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Dividing a Quantity in a Given Ratio

To divide a quantity in a given ratio, find the value of one part by dividing the total by the sum of the ratio parts, then multiply each ratio number by one part.

Last updated: 24 January 2026

★★☆☆☆ Level 2mathAlgebraRatiosharingdivision4 min read

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Sharing in a Ratio

Sometimes we split a quantity between two or more groups according to a ratio.

Example: Share £60 in the ratio 2 : 3 between Alice and Bob.

Step-by-Step Method

  1. Add up the parts of the ratio: 2+3=52 + 3 = 5 parts total.
  2. Find the value of one part: 60÷5=£1260 \div 5 = £12 per part.
  3. Multiply to find each share:
    • Alice: 2×12=£242 \times 12 = £24
    • Bob: 3×12=£363 \times 12 = £36
  4. Check: 24+36=6024 + 36 = 60 ✓

Three-way split

Three friends share 270 stickers in the ratio 1 : 2 : 3.

Parts: 1+2+3=61 + 2 + 3 = 6

One part: 270÷6=45270 \div 6 = 45 stickers

  • Friend A: 1×45=451 \times 45 = 45
  • Friend B: 2×45=902 \times 45 = 90
  • Friend C: 3×45=1353 \times 45 = 135

Check: 45+90+135=27045 + 90 + 135 = 270 ✓

Finding the Total from One Share

If you know one person's share and the ratio, you can find the total.

Working backwards

In a ratio of 3 : 5, the smaller share is £24. What is the total?

Smaller share = 3 parts → 1 part=24÷3=£81 \text{ part} = 24 \div 3 = £8

Total parts = 3+5=83 + 5 = 8 → Total = 8×8=£648 \times 8 = £64

Tip

Always check your answer by adding all shares together — they must equal the original total.

Real-World Examples

Real world: sharing prize money

Three friends win €12,000 in a lottery and agree to split it 1 : 2 : 3 based on their ticket contributions.

Total parts =1+2+3=6= 1 + 2 + 3 = 6. One part =12,000÷6=2,000 EUR= 12{,}000 \div 6 = 2{,}000\text{ EUR}

Friend A: €2,000 — Friend B: €4,000 — Friend C: €6,000

Check: 2,000+4,000+6,000=12,000 EUR2{,}000 + 4{,}000 + 6{,}000 = 12{,}000\text{ EUR} ✓

Real world: mixing paint colours

A decorator wants 2 litres of light teal by mixing white and teal paint in the ratio 3 : 1.

Total parts =3+1=4= 3 + 1 = 4. One part =2,000 ml÷4=500 ml= 2{,}000 \text{ ml} \div 4 = 500 \text{ ml}

White: 3×500=1,500 ml3 \times 500 = 1{,}500 \text{ ml} — Teal: 1×500=500 ml1 \times 500 = 500 \text{ ml}

Getting the ratio wrong would produce the wrong shade, wasting expensive paint.

Real world: business profit sharing

Two partners invested €14,000 in a 2 : 5 ratio. After a successful year their profit is €21,000.

Total parts =2+5=7= 2 + 5 = 7. One part =21,000÷7=3,000 EUR= 21{,}000 \div 7 = 3{,}000\text{ EUR}

Partner A: 2×3,000=6,000 EUR2 \times 3{,}000 = 6{,}000\text{ EUR} — Partner B: 5×3,000=15,000 EUR5 \times 3{,}000 = 15{,}000\text{ EUR}

Practice Problems

Share 120 cm of ribbon in the ratio 3 : 5 between two pieces.

Show answer
Parts: 3+5=8. One part = 120 ÷ 8 = 15 cm. Pieces: 3×15=45 cm and 5×15=75 cm. Check: 45+75=120 ✓

A class of 30 students is split into groups in the ratio 2 : 3. How many are in each group?

Show answer
Parts: 2+3=5. One part = 30 ÷ 5 = 6. Group 1: 12 students, Group 2: 18 students.

Orange juice and water are mixed in the ratio 1 : 4 to make 500 ml of squash. How much of each?

Show answer
Parts: 1+4=5. One part = 500 ÷ 5 = 100 ml. Orange juice: 100 ml, water: 400 ml.