Mathematics • Year 8 • Unit 1 • Lesson 17
Sharing It Out, Ratio in Real Life
Split lottery wins, restaurant bills, inheritance, recipes and group gifts using the unitary method. Then explain why "share equally" and "share in a ratio" are different things.
1. Word problems
Each problem uses the lesson's idea: sum of parts, value of 1 part, multiply for each share, sum check. Show your working, a final answer with no working only earns half marks.
1.1, Lottery win. Three friends pooled money to buy a lottery ticket and won $480. They agreed beforehand to split any winnings in the ratio 1 : 2 : 3 because of how much each had contributed.
(a) How much does each friend receive?
(b) Show your sum check. 3 marks
1.2, Group gift. Mia, Jay and Tahlia bought a $96 birthday gift for their friend. They agreed to contribute in the ratio 3 : 4 : 5 because their part-time pay is different.
(a) How much does each pay?
(b) Check the three contributions add to $96. 3 marks
1.3, Concrete bag. A 45 kg bag of pre-mixed dry concrete is in the ratio 2 : 3 : 4 (cement : sand : gravel).
(a) How much of each ingredient is in the bag?
(b) If you only need 15 kg of total mix for a small job, how much cement should you use? 3 marks
1.4, Reverse problem. Lucia and Asha split $120 in the ratio 7 : 5. Lucia gets the bigger share.
(a) How much does Lucia receive?
(b) Asha now realises she actually contributed more than her share suggests. If the ratio were instead 5 : 7 (Asha getting the bigger share), how much would she get? 3 marks
1.5, Inheritance. Three siblings inherit $420 and split it in the ratio 2 : 3 : 5 (in proportion to how much they had contributed to a family business).
(a) Calculate each share.
(b) The middle sibling argues "we should just split it equally, $140 each". By how much would the OLDEST sibling (who got the 5-part share) lose if they switched to an equal split? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate says "$480 split in the ratio 1 : 2 : 3 just means three equal shares of $160 each, there are three people, so divide by three." In your own words, explain (i) why this is wrong, (ii) what the correct shares are, and (iii) what "1 : 2 : 3" actually means in plain English. Use the phrase "the shares are unequal" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1, Lottery win ($480 in 1 : 2 : 3)
(a) Total parts = 1 + 2 + 3 = 6. 1 part = $480 ÷ 6 = $80. Shares: $80, $160, $240.
(b) Check: $80 + $160 + $240 = $480 ✓.
1.2, Group gift ($96 in 3 : 4 : 5)
(a) Total parts = 12. 1 part = $96 ÷ 12 = $8. Mia: $24; Jay: $32; Tahlia: $40.
(b) Check: $24 + $32 + $40 = $96 ✓.
1.3, Concrete bag
(a) Total parts = 9. 1 part = 45 ÷ 9 = 5 kg. Cement: 10 kg; sand: 15 kg; gravel: 20 kg. Check: 10 + 15 + 20 = 45 ✓.
(b) For 15 kg total: 1 part = 15 ÷ 9 = 5/3 kg ≈ 1.67 kg. Cement = 2 parts = 10/3 kg ≈ 3.33 kg (about 3 1/3 kg).
1.4, Reverse problem ($120 in 7 : 5)
(a) Total parts = 12. 1 part = $120 ÷ 12 = $10. Lucia (7 parts) = $70.
(b) If ratio is 5 : 7 with Asha now getting the bigger 7-part share, Asha = 7 × $10 = $70. (The bigger share is always 7 × $10 = $70, no matter who is named.)
1.5, Inheritance ($420 in 2 : 3 : 5)
(a) Total parts = 10. 1 part = $420 ÷ 10 = $42. Shares: $84, $126, $210. Check: 84 + 126 + 210 = $420 ✓.
(b) Equal split = $420 ÷ 3 = $140 each. Oldest currently gets $210, so would lose $70 ($210 − $140).
2.1, Explain your thinking (sample response)
The classmate is wrong because "1 : 2 : 3" doesn't mean three equal shares, it means the shares are unequal. The three numbers tell us the RELATIVE sizes: the second person gets twice as much as the first, and the third person gets three times as much. To split correctly, add the ratio numbers (1 + 2 + 3 = 6 parts), find what 1 part is worth ($480 ÷ 6 = $80), then multiply: $80, $160, $240. Dividing $480 by 3 would only be right if the ratio were 1 : 1 : 1 (three equal shares).
Marking: 1 mark for spotting the mistake (treating ratio as equal); 1 mark for the correct shares ($80, $160, $240); 1 mark for explaining what "1 : 2 : 3" means in plain English; 1 mark for a clear, full-sentence explanation that uses "the shares are unequal".