Simplifying Ratios (No Calculator) — KS3 Maths
A clear, step-by-step KS3 lesson on simplifying ratios: divide every part by the highest common factor to write a ratio in its simplest form, including ratios with different units, no calculator needed.
Writing a ratio in its simplest form is a KS3 skill you'll use constantly — in recipes, scale drawings, maps and almost every ratio question on a test paper. This written lesson covers the same skills as the video: what a ratio actually is, how to simplify one fully, what to do when the units are different, and the mistake that catches so many students out. No calculator needed.
What actually is a ratio?
A ratio tells you how many of one thing there are compared to another thing. If a pond has 6 frogs and 9 lizards, the ratio of frogs to lizards is 6 : 9.
Order matters. "Frogs to lizards" means the frog number comes first — write the ratio in words first (frogs : lizards), then swap in the numbers in the same order.
Worked example
Simplify 6 : 9 (frogs to lizards)
A pond has 6 frogs and 9 lizards, so the ratio of frogs to lizards is .
That's correct, but we can say it more simply. We need a number that divides into both 6 and 9 — the highest common factor of 6 and 9 is 3.
Divide both parts by 3: and .
So in its simplest form, the ratio of frogs to lizards is .
You can see it in the pond: circle groups of three, and the frogs make 2 groups while the lizards make 3. For every 2 frogs there are 3 lizards — the same proportion, just smaller numbers.
Worked example
Simplify 200 : 350 (a fruit punch recipe)
A fruit punch mixes 200 ml of juice with 350 ml of lemonade, so the ratio of juice to lemonade is .
The highest common factor of 200 and 350 is 50.
Divide each part by 50: and .
So juice to lemonade in its simplest form is .
What if the units are different?
A ratio only makes sense when both parts are measured in the same unit — you can't compare centimetres with metres directly. So convert to the same unit first (usually the smaller one), then simplify as normal. The final ratio has no units at all.
Worked example
Different units: a 50 cm model of a 2 m car
A model car is 50 cm long and the real car is 2 m long. What is the ratio of the model to the real car?
Step 1 — make the units the same: m cm, so the ratio is .
Step 2 — divide by the highest common factor, which is 50: and .
So the ratio of model to real car is — the real car is exactly 4 times the length of the model.
Practice questions
Try these yourself, then click to check each answer. Remember: same units first, then divide every part by the highest common factor.
1.Simplify 8 : 12.Show answerHide answer
The highest common factor of 8 and 12 is 4.
and , so .
2.Simplify 15 : 35.Show answerHide answer
The highest common factor of 15 and 35 is 5.
and , so .
3.Simplify 27 : 36.Show answerHide answer
The highest common factor of 27 and 36 is 9.
and , so .
(If you divided by 3 first and got , that's fine — just keep going: 3 divides again, giving .)
4.A car park has 14 red cars and 21 silver cars. Write the ratio red : silver in its simplest form.Show answerHide answer
Red first, because it's named first: .
The highest common factor of 14 and 21 is 7, so and .
Red : silver .
5.Simplify 6 : 9 : 12.Show answerHide answer
The same rule works for three parts — find the highest common factor of all of them, which is 3.
, , , so .
6.Simplify 20 minutes : 1 hour.Show answerHide answer
Make the units the same first: 1 hour minutes, so the ratio is .
The highest common factor is 20: and .
So 20 minutes : 1 hour — no units in the final answer.
7.Spot the mistake: a student simplifies 16 : 24 by dividing by 2 and writes 8 : 12 as their final answer. What went wrong, and what is the correct answer?Show answerHide answer
Dividing by 2 is a correct step, but isn't fully simplified — 4 still divides into both parts. The student stopped too soon.
The highest common factor of 16 and 24 is 8: and .
So in its simplest form.
Want more practice? Download the free worksheet below — 16 questions that build from gentle starters to three-part ratios, mixed units and word problems, with a full worked answer key so you can mark it together.
Practise this skill
A free printable worksheet with 16 questions and a full worked answer key. No sign-up needed.