ratioProportion · Year 7 · Suggested learning sequence
Simplifying a ratio
Simplifying a ratio means writing it with the smallest whole numbers while keeping the same comparison. Find the highest number that divides both terms, then divide both by it. For 8:12, the highest common factor is 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3, so 8:12 = 2:3. You must divide both terms by the same number — different divisors change the ratio. A ratio is fully simplified when no number bigger than 1 divides both terms; if both are still even, or share any factor, keep going.
Sample questions
Simplify the ratio 4:8.
- Find the highest number that divides both 4 and 8: 4.
- 4 ÷ 4 = 1 and 8 ÷ 4 = 2.
- So 4:8 simplifies to 1:2.
Answer: 1:2
Simplify the ratio 16:20.
- Find the highest number that divides both 16 and 20: 4.
- 16 ÷ 4 = 4 and 20 ÷ 4 = 5.
- So 16:20 simplifies to 4:5.
Answer: 4:5
Simplify the ratio 4:12.
- Find the highest number that divides both 4 and 12: 4.
- 4 ÷ 4 = 1 and 12 ÷ 4 = 3.
- So 4:12 simplifies to 1:3.
Answer: 1:3