Lesson Guide
Explanation
A ratio compares quantities in PARTS: cordial to water at 1 : 4 means one measure of cordial for every four of water — whether the measure is a capful or a bucket. Ratios carry no units and no absolute size; they only fix the relationship. Two rules from day one: ORDER MATTERS (1 : 4 is not 4 : 1 — one drowns the drink, the other is syrup), and both sides must be in the SAME units before you write the ratio: 50 cm : 2 m is 50 : 200, not 50 : 2.
Your Turn
A class has 12 girls and 15 boys. Write girls : boys, and boys : girls. Check: 12 : 15 and 15 : 12 — different ratios!
Watch Out
Convert to common units FIRST: 500 g : 2 kg → 500 : 2000 (→ simplifies to 1 : 4, next step!).
Explanation
Ratios simplify like fractions: divide both sides by their highest common factor — 12 : 15 → 4 : 5. Simplest form means whole numbers sharing no factor. Y8 adds messy inputs: decimals multiply UP first (2.5 : 4 → ×2 → 5 : 8), and fractions clear their denominators (¾ : ½ → ×4 → 3 : 2). Whatever you do, do it to BOTH sides — a ratio is a balance.
Your Turn
Simplify: 18 : 24, then 1.5 : 6, then 45 min : 2 h. Check: 3 : 4; 1 : 4; 45 : 120 = 3 : 8.
Watch Out
A ratio like 2.5 : 4 is not finished — simplest form never contains decimals or fractions. Scale up, then reduce.
Explanation
Equivalent ratios power every recipe scale-up. Flour : milk = 2 : 3, and you're using 8 cups of flour: the scale factor from 2 to 8 is ×4, so milk = 3 × 4 = 12 cups. When the factor is ugly, drop to ONE part first (unitary strikes again): if 2 parts = 5 L then 1 part = 2.5 L, and any other side follows. Same engine as equivalent fractions and the percentage unitary method — Y8 maths keeps reusing this one idea.
Your Turn
Concrete is cement : sand = 1 : 3. With 4.5 buckets of sand, how much cement? Check: 1 part = 1.5 → 1.5 buckets.
Watch Out
Scale factors apply to BOTH sides. Scaling only the side you were asked about is the classic recipe disaster.
Explanation
The signature skill: share $120 between Ava and Ben in the ratio 3 : 5. Three moves: total the parts (3 + 5 = 8), find one part (120 ÷ 8 = $15), rebuild each share (Ava 3 × 15 = $45, Ben 5 × 15 = $75). Then the non-negotiable check: 45 + 75 = 120 ✓ — the shares must reassemble the whole. Three-way ratios work identically: 2 : 3 : 5 has 10 parts.
Your Turn
Share 84 lollies in the ratio 2 : 5. And $150 in 1 : 2 : 3. Check: 24 and 60; and 25, 50, 75.
Watch Out
Divide by the TOTAL PARTS (8), never by one side of the ratio. 120 ÷ 3 and 120 ÷ 5 are both meaningless here.
Explanation
Exams twist the sharing question by changing which number they give you. Same 3 : 5 ratio, but now: 'Ben gets $30 more than Ava'. The $30 is the DIFFERENCE — and the difference in parts is 5 − 3 = 2. So 2 parts = $30, one part = $15, and everything unlocks: Ava $45, Ben $75, total $120. Given one SHARE instead? ('Ben gets $75') — divide by his 5 parts. Whatever they hand you, convert it to ONE PART, then rebuild.
Your Turn
Flour : sugar = 7 : 2, and there is 1 kg more flour than sugar. How much of each? Check: 5 parts = 1000 g → 1400 g and 400 g.
Watch Out
Ask: is this number the TOTAL, a SHARE, or the DIFFERENCE? Dividing the difference by total parts is the trap answer.
Explanation
The full ratio playbook: units-then-HCF for simplifying, scale factor for equivalent pairs, total-parts for sharing a whole, part-gap for differences — and one part is always the bridge. Run the gauntlet in the exercises and notice how every variant collapses to the same two questions: 'what does one part equal?' and 'how many parts is the thing I want?' Master those and ratios never surprise you again. Quiz and exercises!
Your Turn
Mixed drill: simplify 0.4 : 1.2; and share 65 in 6 : 7. Check: 1 : 3; and 30, 35.
Watch Out
Always finish with the reassembly check — shares that don't add back to the whole mean a parts miscount upstream.
📌 Key Points — this lesson in a nutshell
- A ratio compares quantities in the SAME units — convert first, then drop the units.
- Simplify by dividing by the HCF; clear decimals or fractions by scaling up first.
- Missing values: find the scale factor between the matching positions.
- Dividing in a ratio: total parts → value of ONE part → rebuild each share.
- When the DIFFERENCE is given, the gap in parts (not the total) is what equals it.
Step 1: Introduction
Step 1 of 6
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