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.

Step	Calculation
Total parts	3 + 5 + 2 = 10
Value of one part	840 ÷ 10 = 84 g
First share (3 parts)	3 × 84 = 252 g
Second share (5 parts)	5 × 84 = 420 g
Third share (2 parts)	2 × 84 = 168 g

Check: 252 + 420 + 168 = 840 ✓

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Finding Just One Share

Often, QR questions only ask for one of the shares, not all of them. You still use the same method but only need to complete the final multiplication for the requested share.

Worked Example

Three friends share a restaurant bill of £75 in the ratio 2:3:5. How much does the friend with the largest share pay?

• Total parts: 2 + 3 + 5 = 10
• One part: £75 ÷ 10 = £7.50
• Largest share (5 parts): 5 × £7.50 = £37.50

Shortcut: The largest share is 5/10 = 1/2 of £75 = £37.50. Recognising the fraction can be faster.

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Finding the Difference Between Shares

Worked Example

Two business partners share profits in the ratio 7:3. Total profit is £4,500. How much more does the first partner receive?

Method 1 (standard):

• Total parts: 10
• One part: £450
• Partner 1: 7 × 450 = £3,150
• Partner 2: 3 × 450 = £1,350
• Difference: 3,150 − 1,350 = £1,800

Method 2 (shortcut):

• Difference in parts: 7 − 3 = 4
• Value of difference: 4 × £450 = £1,800

The shortcut is faster because you calculate the difference directly.

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Working Backwards: Finding the Total from One Share

Worked Example

Two siblings share an inheritance in the ratio 3:5. The younger sibling receives £24,000. What was the total inheritance?

• The younger sibling's share is 3 parts (assuming "younger" gets the smaller share — but read the question carefully!)
• Actually, we need to know which sibling gets which share. If the question says the younger sibling receives £24,000 and gets the "3" part:
  • 3 parts = £24,000
  • One part = £8,000
  • Total = 8 parts = £64,000