Sam and Ava share money in the ratio 4 : 9. Ava gets $35 more than Sam. How much does each get?

5 parts = 35, so one part is 7: Sam $28, Ava $63

Free worksheet · Australian Curriculum

Ratio worksheets with answers

Q: How do you simplify a ratio?

Divide every part of the ratio by the highest common factor. If the ratio has decimals, fractions or different units, change it to whole numbers in the same unit first.

Q: How do you divide an amount in a ratio?

Add the parts of the ratio to find the total number of parts, divide the amount by that total to find one part, then multiply by each part of the ratio.

Q: Do the ratio worksheets include answers?

Yes. Every question on a generated worksheet comes with a fully worked solution showing each step.

A ratio compares quantities, like 2 cups of flour to 3 cups of milk. Learn to simplify, scale and share in a ratio, then make a free worksheet with full solutions.

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Ratios 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 ratios worksheet

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

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Year 7 topics covered

Introduction to ratios
Solving problems with ratios

Sample Year 7 ratios questions

Introduction to ratios
Simplify the ratio $24 : 36$ .
Show the answer
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 $12$ :\
$24 : 36 = (24 \div 12) : (36 \div 12)$
1. Simplify:\
$= 2 : 3$
Answer: $2 : 3$
Solving problems with ratios
Divide $90 between Priya and Joel in the ratio $2 : 3$ .
Show the answer
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.
Introduction to ratios
Write the ratio $12 : 18$ in simplest form.
Show the answer
Answer: $2 : 3$
Solving problems with ratios
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 the answer
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.

Free Year 8 ratios worksheet

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

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Auto-marked test for your class

Teachers: share one link and every student is marked straight away, with worked solutions.

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Printable practice exam

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Year 8 topics covered

Simplifying ratios
Solving ratio problems
Ratios and rates and the unitary method

Sample Year 8 ratios questions

Simplifying ratios
Simplify the ratio $45 : 60$ .
Show the answer
Key idea: Divide both parts of the ratio by their highest common factor.
1. The HCF of $45$ and $60$ is $15$
2. $45 \div 15 : 60 \div 15 = 3 : 4$
Answer: $3 : 4$
Solving ratio problems
In a jar, the ratio of red jelly beans to green jelly beans is $3 : 5$ . There are $24$ red jelly beans. How many green jelly beans are there?
Show the answer
Key idea: Find the value of one part, then multiply by the number of parts needed.
1. $3$ parts $= 24$ , so $1$ part $= 24 \div 3 = 8$ .
2. Green is $5$ parts: $5 \times 8 = 40$ .
Answer: $40$
Ratios and rates and the unitary method
Orange juice is sold in two sizes. A 600 mL bottle costs $3.00 and a 1.5 L bottle costs $6.60. Which size is the better buy?
Show the answer
Key idea: Convert both options to the same unit, then find the cost per millilitre (unit price) for each. The lower unit price is the better buy.
1. Convert 1.5 L to millilitres: $1.5 \text{ L} = 1500 \text{ mL}$
2. Unit price of the 600 mL bottle: $\frac{300}{600} = 0.50 \text{ cents/mL}$
3. Unit price of the 1500 mL bottle: $\frac{660}{1500} = 0.44 \text{ cents/mL}$
4. Compare: $0.44 < 0.50$ , so the 1.5 L bottle has the lower unit price.
Answer: The 1.5 L bottle is the better buy at 0.44 cents/mL.
Simplifying ratios
Simplify the ratio $2.4 : 0.6$ .
Show the answer
Key idea: Multiply both parts by a power of $10$ to remove the decimals, then simplify.
1. Multiply both parts by $10$ : $24 : 6$
2. Divide both parts by $6$ : $4 : 1$
Answer: $4 : 1$

Free Year 9 ratios worksheet

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

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Auto-marked test for your class

Teachers: share one link and every student is marked straight away, with worked solutions.

Create a test

Printable practice exam

Mix in harder questions, with marks and a suggested time.

Build an exam

Year 9 topics covered

Ratios, rates and best buys

Sample Year 9 ratios questions

Ratios, rates and best buys
Runner A completes 10 km in 48 minutes. Runner B runs at 13.5 km/h. Which runner is faster, and by how much (in km/h)?
Show the answer
Key idea: Convert both speeds to the same units before comparing.
1. Convert Runner A's time to hours: $48 \text{ min} = \frac{48}{60} \text{ h} = 0.8 \text{ h}$
2. Find Runner A's speed: $\text{Speed} = \frac{10}{0.8} = 12.5 \text{ km/h}$
3. Compare: Runner B runs at 13.5 km/h and Runner A at 12.5 km/h, so Runner B is faster.
4. Find the difference: $13.5 - 12.5 = 1 \text{ km/h}$
Answer: Runner B is faster by 1 km/h.
Ratios, rates and best buys
A landscape architect draws a plan of a rectangular garden using a scale of 1 : 250. On the plan, the garden measures 8 cm long and 5 cm wide. Paving costs $34 per square metre. Find the total cost to pave the entire garden.
Show the answer
Key idea: Use the scale factor to convert plan measurements to real measurements, then calculate area and cost.
1. Convert plan dimensions to real dimensions (1 cm on the plan = 250 cm = 2.5 m in real life): $\text{Length} = 8 \times 2.5 = 20 \text{ m}, \text{Width} = 5 \times 2.5 = 12.5 \text{ m}$
2. Find the real area: $\text{Area} = 20 \times 12.5 = 250 \text{ m}^2$
3. Calculate the cost: $\text{Cost} = 250 \times 34 = 8500$
Answer: The total cost to pave the garden is $8500.
Ratios, rates and best buys
A car travels at a constant speed and covers 270 km in 3 hours. A map of the route uses a scale of 1 : 4 000 000. How long, in centimetres correct to 1 decimal place, is the route on the map?
Show the answer
Key idea: In a scale of 1 : 4 000 000, every 1 cm on the map represents 4 000 000 cm in real life, so real distance (cm) ÷ 4 000 000 = map distance (cm).
1. Find the real distance: the car covers 270 km.
2. Convert to centimetres: $270 \text{ km} = 270 \times 1000 \times 100 \text{ cm} = 27\,000\,000 \text{ cm}$ .
3. Apply the scale: $\text{map distance} = \dfrac{27\,000\,000}{4\,000\,000} \text{ cm}$ .
4. Calculate: $\dfrac{27\,000\,000}{4\,000\,000} = 6.75 \text{ cm}$ .
5. Round to 1 decimal place: $6.75 \approx 6.8 \text{ cm}$ .
Answer: $6.8 \text{ cm}$
Ratios, rates and best buys
A map has a scale of $1 : 50\,000$ . Two towns are $4 \text{ cm}$ apart on the map. How far apart are they in real life, in kilometres?
Show the answer
Answer: $2 \text{ km}$ ( $4 \times 50\,000 = 200\,000 \text{ cm}$ )

Topic guide

Ratios, explained

Simplifying a ratio works just like simplifying a fraction. Here is every common question type, step by step.

1. Simplifying ratios

Divide every part by the highest common factor. For $12 : 18$ the HCF is $6$ :

$12 : 18 = 2 : 3$

Three-part ratios work the same way: $20 : 30 : 45 = 4 : 6 : 9$ , dividing each part by $5$ .

2. Ratios with decimals or fractions

Multiply every part by the same number to get whole numbers, then simplify:

$1.5 : 2.5 = 15 : 25 = 3 : 5$

For fractions, multiply by the lowest common denominator. With $\frac{2}{3} : \frac{3}{4}$ , multiply both parts by $12$ :

$\frac{2}{3} : \frac{3}{4} = 8 : 9$

3. Ratios with different units

Change both quantities to the same unit first, then simplify and leave the units off:

$40 \text{ cm} : 2 \text{ m} = 40 : 200 = 1 : 5$

$45 \text{ min} : 2 \text{ h} = 45 : 120 = 3 : 8$

4. Equivalent ratios

Multiply or divide both parts by the same number. To find the missing number in $3 : 5 = 12 : ?$ , notice $3 \times 4 = 12$ , so

$3 : 5 = 12 : 20$

A recipe uses flour and milk in the ratio $2 : 3$ . With $8$ cups of flour, multiply both parts by $4$ : $8 : 12$ , so $12$ cups of milk.

5. Dividing a quantity in a ratio

Add the parts, find the value of one part, then multiply. Share $120 in the ratio $3 : 5$ :

$3 + 5 = 8 \text{ parts}, 120 \div 8 = 15 \text{ per part}$

$3 \times 15 = 45, 5 \times 15 = 75$

The shares are $45 and $75. Check they add to $120.

6. The unitary method

Find the value of one unit first, then scale up. If $5$ pens cost $8.50, then one pen costs $8.50 \div 5 = 1.70$ , and $8$ pens cost $8 \times 1.70 = 13.60$ , so $13.60.

The same idea works with ratio parts. Money is shared in the ratio $2 : 7$ and the larger share is $56. One part is $56 \div 7 = 8$ , so the smaller share is $2 \times 8 = 16$ , or $16.

Quick check: 10 questions

Try each one, then open the answer.

Simplify $10 : 15$ .
Answer
$2 : 3$
Simplify $24 : 40$ .
Answer
$3 : 5$
Simplify $18 : 27 : 45$ .
Answer
$2 : 3 : 5$
Find $x$ if $4 : 7 = x : 35$ .
Answer
$x = 20$
Simplify $0.6 : 1.5$ .
Answer
$6 : 15 = 2 : 5$
Simplify $\frac{1}{2} : \frac{2}{5}$ .
Answer
Multiply by $10$ : $5 : 4$
Simplify $750$ g $: 2$ kg.
Answer
$750 : 2000 = 3 : 8$
Divide $96 in the ratio $5 : 3$ .
Answer
One part is $12$ , so $60 and $36
Six apples cost $4.20. How much do ten apples cost?
Answer
One apple costs $0.70$ , so $7.00
Sam and Ava share money in the ratio $4 : 9$ . Ava gets $35 more than Sam. How much does each get?
Answer
$5$ parts $= 35$ , so one part is $7$ : Sam $28, Ava $63

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

Year 7 worksheetRatios Year 8 worksheetRates Year 9 worksheetDirect proportion, rates and scale Year 7 worksheetFraction operations

Questions

How do you simplify a ratio?

Divide every part of the ratio by the highest common factor. If the ratio has decimals, fractions or different units, change it to whole numbers in the same unit first.

How do you divide an amount in a ratio?

Add the parts of the ratio to find the total number of parts, divide the amount by that total to find one part, then multiply by each part of the ratio.

Do the ratio worksheets include answers?

Yes. Every question on a generated worksheet comes with a fully worked solution showing each step.

More skill worksheets

Skill worksheetFraction Skill worksheetEquivalent fractions Skill worksheetArea of composite shapes Skill worksheetArea of a triangle Skill worksheetMultiplying fractions Skill worksheetLinear equations Skill worksheetAdding fractions Skill worksheetPercentage

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Choose your year level

Ratios, explained

1. Simplifying ratios

2. Ratios with decimals or fractions

3. Ratios with different units

4. Equivalent ratios

5. Dividing a quantity in a ratio

6. The unitary method

Quick check: 10 questions

Generate a free maths worksheet

Practice built from mistakes.

Topic worksheets with worked examples

Questions

How do you simplify a ratio?

How do you divide an amount in a ratio?

Do the ratio worksheets include answers?

More skill worksheets

Better maths marks start with the next wrong answer.