Mathematics • Year 8 • Unit 1 • Lesson 16
Ratios in the Real World
Simplify ratios that appear in real recipes, classrooms, sports squads, drink mixes and concrete bags — then explain your thinking in your own words.
1. Word problems
Each problem uses the lesson's idea: simplify a ratio by dividing all parts by the HCF, and CONVERT units first if they don't match. Show your working — a final answer with no working only earns half marks.
1.1 — Concrete mix. A small batch of concrete uses 8 kg cement, 12 kg sand and 20 kg gravel.
(a) Write the ratio cement : sand : gravel in simplest form.
(b) What fraction of the whole mix is gravel? 3 marks
1.2 — Class survey. In a Year 8 class there are 12 girls and 18 boys.
(a) Write the ratio girls : boys in simplest form.
(b) Write the ratio girls : whole class in simplest form. (Remember: whole class = girls + boys.) 3 marks
1.3 — Cordial drink. A cordial recipe uses 250 mL of syrup mixed with 1.25 L of water.
(a) Why can't you write the ratio as 250 : 1.25 straight away?
(b) Convert to the same unit, then write the syrup : water ratio in simplest form. 3 marks
1.4 — Soccer squad. A school's under-14 soccer squad has 11 starters, 4 reserves and 1 goalkeeper.
(a) Write the ratio starters : reserves : goalkeeper.
(b) Is it already in simplest form? Explain why or why not. 3 marks
1.5 — Salad recipe. A salad uses 200 g spinach, 400 g tomatoes and 300 g chicken.
(a) Write the ratio spinach : tomato : chicken in simplest form.
(b) Use your simplified ratio to work out how many "parts" of the whole salad each ingredient is, then find what fraction of the salad is chicken. 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate writes "$2 : 50 cents simplifies to 1 : 25". In your own words, explain (i) what mistake they have made, (ii) what the ratio $2 : 50 cents actually simplifies to, and (iii) the one extra step they forgot. Use the phrase "same unit first" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Concrete mix
(a) HCF(8, 12, 20) = 4. 8 ÷ 4 : 12 ÷ 4 : 20 ÷ 4 = 2 : 3 : 5.
(b) Total parts = 2 + 3 + 5 = 10. Gravel = 5/10 = 1/2 of the mix.
1.2 — Class survey
(a) HCF(12, 18) = 6. 12 ÷ 6 : 18 ÷ 6 = 2 : 3.
(b) Whole class = 12 + 18 = 30. Girls : class = 12 : 30. HCF = 6. 2 : 5.
1.3 — Cordial drink
(a) The units are different — mL on one side and L on the other. You can't compare them directly.
(b) Convert: 1.25 L = 1250 mL. So 250 : 1250. HCF = 250. 1 : 5.
1.4 — Soccer squad
(a) Starters : reserves : goalkeeper = 11 : 4 : 1.
(b) Yes, already simplest form. HCF(11, 4, 1) = 1, so there's nothing left to divide by.
1.5 — Salad recipe
(a) 200 : 400 : 300. HCF = 100. 2 : 4 : 3.
(b) Total parts = 2 + 4 + 3 = 9. Chicken = 3/9 = 1/3 of the salad.
2.1 — Explain your thinking (sample response)
The classmate forgot to put both sides into the same unit first. $2 is 200 cents (not 2 cents), so the ratio is really 200 : 50, which simplifies to 4 : 1 — that is, the $2 side is FOUR TIMES the 50-cent side, not 1/25 of it. The one extra step they forgot is: convert to the SAME UNIT FIRST, then simplify. Their answer 1 : 25 is what you'd get if you treated the $2 as just "2", which is the opposite size to the real ratio.
Marking: 1 mark for spotting the missing unit conversion; 1 mark for the correct simplified ratio (4 : 1); 1 mark for naming the missing step (convert to same unit first); 1 mark for a clear, full-sentence explanation that uses "same unit first".