Year 7 - Ratios - Free practice

Year 7 Ratios Worksheets & Practice Tests

Simplify, scale, divide in a ratio - the Year 7 foundations.

Quick answer

What are ratios and how do you use them in Year 7?

A ratio compares two or more quantities of the same kind. Write it as a:b, simplify by dividing by the highest common factor, and scale up or down by multiplying or dividing both parts by the same number. For example, 12:8 simplifies to 3:2. Use equivalent ratios to divide quantities or solve recipe and scale problems.

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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 ratios: 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 · Simplifying a ratio
Simplify the ratio $24 : 36$ .
Show worked solution
Key idea: Divide both parts of the ratio by their highest common factor (HCF).
1. Find the HCF of $24$ and $36$ : the HCF is $12$ .
2. Divide both parts by $12$ :
  $24 : 36 = (24 \div 12) : (36 \div 12)$
3. Simplify:
  $= 2 : 3$
Answer: $2 : 3$
Example 2 · Dividing a quantity in a ratio
Divide $90 between Priya and Joel in the ratio $2 : 3$ .
Show worked solution
Key idea: Find the value of one part by dividing the total by the number of parts, then multiply for each share.
1. Count the total number of parts: $2 + 3 = 5$ parts.
2. Find the value of one part: $90 \div 5 = 18$ , so one part is worth $18.
3. Calculate Priya's share ( $2$ parts): $2 \times 18 = 36$ , so Priya gets $36.
4. Calculate Joel's share ( $3$ parts): $3 \times 18 = 54$ , so Joel gets $54.
5. Check: $36 + 54 = 90$ . ✓
Answer: Priya gets $36 and Joel gets $54.
Example 3 · Ratio in a real-life context
A baker makes a batch of dough using flour and water in the ratio $5 : 2$ by weight. She wants to make $980$ grams of dough in total. How many grams of flour and how many grams of water does she need?
Show worked solution
Key idea: The total weight is split into parts according to the ratio, so find the value of one part first.
1. Count the total number of parts: $5 + 2 = 7$ parts.
2. Find the value of one part: $980 \div 7 = 140$ grams per part.
3. Calculate the flour ( $5$ parts): $5 \times 140 = 700$ grams.
4. Calculate the water ( $2$ parts): $2 \times 140 = 280$ grams.
5. Check: $700 + 280 = 980$ grams. ✓
Answer: The baker needs $700$ g of flour and $280$ g of water.

Common mistakes

Where students usually lose marks

Not dividing both parts by the HCF

$24 : 36 = 12 : 18$ (divided by $2$ instead of the HCF of $12$ )

Always find the highest common factor, not just any common factor. Keep dividing until the two parts share no common factor other than $1$ .

Adding the ratio instead of finding parts

Ratio is $2:3$ , so Priya gets $2$ dollars and Joel gets $3$ dollars from $90.

The numbers in a ratio show parts, not the actual amounts. Always divide the total by the sum of the parts first to find what one part is worth.

Mixing up which quantity goes first

"Flour to water is $5:2$ " written as water $:$ flour $= 5 : 2$ .

Write the ratio in the same order as the words. If the question says flour to water, the flour number comes first. Re-read the question carefully before writing the ratio.

Forgetting to check the parts add up to the total

Priya gets $36 and Joel gets $54, no check performed, so an arithmetic error goes unnoticed.

Always add the two shares at the end and confirm they equal the original total. This catches arithmetic mistakes before they cost you marks.

Try one yourself

Your turn

A recipe uses flour and sugar in the ratio $3:2$ . If you use $360\text{ g}$ of flour, how many grams of sugar do you need?

Got a different ratios 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

Ratios show up in everything from recipes to map scales to currency exchange. These Year 7 worksheets give your student practice across all the standard ratio question types so the topic feels routine rather than tricky by the time tests roll around.

What's covered

Sub-skills your student will practise

✓Writing and simplifying ratios
✓Equivalent ratios
✓Dividing a quantity in a given ratio
✓Comparing ratios using a common term
✓Word problems involving recipes, scale and proportion

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 ratios

How are ratios different from fractions?

A fraction compares a part to a whole (3/5 of the pizza). A ratio compares two parts to each other (3:5 of red to blue marbles). The arithmetic is the same but the way you read the answer differs.

How do students divide a quantity in a given ratio?

Add the parts of the ratio to get the total number of shares, then divide the quantity by that total to find one share. For $80 split 3:5, total = 8 shares, one share = $10, so the split is $30 and $50.

Why do students get ratio problems wrong?

Usually they treat the ratio as a fraction and divide by the second number instead of the total. The other common mistake is leaving the answer in shares ($30 and $50 written as 3 and 5).

What real-world contexts use ratios in Year 7?

Recipes (mix the cordial 1:4 with water), map scales, currency exchange, and sharing money or items between people are the most common contexts. These worksheets use varied contexts so students can't memorise one type.

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