Mathematics • Year 7 • Unit 1 • Lesson 11
Decimals in the Real World
Use decimal operations to total grocery bills, work out petrol cost, split restaurant bills, and check change. Every real number you meet (money, distance, time) is a decimal.
1. Word problems
Each problem uses one of the four decimal operations from Lesson 11. Estimate first, then calculate. A final answer with no working only earns half marks.
1.1 — Petrol pump. Petrol costs $1.749 per litre. You fill the tank with 35.5 litres.
(a) Estimate the total cost (round both numbers).
(b) Calculate the exact cost. Show your working with dots lined up. 3 marks
1.2 — Grocery total. Maya's basket has these items: bread $4.95, milk $3.20, apples $6.50, chocolate $2.85.
(a) Write each price stacked with the dots lined up.
(b) Total the basket.
(c) Maya pays with a $20 note. How much change does she get? 3 marks
1.3 — Split the bill. Four friends share a pizza meal that costs $58.40 in total. They split the bill evenly.
(a) How much does each person pay?
(b) If a fifth friend joins late and they re-split, how much does each now pay? 2 marks
1.4 — Running times. A runner's three lap times for a 1500 m race are: 1.42 min, 1.38 min, and 1.45 min.
(a) What is her total time? Show the addition with dots lined up.
(b) How much faster is her fastest lap than her slowest? 3 marks
1.5 — Cutting ribbon. A craft shop has a 12.6 m length of ribbon. They cut it into pieces of 0.7 m each for gift wrapping.
(a) How many pieces of ribbon do they get?
(b) Each piece is sold for $1.25. What is the total value of the cut ribbon? 3 marks
2. Explain your thinking
This question is about communication. Use full sentences. 4 marks
2.1 A classmate says "When you multiply two decimals, the answer always gets smaller because decimals are small numbers." In your own words explain (i) whether the statement is always, sometimes or never true, (ii) give one example where multiplying decimals produces a smaller answer, and (iii) give one example where multiplying decimals produces a larger answer. Use the lesson's rule about decimal places to justify each example.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Petrol cost
(a) Estimate: $1.75 × 36 ≈ $63 (or $1.75 × 35 ≈ $61.25).
(b) Exact: 1749 × 355 = 620,895. Total d.p. = 3 + 1 = 4 → 62.0895. Round to dollars and cents: $62.09 (to the nearest cent). Estimate $63 ✓.
1.2 — Grocery total
(a) Column: 4.95 + 3.20 + 6.50 + 2.85 (all 2 d.p.).
(b) Total: hundredths 5+0+0+5 = 10, write 0 carry 1. Tenths: 9+2+5+8+1 = 25, write 5 carry 2. Ones: 4+3+6+2+2 = 17. Answer: $17.50.
(c) Change: $20.00 − $17.50 = $2.50.
1.3 — Split the bill
(a) 58.40 ÷ 4 = $14.60 each.
(b) 58.40 ÷ 5 = $11.68 each.
1.4 — Running times
(a) 1.42 + 1.38 + 1.45. Hundredths: 2+8+5 = 15, write 5 carry 1. Tenths: 4+3+4+1 = 12, write 2 carry 1. Ones: 1+1+1+1 = 4. Total: 4.25 min.
(b) Fastest = 1.38, slowest = 1.45. 1.45 − 1.38 = 0.07 min faster.
1.5 — Cutting ribbon
(a) 12.6 ÷ 0.7: shift both 1 place → 126 ÷ 7 = 18 pieces.
(b) 18 × $1.25. Ignore dots: 18 × 125 = 2250. Total d.p. = 0 + 2 = 2 → $22.50.
2.1 — Explain your thinking (sample response)
The statement is sometimes true, not always. When you multiply by a decimal less than 1, the answer is smaller than the bigger of the two numbers — for example, 0.5 × 0.4 = 0.20, which is smaller than both 0.5 and 0.4. But when one of the decimals is greater than 1, multiplication makes the answer bigger — for example, 0.5 × 1.6 = 0.80, which is bigger than 0.5. The lesson's rule still holds in both cases: count the total decimal places to place the dot. (Count: 0.5 × 0.4 → 5×4 = 20, 2 d.p. → 0.20 ✓; 0.5 × 1.6 → 5×16 = 80, 2 d.p. → 0.80 ✓.)
Marking: 1 for saying "sometimes true"; 1 for a less-than-1 example; 1 for a greater-than-1 example; 1 for using the count-d.p. rule to verify.