Mathematics • Year 7 • Unit 1 • Lesson 8
Adding & Subtracting Fractions — Real World
Add fractions of pizza eaten, work out how much homework time is left, combine recipe quantities, and check whether the leftover pieces of a project add up correctly.
1. Word problems
Each problem uses the rules from Lesson 8: same-denominator add/subtract, different-denominator with LCD, or mixed-number addition/subtraction with borrowing. Show your working — a single answer with no working only earns half marks.
1.1 — Pizza party. A pizza is cut into 8 equal slices. Liam ate 3/8 of the pizza and Aisha ate 1/4.
(a) What fraction of the pizza did they eat altogether? (Convert 1/4 to eighths first.)
(b) What fraction of the pizza is left? 3 marks
1.2 — Homework time. Jordan needs to spend 3/4 of an hour on Maths and 2/3 of an hour on Science.
(a) Find the total time in hours. Write as a mixed number.
(b) If Jordan has already spent 1 hour, how many minutes more does he still need? 3 marks
1.3 — Sharing a cake. A birthday cake is cut into 12 equal pieces. Maya eats 1/6 of the cake, Noah eats 1/4, and the family dog (oops!) gets 1/3.
(a) What fraction of the cake is gone in total?
(b) What fraction is left for the rest of the family? 3 marks
1.4 — Cookie recipe. A recipe uses 1 3/4 cups of flour and 1 1/2 cups of sugar. The total dry ingredients are flour + sugar.
(a) Find the total cups of dry ingredients. Write as a mixed number.
(b) If the bowl already holds 3 cups, will all the dry ingredients fit? Show why or why not. 3 marks
1.5 — Water bottle drinks. A 1 L water bottle is full. During morning recess you drink 1/3 of the bottle. At lunch you drink another 2/5.
(a) What fraction of the bottle have you drunk in total?
(b) What fraction is left at the end of lunch?
(c) Express the leftover amount in millilitres (1 L = 1000 mL). 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A Year 7 student writes: "1/2 + 1/3 = 2/5 because 1 + 1 = 2 and 2 + 3 = 5." Explain in your own words: (i) is the answer 2/5 correct, (ii) what specific rule the student broke, (iii) what the correct method is, and (iv) what the correct answer is. Use the idea of "same-size slices" to back up your explanation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Pizza party
(a) 1/4 = 2/8. Total eaten = 3/8 + 2/8 = 5/8.
(b) Left = 8/8 − 5/8 = 3/8. (Check: eaten + left = 5/8 + 3/8 = 1 whole pizza ✓.)
1.2 — Homework time
(a) LCD(4, 3) = 12. 3/4 = 9/12, 2/3 = 8/12. Sum = 9/12 + 8/12 = 17/12 = 1 5/12 hours.
(b) Already done 1 hour = 12/12. Still to do: 17/12 − 12/12 = 5/12 of an hour. In minutes: 5/12 × 60 = 25 minutes.
1.3 — Sharing a cake
LCD(6, 4, 3) = 12. Convert: 1/6 = 2/12, 1/4 = 3/12, 1/3 = 4/12.
(a) Gone = 2/12 + 3/12 + 4/12 = 9/12 = 3/4.
(b) Left = 12/12 − 9/12 = 3/12 = 1/4.
1.4 — Cookie recipe
(a) Wholes: 1 + 1 = 2. Fractions: 3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1 1/4. Total = 2 + 1 1/4 = 3 1/4 cups.
(b) The bowl holds 3 cups but the total is 3 1/4 cups, which is more than 3. So no, the dry ingredients will not all fit — you'll be 1/4 cup over the top.
1.5 — Water bottle
LCD(3, 5) = 15. 1/3 = 5/15, 2/5 = 6/15.
(a) Drunk = 5/15 + 6/15 = 11/15.
(b) Left = 15/15 − 11/15 = 4/15.
(c) 4/15 of 1000 mL = (1000 ÷ 15) × 4 ≈ 66.67 × 4 ≈ 266.67 mL (about 267 mL).
2.1 — Explain your thinking (sample response)
(i) The answer 2/5 is wrong.
(ii) The student broke the rule that denominators cannot be added directly. Adding 2 + 3 = 5 in the denominator gives a different-sized slice from either of the originals, so the result no longer represents the same amount of pizza.
(iii) The correct method: find the LCD of 2 and 3 (= 6), convert both fractions to sixths (1/2 = 3/6 and 1/3 = 2/6), then add the tops: 3 + 2 = 5. Keep the denominator 6.
(iv) Correct answer: 5/6.
Same-size slice check: 1/2 of a pizza is bigger than 1/2 of a pizza cut into 5 pieces would be — clearly 1/2 + 1/3 is much more than 2/5 (which is less than half). So the answer 2/5 fails a common-sense check.
Marking: 1 for saying 2/5 is wrong; 1 for naming "you can't add denominators"; 1 for the correct LCD method; 1 for the correct answer 5/6 with a sensible check.