Ratio, Proportion & Partnership • Topic 1 of 4

Ratio Basics

Express a ratio in lowest terms by dividing by the HCF. To compare ratios, cross-multiply or convert to decimals. To combine a:b and b:c into a:b:c, scale so the common term b matches (take its LCM). The multiplier method — letting the parts be 2x, 3x, 5x — turns almost every ratio word problem into one linear equation.

✅ Solved examples

1. Simplify the ratio 36:48.
HCF 12. 36/12 : 48/12 = 3:4.
2. Divide 350 in the ratio 3:4.
Parts 3x + 4x = 7x = 350 -> x = 50. Shares 150 and 200.
3. If a:b = 2:3 and b:c = 4:5, find a:b:c.
Make b common (LCM 12): a:b = 8:12, b:c = 12:15. So a:b:c = 8:12:15.
4. Two numbers are in ratio 5:7 and their sum is 96. Find them.
12x = 96 -> x = 8. Numbers 40 and 56.

✏️ Practice — try these, take hints as needed

1. Simplify 45:60.
HCF 15.
Divide both.
—
3:4
2. Divide 240 in ratio 5:3.
8x = 240.
x = 30.
Shares.
150 and 90
3. a:b = 3:4, b:c = 6:7. Find a:b:c.
Make b common (LCM 12).
a:b = 9:12, b:c = 12:14.
—
9:12:14
4. Two numbers ratio 7:9, difference 30. Find them.
2x = 30.
x = 15.
7x and 9x.
105 and 135
5. Ratio 2:3:5, total 200. Largest share?
10x = 200.
x = 20.
5x.
100

📝 Topic test — 8 questions

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