Mathematics • Year 8 • Unit 1 • Lesson 4
Quantity as a Percentage
Build fluency with the formula from Lesson 4: A as a % of B = (A ÷ B) × 100%. One worked example, one guided example with blanks, then eight independent problems on test marks, surveys and same-unit comparisons.
1. I do — fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. Tahlia scored 34 out of 40 on a test. What is her percentage score?
Step 1 — Identify the PART and the WHOLE.
Part (A) = 34 marks earned. Whole (B) = 40 marks possible.
Reason: the PART is what she got; the WHOLE is the maximum possible. The part goes on top of the fraction, the whole goes on the bottom.
Step 2 — Write the fraction part/whole.
34/40
Reason: this is "34 out of 40" written as a fraction.
Step 3 — Multiply by 100 to turn it into a percentage.
(34 ÷ 40) × 100 = 0.85 × 100 = 85
Reason: dividing turns the fraction into a decimal (0.85); multiplying by 100 turns the decimal into a percentage.
Step 4 — Add the percent symbol.
85%
Reason: a percentage always needs the % sign to make clear it's "out of 100".
Answer: Tahlia scored 85%.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. Jay scored 43 out of 50 on a test. What is his percentage score?
Step 1 — Identify part and whole: Part = ______ marks, Whole = ______ marks.
Step 2 — Write the fraction part/whole:
______ / ______
Step 3 — Multiply by 100:
(______ ÷ ______) × 100 = ______ × 100 = ______
Step 4 — Add the % symbol and write the final answer:
Jay scored ______%
3. You do — independent practice
Show your working under each problem. The first four are foundation (clean numbers). The middle two are standard (need rounding or unit conversion). The last two are extension (compare two values).
Foundation — clean numbers
3.1 Express 12 out of 25 as a percentage. 1 mark
3.2 Express 9 out of 20 as a percentage. 1 mark
3.3 Express 15 out of 60 as a percentage. 1 mark
3.4 Express $20 out of $80 as a percentage. 1 mark
Standard — round or convert units
3.5 Express 27 out of 45 as a percentage. Round your answer to 1 decimal place. 2 marks
3.6 Express 450 g as a percentage of 1.5 kg. (Hint: convert to the same units first — 1.5 kg = 1500 g.) 2 marks
Extension — compare
3.7 Asha scored 47/60 on Test 1. Eli scored 74/95 on Test 2. (a) Convert each to a percentage (1 dp). (b) Who scored higher? 3 marks
3.8 Express 30 minutes as a percentage of 2 hours. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (faded Jay 43/50)
Step 1: Part = 43, Whole = 50.
Step 2: 43/50.
Step 3: (43 ÷ 50) × 100 = 0.86 × 100 = 86.
Step 4: Jay scored 86%.
Comparison: Tahlia's 85% vs Jay's 86% — Jay edges ahead by 1 percentage point.
3.1 — 12 out of 25
(12 ÷ 25) × 100 = 0.48 × 100 = 48%.
3.2 — 9 out of 20
(9 ÷ 20) × 100 = 0.45 × 100 = 45%.
3.3 — 15 out of 60
(15 ÷ 60) × 100 = 0.25 × 100 = 25%. (Quick check: 15 is one-quarter of 60.)
3.4 — $20 out of $80
(20 ÷ 80) × 100 = 0.25 × 100 = 25%.
3.5 — 27 out of 45
(27 ÷ 45) × 100 = 0.6 × 100 = 60.0% (or exactly 60%).
3.6 — 450 g out of 1.5 kg
Convert: 1.5 kg = 1500 g. Then (450 ÷ 1500) × 100 = 0.3 × 100 = 30%.
If you skip the unit conversion you'd get nonsense like 450/1.5 × 100 = 30,000%.
3.7 — Asha vs Eli
(a) Asha: (47 ÷ 60) × 100 = 78.3% (to 1 dp). Eli: (74 ÷ 95) × 100 = 77.9% (to 1 dp).
(b) Asha scored higher (78.3% > 77.9%) by 0.4 percentage points.
3.8 — 30 min as % of 2 hr
Convert: 2 hr = 120 min. Then (30 ÷ 120) × 100 = 0.25 × 100 = 25%. (Quick check: 30 min is one-quarter of 2 hours.)