π
∞
∑
∫
θ
E = mc²
y = mx+b
√
Δ
φ
∇
λ
About this video
What a ratio means — 'for every 1 sweet John has, Stacy has 3' — how to simplify a ratio by writing it as a fraction, and how to share an amount in a ratio with one formula: your part over the parts added, times the total.
What it covers
- Reading a ratio: for every 1 of the first, there are 3 of the second
- Simplifying: write it as a fraction, divide by the HCF, write it back as a ratio
- Sharing: your part over the parts added, times the amount
- Checking that the shares add back to the total
- Reading the order of the sentence and of the numbers
Extra worked examples
✍️ Extra example: simplify 18 : 24
- 118/24Write the ratio as a fraction.
- 2(18 ÷ 6)/(24 ÷ 6) = 3/4The HCF of 18 and 24 is 6 — divide the top and the bottom by it.
- 318 : 24 = 3 : 4Write it back as a ratio: the numerator on the left, the denominator on the right.
✍️ Extra example: share R240 between Thabo and Lerato in the ratio 3 : 5
- 1Parts added: 3 + 5 = 8This is the bottom of every share's fraction.
- 2Thabo: 3/8 × R240 = R90His part over the parts added, times what is being shared.
- 3Lerato: 5/8 × R240 = R150Her part over the parts added — the 5 belongs to the second name.
- 4R90 + R150 = R240 ✓If the shares do not add back to the total, there is a mistake.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Simplify 12 : 18.
Show answer ▾Hide answer ▴
12/18 = 2/3 (÷ 6), so 2 : 3 - 2Simplify 35 : 7.
Show answer ▾Hide answer ▴
35/7 = 5/1, so 5 : 1 (keep the 1 — a ratio has two sides) - 3Share 35 sweets in the ratio 2 : 3.
Show answer ▾Hide answer ▴
2/5 × 35 = 14 and 3/5 × 35 = 21; 14 + 21 = 35 ✓ - 4A class of 36 has boys and girls in the ratio 4 : 5. How many girls are there?
Show answer ▾Hide answer ▴
5/9 × 36 = 20 girls (and 4/9 × 36 = 16 boys) - 560 counters are red, blue and yellow in the ratio 1 : 2 : 3. How many of each?
Show answer ▾Hide answer ▴
Parts added: 6 → 1/6 × 60 = 10 red, 2/6 × 60 = 20 blue, 3/6 × 60 = 30 yellow
Read the full lesson
Practise this topic
Download matching Grade 8–9 papers and worksheets.
