplying fractions, including simplifying before multiplying
✓Dividing fractions using the keep, change, flip method
✓Working with improper fractions and converting to mixed numbers
✓Solving word problems using all four fraction operations

From our families

Parents on the practice questions.

“Tuterly has been exactly what we needed since Tom started secondary school. Once the topic tests began, he was struggling to keep up. Now he has unlimited practice, all matched to what his class is actually covering, and his Maths results have improved noticeably.”

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Year 10 · Maths

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Frequently asked

Questions parents ask about fraction operations

Why do you need a common denominator for adding and subtracting fractions but not for multiplying?

When adding or subtracting, you are combining parts of the same whole, so the parts must be the same size first. When multiplying, you are finding a fraction of a fraction, so you simply multiply the numerators and denominators straight across.

What is the 'keep, change, flip' method for dividing fractions?

Keep the first fraction as it is, change the division sign to multiplication, then flip the second fraction upside down (its reciprocal). For example, 3/4 ÷ 2/5 becomes 3/4 × 5/2, which equals 15/8 or 1 and 7/8.

How do mixed numbers fit into Year 7 fraction work?

Students are expected to convert mixed numbers to improper fractions before adding, subtracting, multiplying or dividing, then convert the answer back. It is a key step and a common place for errors to creep in.

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