Dividing Quantities in a Given Ratio

"Share £600 in the ratio 3:2" — this type of question appears regularly in QR, whether it involves money, weight, time, or any other quantity. The method is straightforward, but the variations (three-way splits, finding just one share, working backwards) require practice.

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The Standard Method

To divide a quantity in a given ratio:

1. Add the parts of the ratio to find the total number of parts
2. Divide the total quantity by the total number of parts to find the value of one part
3. Multiply each ratio part by the value of one part

Worked Example

Share £600 in the ratio 3:2.

Step	Calculation
Total parts	3 + 2 = 5
Value of one part	£600 ÷ 5 = £120
First share (3 parts)	3 × £120 = £360
Second share (2 parts)	2 × £120 = £240

Check: £360 + £240 = £600 ✓

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Three-Way (or More) Splits

Worked Example

Divide 840 g in the ratio 3:5:2.