Mathematics • Year 7 • Unit 1 • Lesson 13
Percentages in the Real World
Use percentages to work out sale prices, score tests, calculate tips, and read survey results. Per cent is the universal way to compare any "part of a whole" in everyday life.
1. Word problems
Each problem uses one of the percentage ideas from Lesson 13: % of an amount, % from a fraction, % discount or increase. Show working — a final answer with no working only earns half marks.
1.1 — Jacket on sale. A $200 jacket is on sale at 30% off.
(a) How much do you save?
(b) What is the final sale price?
(c) Show the answer to (b) using the "multiplier" method (pay 70%). 3 marks
1.2 — Test score. A maths test has 50 questions. You get 42 of them correct.
(a) What percentage did you score?
(b) The school's "high distinction" mark is 90%. By how many marks did you miss out on HD? 3 marks
1.3 — Restaurant tip. A meal costs $65. You decide to leave a 10% tip.
(a) How much is the tip?
(b) What is the total amount you pay? 2 marks
1.4 — Survey results. A survey asks 200 Year 7 students "What is your favourite subject?" 80 students say Maths, 60 say English, 40 say PE, and the rest say "other".
(a) What percentage chose Maths?
(b) What percentage chose "other"?
(c) Express the Maths total as a fraction in simplest form. 3 marks
1.5 — Mobile phone discount. A new phone usually costs $480. The shop is running two deals on the same model: Deal A gives 25% off, Deal B gives $120 off.
(a) What is the final price under Deal A?
(b) What is the final price under Deal B?
(c) Which deal is the better value, and by how much? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate says "To find 15% of an amount, I just divide by 15." In your own words explain (i) why this is wrong, (ii) what the correct method is for finding 15% of $300, (iii) show your working using both the decimal × method and the 10% mental method, and (iv) end with a sentence about why dividing by 100 is the key idea behind every percentage calculation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Jacket on sale
(a) Saving = 30% of $200 = 0.30 × 200 = $60.
(b) Sale price = $200 − $60 = $140.
(c) Multiplier method: pay 70%. 0.70 × $200 = $140 ✓ (same answer).
1.2 — Test score
(a) 42/50 × 100 = 4200 ÷ 50 = 84%.
(b) 90% of 50 = 0.90 × 50 = 45 questions. Missed by 45 − 42 = 3 marks.
1.3 — Restaurant tip
(a) 10% of $65 = $65 ÷ 10 = $6.50.
(b) Total = $65 + $6.50 = $71.50.
1.4 — Favourite subject survey
(a) Maths: 80/200 × 100 = 8000 ÷ 200 = 40%.
(b) Other = 200 − (80 + 60 + 40) = 20 students. 20/200 × 100 = 10%.
(c) Maths as a fraction: 80/200 = 2/5 (÷ 40).
1.5 — Mobile phone deals
(a) Deal A: 25% of $480 = 0.25 × 480 = $120 off. Final = $480 − $120 = $360.
(b) Deal B: $480 − $120 = $360.
(c) The two deals give exactly the same final price ($360 each), so they are equal value. The 25%-off deal saves $120 on a $480 phone, which is exactly the flat $120-off amount.
2.1 — Explain your thinking (sample response)
The classmate is wrong because per cent means "per hundred" — the 100 is what you divide by, not the percentage itself. Dividing by 15 would give you 1/15 of the amount, not 15/100 of it. For 15% of $300, the correct two methods are:
Decimal × method: 15% = 0.15. 0.15 × $300 = $45.
10% mental method: 10% of $300 = $30 (divide by 10). 5% = half of 10% = $15. 15% = $30 + $15 = $45. ✓
Both methods rely on the same idea: dividing by 100 turns the percentage into a fraction of the whole, and then you multiply by the amount. Every percentage calculation is really just "fraction of an amount" in disguise.
Marking: 1 for spotting that ÷15 is wrong; 1 for the decimal method giving $45; 1 for the 10% method giving $45; 1 for the ÷100 insight.