Mathematics • Year 7 • Unit 1 • Lesson 9
Multiply & Divide Fractions — Real World
Use × and ÷ with fractions to scale recipes up, share a pizza into smaller slices, work out how many half-cups fit in 3 cups, and figure out a fraction of a quantity.
1. Word problems
Each problem uses the multiply / divide ideas from Lesson 9: "of means ×", keep-change-flip for ÷, cross-cancelling before multiplying, or converting mixed numbers to improper fractions first. Show your working — a single answer with no working only earns half marks.
1.1 — Cupcake recipe. A cupcake recipe makes 12 cupcakes using 3/4 cup of sugar. Maya wants to make only half a batch.
(a) How many cupcakes will she make?
(b) How much sugar will she need? (Find 1/2 of 3/4.) 2 marks
1.2 — Pizza slicing. A whole pizza is cut into 3 equal slices, and one of those slices is then cut into 4 equal pieces. Each tiny piece is what fraction of the whole pizza?
2 marks
1.3 — Pancake mix. Jordan has 3 cups of pancake mix. Each pancake uses 1/4 of a cup.
(a) How many pancakes can he make? (Use division: how many quarter-cups fit in 3 cups?)
(b) Explain in one sentence why dividing by a fraction less than 1 gives a bigger answer than 3. 3 marks
1.4 — Lollies share. A bag holds 24 lollies. You give 2/3 of the bag to your friend.
(a) How many lollies does your friend get? (Use 2/3 × 24.)
(b) How many do you have left? 2 marks
1.5 — Slime kit. A slime kit recipe uses 1 1/2 cups of glue per batch. Aisha wants to make 2 1/3 batches.
(a) How many cups of glue will she need in total? (Multiply 1 1/2 × 2 1/3 by converting both to improper fractions.)
(b) Write the answer as a mixed number. 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 says: "When you multiply two fractions, the answer is always smaller than both of them — that doesn't make sense. Multiplication is supposed to make things bigger!" Explain in your own words: (i) is the student's statement always true, (ii) why fraction multiplication usually gives a smaller answer than each starting fraction, (iii) when fraction multiplication actually does give a larger answer. Use a real-life example (such as pizza slices or "half of a half") to back up your explanation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Cupcake recipe
(a) Half batch = 12 ÷ 2 = 6 cupcakes.
(b) 1/2 × 3/4 = 3/8. So she needs 3/8 of a cup of sugar.
1.2 — Pizza slicing
Each tiny piece = 1/4 × 1/3 = (1 × 1)/(4 × 3) = 1/12 of the whole pizza.
(Sense check: 3 thirds × 4 pieces each = 12 tiny pieces in total, so each is 1/12.)
1.3 — Pancake mix
(a) 3 ÷ 1/4 = 3/1 × 4/1 = 12 pancakes.
(b) Dividing by a fraction smaller than 1 is the same as asking "how many small pieces fit into a bigger amount". Because each piece is small, lots of them fit, so the answer is larger than the original 3.
1.4 — Lollies share
(a) 2/3 × 24/1. Cross-cancel 24 and 3 (share 3): becomes 2/1 × 8/1 = 16. Friend gets 16 lollies.
(b) Left: 24 − 16 = 8 lollies. (Check: 1/3 of 24 = 8. ✓)
1.5 — Slime kit
(a) Convert: 1 1/2 = 3/2 and 2 1/3 = 7/3. Multiply: 3/2 × 7/3. Cross-cancel: 3 and 3 share 3 (→ 1 and 1). Result: 1/2 × 7/1 = 7/2.
(b) 7/2 = 3 1/2 cups of glue.
2.1 — Explain your thinking (sample response)
(i) The statement is not always true.
(ii) When you multiply two proper fractions (both less than 1), the answer is smaller than each one because you're taking "a part of a part". For example, 1/2 × 1/2 = 1/4 — half of a half is a quarter. The pizza analogy: a half-pizza cut in half gives a quarter-pizza, which is smaller than either half.
(iii) Multiplication gives a larger answer if at least one fraction is improper (more than 1). For example, 2/3 × 3/2 = 1, and 2 × 3/4 = 6/4 = 1 1/2, which is bigger than 3/4. In general, "× 1" leaves a number the same, "× less than 1" shrinks it, and "× more than 1" enlarges it.
Marking: 1 for saying the statement isn't always true; 1 for the "part of a part" explanation with example; 1 for naming improper fractions as the exception; 1 for the "× more/less than 1" general rule.