SkillrHub • Year 7 Maths • AC9M7N08

Ratios — Homework

Show working, label ratio parts clearly and interpret answers in context.

Part A — 5 × 2-mark questions

1. Represent the ratio 1:4 with counters. How many counters are needed altogether?

2. A set is divided in the ratio 1:2. What fraction of the whole is the larger part? Explain briefly.

3. Share $30 in the ratio 2:3. Find the smaller share.

4. A concentrate:water mixture is 1:5. What fraction of the final mixture is water?

5. Red:blue beads = 3:7. What fraction of all beads are red?

Part B — 5 × 5-mark questions

6. Red:green:blue beads = 1:1:2 and there are 48 beads. Find total parts, one-part value, each colour count, sketch a bar/counter model, and explain why this is a part-part-whole relationship.

7. Oil:vinegar = 2:3 in a 250 mL dressing. Find total parts, one-part value, oil and vinegar volumes, draw a bar model, and explain how fractions of the whole connect to the ratio.

8. Share $84 among three people in the ratio 3:5:4. Find all shares, show a strip diagram and explain why the shares remain proportional.

9. A drink concentrate:water ratio is 1:4 and 600 mL is required. Calculate both volumes, represent the mixture with a bar model and explain why concentrate is 1/5 of the whole rather than 1/4.

10. A class has students in the ratio 5:7 and 96 students altogether. Find both groups, show a double-bar representation and explain the difference between a ratio and an absolute count.

Part C — Enrichment investigation

Design a sports drink mixing guide. A drink is mixed powder:water = 1:5. Create a table for final volumes of 600 mL, 1.2 L, 2.4 L and 3 L. For each, calculate powder and water quantities, explain the fraction of the whole represented by each component, and show how you know the concentration stays constant. Then investigate what would happen if someone mistakenly treated 1:5 as “one fifth powder”. Quantify the error for the 2.4 L batch and explain why correct ratio interpretation matters.