Lesson Guide
Explanation
Per cent means 'per hundred', and that one fact powers every conversion. 45% = 45/100 = 9/20 = 0.45. The mechanics: % → decimal is ÷100 (45% → 0.45); decimal → % is ×100 (0.7 → 70%); % → fraction is over-100-then-simplify. At Y8 you also meet awkward ones: 12.5% = 0.125 = 1/8, and 150% = 1.5 — percentages happily exceed 100.
Your Turn
Convert: 65% to a simplified fraction; 0.08 to a %; and 7/20 to a %. Check: 13/20; 8%; 35%.
Watch Out
5% = 0.05, not 0.5! Single-digit percentages need the leading zero — the ÷100 moves the digits TWO places.
Explanation
35% of $80, two ways. BUILDING BLOCKS: 10% is 8, so 30% is 24; 5% is half of 10% — 4; total $28. Brilliant for mental maths. THE MULTIPLIER: 35% = 0.35, and 'of' means ×, so 0.35 × 80 = $28. One step, and it's the road that scales — next lesson the multiplier does percentage increase, decrease and reverse problems that blocks can't touch. Learn both; use blocks in your head, the multiplier on paper.
Your Turn
Blocks: 15% of $60. Multiplier: 12.5% of 240. Check: 6 + 3 = $9; and 0.125 × 240 = 30.
Watch Out
The 1% block rescues awkward percentages: 23% of 300 → 1% = 3 → 69. Everything builds from 10%, 5% and 1%.
Explanation
Reverse question: express 36 out of 40 as a percentage. Recipe: PART over WHOLE, times 100 — 36/40 = 9/10 = 90%. Two traps guard this skill. Units must match first: 45 minutes as a percentage of 2 hours is 45/120 (not 45/2!) = 37.5%. And identify the whole correctly — it's whatever follows 'of'. Swap part and whole and you'll get 111%, which the sense check should catch: a part of a whole can't exceed 100% (unless the question genuinely means growth beyond it).
Your Turn
Express: 27 out of 60 as a %; and 30 cm as a % of 1.5 m. Check: 45%; and 30/150 = 20%.
Watch Out
Convert units BEFORE dividing. Mixed units (min/hours, cm/m, g/kg) are deliberately planted in Y8 problems.
Explanation
Memorise this family and percentage work accelerates: 50%=½, 25%=¼, 75%=¾, 20%=⅕, 10%=⅒, 12.5%=⅛, 33⅓%=⅓, 66⅔%=⅔. The fraction route is often FASTER than the multiplier: 25% of 88 is just a quarter — 22; 33⅓% of 66 is a third — 22, which no decimal handles cleanly (0.333… never ends!). Seeing 12.5% and thinking '⅛' instead of reaching for 0.125 is a genuine Y8 superpower.
Your Turn
Fraction route: 75% of 48; 12.5% of 64; 66⅔% of 90. Check: 36; 8; 60.
Watch Out
33⅓% is exactly ⅓ — using 0.33 introduces error. The recurring ones MUST travel as fractions.
Explanation
Why do percentages exist? To compare fairly across different totals. Priya scored 21/25, Marco 33/40 — Marco has more raw marks, but convert both: Priya 84%, Marco 82.5%. Priya did better! Percentages put everything on the same 0–100 scale — that's the whole point. Any 'who did better / which is the better deal' question: convert to %, then judge. This referee role is why the skill matters far beyond the maths classroom. Quiz and exercises now!
Your Turn
Better free-throw shooter: 17/20 or 42/50? Check: 85% vs 84% — the 17/20 shooter, just.
Watch Out
Never compare raw scores across different totals — the conversion to % IS the comparison.
📌 Key Points — this lesson in a nutshell
- Percent means "per 100" — the triangle links % ↔ fraction ↔ decimal.
- x% of Q = (x ÷ 100) × Q.
- A as a percentage of B = A ÷ B × 100 — match the units first.
- Know the family: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 1/3 = 33⅓%.
- Percentages let you compare scores out of different totals fairly.
Step 1: Introduction
Step 1 of 5
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