Year 7 - Fractions and decimals - Free practice

Year 7 Fractions & Decimals Worksheets

Multiply, divide, convert. The fluency drills Year 7 needs.

Quick answer

How do you multiply and divide fractions and decimals?

To multiply fractions, multiply the numerators together and the denominators together, then simplify. To divide fractions, keep the first fraction, change division to multiplication, and flip the second fraction (keep, change, flip). For example, 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3. Decimals multiply and divide like whole numbers, then place the decimal point correctly.

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

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Based on the actual school test marks of 100+ Bayside Academics students (in person and online) in Years 7 to 10, before and after using Tuterly at least once a week. How we measured this

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Worked examples

Year 7 fractions and decimals: 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 · Multiplying fractions
Calculate $\dfrac{3}{4} \times \dfrac{2}{5}$ .
Show worked solution
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: $\dfrac{3}{10}$
Example 2 · Dividing a mixed number by a fraction
Calculate $2\dfrac{1}{2} \div \dfrac{3}{4}$ .
Show worked solution
Key idea: Convert any mixed numbers to improper fractions, then use keep, change, flip (multiply by the reciprocal).
1. Convert the mixed number: $2\dfrac{1}{2} = \dfrac{5}{2}$
2. Keep the first fraction, change $\div$ to $\times$ , flip the second fraction: $\frac{5}{2} \div \frac{3}{4} = \frac{5}{2} \times \frac{4}{3}$
3. Multiply numerators and denominators: $\frac{5 \times 4}{2 \times 3} = \frac{20}{6}$
4. Simplify: $\dfrac{20}{6} = \dfrac{10}{3} = 3\dfrac{1}{3}$
Answer: $3\dfrac{1}{3}$
Example 3 · Real-life problem with decimal multiplication
Priya is buying ribbon to decorate party bags. Each party bag needs 0.35 metres of ribbon. She is making 12 party bags. Ribbon costs $2.40 per metre. How much will the ribbon cost in total?
Show worked solution
Key idea: First find the total length of ribbon needed by multiplying decimals, then multiply by the cost per metre.
1. Find the total length: $0.35 \times 12$
  $0.35 \times 12 = 0.35 \times 10 + 0.35 \times 2 = 3.50 + 0.70 = 4.20 \text{ metres}$
2. Find the total cost: $4.20 \times 2.40$
  $4.20 \times 2.40 = 4.20 \times 2 + 4.20 \times 0.40 = 8.40 + 1.68 = 10.08$
3. The total cost is $10.08.
Answer: $10.08

Common mistakes

Where students usually lose marks

Adding instead of multiplying numerators and denominators

$\dfrac{3}{4} \times \dfrac{2}{5} = \dfrac{3+2}{4+5} = \dfrac{5}{9}$

When multiplying fractions, multiply the top numbers together and the bottom numbers together separately. Adding the numerators and denominators is a common mix-up with a different skill.

Forgetting to flip the second fraction when dividing

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

Keep, change, flip means you keep the first fraction as it is, change the operation from division to multiplication, and flip (find the reciprocal of) the second fraction only. Here the second fraction becomes $\dfrac{4}{3}$ , not $\dfrac{3}{4}$ .

Not converting mixed numbers before dividing or multiplying

$2\dfrac{1}{2} \times \dfrac{3}{4} = \dfrac{2 \times 3}{2 \times 4} + \dfrac{1}{2} = \dfrac{6}{8} + \dfrac{1}{2}$

Always convert mixed numbers to improper fractions before multiplying or dividing. For $2\dfrac{1}{2}$ : multiply the whole number by the denominator and add the numerator to get $\dfrac{5}{2}$ , then proceed.

Misplacing the decimal point when multiplying decimals

$0.35 \times 12 = 42$ (forgetting to count decimal places)

Count the total number of decimal places in the numbers you are multiplying, and make sure the answer has the same number of decimal places. Here $0.35$ has 2 decimal places, so $0.35 \times 12 = 4.20$ , not 42.

Try one yourself

Your turn

Calculate $\dfrac{3}{4} \div \dfrac{3}{8}$ . Give your answer as a simplified fraction or whole number.

Got a different fractions and decimals 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

Year 7 builds on the primary-school fraction work and pushes into multiplication, division, and conversion between fractions and decimals. These worksheets isolate that exact skill set so your student gets the repetition they need without slogging through unrelated topics.

What's covered

Sub-skills your student will practise

✓Multiplying fractions (proper, improper, mixed)
✓Dividing fractions ("keep, change, flip")
✓Multiplying and dividing decimals
✓Converting between fractions and decimals
✓Mixed-operation problems with rational numbers

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.”

Rebecca M.

Year 8 · Maths

“My daughter used to leave revision until the night before. Having a platform she can dip into for fifteen minutes after dinner has completely changed that. She's calmer going into assessments, and honestly, so am I.”

Priya S.

Year 9 · Maths

“I like that I can just keep doing questions until it clicks. If I get something wrong, it shows me why, and then gives me another one like it.”

Ella, student

Year 10 · Maths

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Frequently asked

Questions parents ask about fractions and decimals

Why do Year 7 students still struggle with fractions?

Most students come into Year 7 strong on adding and subtracting fractions but weak on multiplication and division. The 'keep, change, flip' rule for division feels arbitrary unless they've seen why it works - so worked solutions matter more here than in other topics.

Is it OK to use a calculator for Year 7 fraction problems?

Not for the calculations themselves - the curriculum expects students to multiply and divide fractions and decimals fluently without a calculator at this level. A calculator is OK for checking, not for solving.

How are fractions and decimals connected in Year 7?

Year 7 students are expected to convert between fractions, decimals, and percentages and to move fluently between the three representations. The same question might be set as 0.6, 3/5, or 60% and students need to spot the equivalence.

What comes after fractions and decimals in Year 7?

Percentages and ratios build directly on this work. Once students are fluent with fractions and decimals, the percentages and ratios topics feel routine rather than tricky.

Better maths marks start with the next wrong answer.

Tuterly turns every missed maths question into practice tailored towards the student, not just a generic worksheet.