Mathematics • Year 7 • Unit 1 • Lesson 7
Simplifying in the Real World
Use equivalent fractions and simplifying to read survey results, share food fairly, check whether scores are really the same, and rewrite ugly fractions into lowest terms.
1. Word problems
Each problem uses the equivalent-fraction and simplifying ideas from Lesson 7: building an equivalent, simplifying to lowest terms, or cross-multiplying to check whether two fractions describe the same amount. Show your working — a single answer with no working only earns half marks.
1.1 — Class survey. In a class of 24 students, 18 said pizza is their favourite lunch.
(a) Write the fraction of students who chose pizza.
(b) Simplify that fraction fully. 2 marks
1.2 — Same score, different fractions? Liam scored 12 out of 20 on a quiz. Noah scored 15 out of 25 on a different quiz.
(a) Use cross-multiplication to check whether 12/20 and 15/25 represent the same score.
(b) Simplify both fractions to confirm your answer. 3 marks
1.3 — Sharing chocolate. A chocolate bar has 16 squares. Aisha eats 6 squares.
(a) Write the fraction she ate, and simplify it fully.
(b) Write the fraction left over, and simplify it fully. 3 marks
1.4 — Recipe scaling. A cookie recipe says use 2/3 cup of sugar to make 12 cookies. Maya wants to write it as an equivalent fraction with denominator 12 so it's easier to compare to the cookie count.
(a) Find the missing number: 2/3 = ?/12.
(b) Write a one-sentence reason why your fraction has the same value as 2/3. 2 marks
1.5 — Football stats. A junior soccer player attempted 30 shots at goal during a season and scored 18 of them. The team statistician wants to express the scoring rate in lowest terms.
(a) Write the scoring rate as a fraction.
(b) Simplify the fraction fully.
(c) Use your simplified fraction to fill in: out of every _____ shots, she scored _____. 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: "To simplify 4/6, I subtract 2 from the top and 2 from the bottom and get 2/4." Explain in your own words: (i) is the answer 2/4 a correct simplification of 4/6, (ii) what rule the student broke when they subtracted, (iii) what the correct rule is for making equivalent fractions. Use a real-life example (such as pizza slices or chocolate squares) to show why the student's method is wrong.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Class survey (18/24)
(a) Fraction = 18/24.
(b) HCF(18, 24) = 6. 18 ÷ 6 = 3, 24 ÷ 6 = 4. So 3/4. Check HCF(3, 4) = 1 ✓.
1.2 — Same score?
(a) Cross-multiply: 12 × 25 = 300 and 20 × 15 = 300. Both equal 300, so yes, the same score.
(b) Simplify: 12/20 = 3/5 (÷ 4). 15/25 = 3/5 (÷ 5). Both give 3/5. ✓
1.3 — Chocolate
(a) Ate: 6/16. HCF(6, 16) = 2. 6 ÷ 2 = 3, 16 ÷ 2 = 8. So 3/8.
(b) Left: 16 − 6 = 10 squares, so 10/16. HCF(10, 16) = 2. 10 ÷ 2 = 5, 16 ÷ 2 = 8. So 5/8.
Check: 3/8 + 5/8 = 8/8 = 1 (whole bar). ✓
1.4 — Recipe scaling
(a) Bottom 3 → 12 is × 4. Top: 2 × 4 = 8. So 2/3 = 8/12.
(b) The new fraction is equivalent because we multiplied both top and bottom by the same number (4), which is the same as multiplying by 4/4 = 1, and multiplying by 1 doesn't change the value.
1.5 — Football stats
(a) Scoring rate = 18/30.
(b) HCF(18, 30) = 6. 18 ÷ 6 = 3, 30 ÷ 6 = 5. So 3/5.
(c) Out of every 5 shots, she scored 3.
2.1 — Explain your thinking (sample response)
(i) The answer 2/4 happens to equal the correctly simplified version of 4/6? Actually no — 4/6 simplifies to 2/3, not 2/4. So the student's answer 2/4 is not correct.
(ii) The student broke the rule that says equivalent fractions are made by multiplying or dividing top and bottom by the same number, not by adding or subtracting. Subtracting 2 from both parts changes the value.
(iii) The correct rule is "whatever you do to the top, do to the bottom — and it must be multiplication or division." To simplify 4/6, divide top and bottom by 2 (the HCF) to get 2/3.
Real-life check: 4/6 of a pizza means 4 of 6 equal slices. If we subtracted 2 from each, we'd be claiming 2/4 = 4/6, but 2/4 = half a pizza and 4/6 is more than half — they can't be the same.
Marking: 1 for noting 2/4 ≠ correct simplification of 4/6; 1 for naming "multiply/divide, not add/subtract"; 1 for the correct rule with the HCF; 1 for a clear real-life example.