Mathematics • Year 7 • Unit 2 • Lesson 13

One-Step Multiply/Divide in the Real World

Set up one-step × or ÷ equations from everyday situations — sharing chocolate, paving paths, planning a road trip — solve, and check.

Apply · Real-World Maths

1. Word problems

For each: choose a letter for the unknown, write a one-step equation (× or ÷ only), solve, then write a sentence answering the question. Always check.

1.1 — Length of a rectangle. A rectangle has an area of 72 cm² and a width of 8 cm. (Recall: area = length × width.)

(a) Let L be the length in centimetres. Write an equation.
(b) Solve for L and write the answer in a sentence. 2 marks

Stuck? area = length × width gives 8 × L = 72, i.e. 8L = 72.

1.2 — Sharing chocolate. A bag of jelly beans was shared equally between 7 friends. Each friend received 12 jelly beans.

(a) Let j be the total number of jelly beans. Write an equation using division.
(b) Solve for j. 2 marks

Stuck? "Total divided by 7 = 12 per friend" gives j⁄7 = 12.

1.3 — Paving a path. A school path is made of square tiles, each 0.5 m long. The finished path is 12 m long.

(a) Let n be the number of tiles needed (assume tiles line up end to end). Write an equation.
(b) Solve for n. 2 marks

Stuck? "Number of tiles × length of one tile = total length" gives 0.5n = 12.

1.4 — Road trip. A family drives a steady 80 km/h on the highway. The trip from home to the beach takes t hours. The beach is 200 km from home.

(a) Write an equation using t. (Distance = speed × time.)
(b) Solve for t and give your answer in a sentence (decimal hours is fine). 2 marks

Stuck? distance = speed × time gives 200 = 80t, i.e. 80t = 200.

1.5 — Temperature drop. A freezer's temperature drops by 4 °C every hour. After some hours, the total drop was −24 °C (i.e. the temperature is 24 °C lower).

(a) Let h be the number of hours. Using "−4 °C per hour × h hours = total drop", write the equation.
(b) Solve for h. 2 marks

Stuck? −4 × h = −24 gives −4h = −24. Negative ÷ negative = positive.

2. Explain your thinking

This question is about communication, not just symbols. Use full sentences. 4 marks

2.1 A classmate says: "To solve 5x = 35, I multiply both sides by 5 to undo the x." In your own words, explain (i) why their method is wrong, (ii) what they should do instead and why, (iii) what real-world meaning 5x = 35 might have, and (iv) why the rule for ÷ equations (e.g. x⁄3 = 9) is the opposite — you multiply, not divide.

Stuck? Their method gives x = 175, which doesn't satisfy 5x = 35. Try it: 5 × 175 = 875, not 35.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

1.1 — Length of a rectangle

(a) Equation: 8L = 72.
(b) Divide both sides by 8: L = 72 ÷ 8 = 9. The rectangle is 9 cm long. Check: 8 × 9 = 72 ✓.

1.2 — Sharing chocolate

(a) Equation: j ÷ 7 = 12 (i.e. j⁄7 = 12).
(b) Multiply both sides by 7: j = 12 × 7 = 84 jelly beans. Check: 84 ÷ 7 = 12 ✓.

1.3 — Paving a path

(a) Equation: 0.5n = 12.
(b) Divide both sides by 0.5: n = 12 ÷ 0.5 = 24 tiles. Check: 0.5 × 24 = 12 ✓.

1.4 — Road trip

(a) Equation: 80t = 200.
(b) Divide both sides by 80: t = 200 ÷ 80 = 2.5 hours. The trip takes 2.5 hours (2 hours 30 minutes). Check: 80 × 2.5 = 200 ✓.

1.5 — Temperature drop

(a) Equation: −4h = −24.
(b) Divide both sides by −4: h = −24 ÷ (−4) = 6 hours. Check: −4 × 6 = −24 ✓.

2.1 — Explain your thinking (sample response)

(i) Multiplying both sides by 5 gives 25x = 175, which is even further from isolating x. Multiplication doesn't undo multiplication — it makes it worse.
(ii) They should divide both sides by 5. Division is the inverse of multiplication: 5x ÷ 5 = x, leaving x by itself. So x = 35 ÷ 5 = 7.
(iii) A real meaning of 5x = 35 might be: "Five identical chocolate bars cost a total of $35. What does one bar cost?" Each bar costs $7.
(iv) For x⁄3 = 9, the x is being divided. Division is undone by multiplication, so we multiply both sides by 3. The rule is consistent: always use the INVERSE of whatever is being done to x.

Marking: 1 for showing the wrong method makes things worse; 1 for the correct method and reason; 1 for a sensible real-world meaning; 1 for explaining the consistent inverse-operation rule.