Mathematics • Year 8 • Unit 1 • Lesson 15

Ratios in the Real World

Use ratios where they actually show up: recipe scaling, dividing students into class groups, sport-team gender splits, paint mixes. Then explain why a ratio is NOT a fraction even though they look similar.

Apply · Real-World Maths

1. Word problems

Each problem uses the idea that a ratio is a recipe of parts. Show your working — a single final answer with no working only earns half marks.

1.1 — Flour-and-sugar biscuits. A biscuit recipe uses flour and sugar in the ratio 3 : 1. The whole mix weighs 400 g.

(a) How many parts in total?
(b) How many grams per part?
(c) How much flour and how much sugar are in the 400 g mix? 3 marks

Stuck? Total parts = 3 + 1 = 4. 400 g ÷ 4 = 100 g per part. Flour = 3 parts, sugar = 1 part.

1.2 — Class groups. A teacher needs to split 24 students into project teams using a girls-to-boys ratio of 5 : 3.

(a) How many parts in the ratio in total?
(b) How many students per part?
(c) How many girls and how many boys does the teacher need? 3 marks

Stuck? 5 + 3 = 8 parts. 24 ÷ 8 = 3 students per part. Girls = 5 × 3, boys = 3 × 3.

1.3 — Cordial mix. A drinks bottle is labelled “cordial : water = 1 : 7”. Mia wants to make 800 mL of drink.

(a) How many parts total?
(b) How many mL of cordial does she need?
(c) How many mL of water?
(d) What fraction of the finished drink is cordial? 3 marks

Stuck? 8 parts total; 800 mL ÷ 8 = 100 mL per part. Cordial = 1 × 100, water = 7 × 100.

1.4 — Paint mix. An artist mixes red, yellow and white paint in the ratio 2 : 3 : 5 to make an orange-pink. He needs a total of 200 mL of mix for a painting.

(a) How many parts total?
(b) How many mL per part?
(c) How much red, how much yellow, how much white? (Add the three to check they sum to 200 mL.) 3 marks

Stuck? 2 + 3 + 5 = 10 parts. 200 ÷ 10 = 20 mL per part.

1.5 — Sport team ratios. A junior basketball squad has 18 players. The ratio of guards : forwards : centres is 4 : 4 : 1.

(a) How many parts total?
(b) How many players per part?
(c) Find the number of guards, forwards and centres. (Check they sum to 18.) 3 marks

Stuck? 4 + 4 + 1 = 9 parts. 18 ÷ 9 = 2 players per part.

2. Explain your thinking

This question is about communication, not just answers. Use full sentences. 4 marks

2.1 A friend says “a 3 : 1 ratio just means three-quarters of something is one thing and one-quarter is the other — ratios and fractions are basically the same”. In your own words, explain (i) what is RIGHT about your friend's claim, (ii) what is WRONG (or misleading) about it, (iii) the difference between writing 3 : 1 and writing 3/4, and (iv) one situation where the ratio form is more useful than the fraction form. Use the phrases “total parts” and “part of a whole” somewhere in your answer.

Stuck? 3 : 1 tells you how parts compare to EACH OTHER. 3/4 tells you a part OF THE WHOLE. Ratios are useful when you don't yet know the total amount — e.g., a recipe that scales.

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Answers — Do not peek before attempting

1.1 — Biscuit mix 3 : 1, 400 g

(a) Total parts = 3 + 1 = 4.
(b) Per part: 400 ÷ 4 = 100 g.
(c) Flour = 3 × 100 = 300 g; sugar = 1 × 100 = 100 g. (Check: 300 + 100 = 400 g ✓.)

1.2 — 24 students at 5 : 3

(a) Total parts = 8.
(b) Per part: 24 ÷ 8 = 3 students.
(c) Girls = 5 × 3 = 15; boys = 3 × 3 = 9. (Check: 15 + 9 = 24 ✓.)

1.3 — Cordial 1 : 7 in 800 mL

(a) Total parts = 8.
(b) Per part: 800 ÷ 8 = 100 mL. Cordial = 100 mL.
(c) Water = 7 × 100 = 700 mL. (Check: 100 + 700 = 800 mL ✓.)
(d) Fraction cordial = 1/8 of the drink.

1.4 — Paint mix 2 : 3 : 5 in 200 mL

(a) Total parts = 2 + 3 + 5 = 10.
(b) Per part: 200 ÷ 10 = 20 mL.
(c) Red = 2 × 20 = 40 mL; yellow = 3 × 20 = 60 mL; white = 5 × 20 = 100 mL. (Check: 40 + 60 + 100 = 200 mL ✓.)

1.5 — Squad 4 : 4 : 1 in 18 players

(a) Total parts = 9.
(b) Per part: 18 ÷ 9 = 2 players.
(c) Guards = 4 × 2 = 8; forwards = 4 × 2 = 8; centres = 1 × 2 = 2. (Check: 8 + 8 + 2 = 18 ✓.)

2.1 — Explain your thinking (sample response)

What the friend gets RIGHT is that a 3 : 1 ratio and a 3/4 fraction are linked — in a 3 : 1 mix, three-quarters of the whole IS the first thing and one-quarter is the second. What's WRONG (or misleading) is calling them “basically the same”: a ratio compares two things to EACH OTHER (3 parts of one for every 1 part of the other), while a fraction describes a part of a whole — you need the total parts (3 + 1 = 4) before you can turn the ratio into the fraction 3/4. Writing 3 : 1 keeps the recipe-style relationship visible (“triple the flour amount”), while 3/4 tells you the share of the finished mix; they describe the same situation from different angles. The ratio form is more useful when you don't yet know the total amount — a biscuit recipe in the ratio 3 : 1 lets you scale up to 400 g, 800 g, or any other total, while a fraction like 3/4 needs a total to mean a number of grams.

Marking: 1 mark for explaining the “right” bit (3 : 1 and 3/4 are linked via total parts); 1 mark for the difference (ratio = part:part vs fraction = part of whole); 1 mark for using both phrases “total parts” and “part of a whole”; 1 mark for a sensible example where ratio is more useful (recipes that scale without a fixed total).