Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Simplify 6 : 8.
Show worked solution
Divide both by 2: 3 : 4.
2 Simplify 10 : 15.
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Divide both by 5: 2 : 3.
3 Simplify 12 : 20.
Show worked solution
The HCF is 4, so 12 divided by 4 is 3 and 20 divided by 4 is 5, giving 3 : 5.
Level 2 · Core
4 Simplify 45 : 27.
Show worked solution
The HCF is 9, so 45 divided by 9 is 5 and 27 divided by 9 is 3, giving 5 : 3. Keep the larger number first.
5 Simplify 40 cm : 1 m.
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1 m = 100 cm, so the ratio is 40 : 100. Dividing both by 20 gives 2 : 5.
6 Simplify 6 : 9 : 15 (as a ratio, a : b : c).
Show worked solution
All three divide by 3, giving 2 : 3 : 5.
Level 3 · Challenge
7 Simplify 500 g : 2 kg.
Show worked solution
2 kg = 2000 g, so the ratio is 500 : 2000. Dividing both by 500 gives 1 : 4.
8 Simplify 40 minutes : 2 hours.
Show worked solution
2 hours = 120 minutes, so the ratio is 40 : 120. Dividing both by 40 gives 1 : 3.
9 A ratio becomes 3 : 4 when both of its parts are divided by 7. What was the original ratio?
Show worked solution
Multiply both parts by 7: 3 x 7 = 21 and 4 x 7 = 28, so the original was 21 : 28.