1. Simplify the ratio $18:24$.

Answer: $3:4$. Divide both parts by $6$.

2. The ratio of red to blue counters is $3:5$. There are $24$ counters. How many are blue?

Answer: There are $15$ blue counters.

3. Share £56 in the ratio $3:5$.

Answer: £21 and £35. One part is £56 ÷ 8 = £7.

4. Write $2.4:0.8$ in its simplest whole-number form.

Answer: $3:1$.

5. A drink uses juice and water in the ratio $2:7$. How much juice is needed for $630$ ml of drink?

Answer: $140$ ml.

6. A length is split in the ratio $4:7$. The shorter part is $20$ cm. Work out the total length.

Answer: $55$ cm.

7. Are the ratios $12:20$ and $3:5$ equivalent?

Answer: Yes. Both equal $3/5$.

8. A class has 12 boys and 18 girls. Write boys:girls in simplest form.

Answer: $2:3$.

9. Share £96 between A and B in the ratio $5:7$.

Answer: A gets £40 and B gets £56.

10. The ratio of cats to dogs is $4:9$. There are 36 dogs. How many cats are there?

Answer: 16 cats.

11. Simplify $45:60:75$.

Answer: $3:4:5$.

12. A pupil simplifies $8:12$ to $2:3$. Explain why both quantities must be divided by the same number.

Answer: $8$ and $12$ are both divided by $4$, so the multiplicative relationship stays unchanged.