Simplifying Ratios (Year 6 & 11+)

R2Simplifying Ratios

Divide both sides by the same number.

Simplify ratios exactly like fractions — divide both parts by a common factor.

6 : 4 in simplest form.

6 : 4 → ÷2 both → 3 : 2

Same skill as simplifying fractions — biggest common factor, both sides.

Learn the 3-Step Method

1Find a common factor.

6 and 4 both divide by 2.

factor: 2

2Divide BOTH parts.

6 ÷ 2 = 3 and 4 ÷ 2 = 2 → 3 : 2.

3 : 2

3Keep going to simplest form.

12 : 18 → ÷2 → 6 : 9 → ÷3 → 2 : 3. Stop when only 1 divides both.

2 : 3

💡 Key IdeaRatios with units must share the unit first: 50p : £2 = 50 : 200 = 1 : 4.

Worked Example

Simplify each ratio.

10 : 15

÷5

2 : 3

12 : 18

÷6

2 : 3

50p : £2

same units: 50 : 200

1 : 4

Watch Out! Common Mistakes

Dividing one side only.

6 : 4 → 3 : 4 ✕

Both sides! Divide each part by the same number: 3 : 2.

Mixing units.

50p : £2 = 50 : 2 = 25 : 1 ✕

Same units first! £2 = 200p → 50 : 200 = 1 : 4.

Stopping too early.

12 : 18 = 6 : 9 ✓but…

Keep going! 6 and 9 still share 3: simplest form is 2 : 3.

⬇ Cheat Sheet

SIMPLIFYING RATIOS

Same units before anything else.
Divide BOTH parts by a common factor.
Repeat until only 1 divides both.
It's fraction simplifying with a colon.

Examples: 6:4 = 3:2 · 12:18 = 2:3 · 50p:£2 = 1:4.

📖 Continue Your Journey

✓ R1 What Is Ratio?R2 Simplifying Ratios R3 Sharing in a Ratio R4 Ratio and Fractions R5 Direct Proportion R6 Best Value R7 Scale Drawings and Maps R8 Recipes and Scaling R9 Ratio and Percentages R10 Ratio Problem Solving

→

Next Lesson: R3 Sharing in a RatioParts first, value of one part second.

📄 Free printable: Download the Simplifying Ratios cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Divide both parts of the ratio by the same common factor.
6 : 4 simplifies to 3 : 2; 12 : 18 to 2 : 3.
Convert to the same units before simplifying: 50p : £2 = 50 : 200 = 1 : 4.
Keep dividing until only 1 divides both parts.

Frequently asked questions

How do you simplify a ratio?

Divide both parts by their highest common factor: 6 : 4 ÷ 2 gives 3 : 2 — exactly like simplifying a fraction.

How do you simplify a ratio with different units?

Convert to the same unit first: 50p : £2 becomes 50 : 200 in pence, which simplifies to 1 : 4.

What is the simplest form of a ratio?

When the only whole number dividing both parts is 1 — like 2 : 3. If any bigger factor divides both, keep simplifying.

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R1 What Is Ratio?

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R3 Sharing in a Ratio