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Sharing in a ratio

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Ratio and proportion

Sharing in a ratio

Sally paid twice as much for the car as Bob did, so when they sell it she should get twice as much back. A ratio tells you how to split the money fairly.

Share $9000 in the ratio 2 : 1$3000$3000$3000partsSally: 2 parts = $6000Bob: $30001. add the parts2 + 1 = 32. find one part9000 ÷ 3 = 30003. multiply back3000 × 2 and × 1check: $6000 + $3000 = $9000 ✓
Add the parts, divide, then multiply back.

The three steps

To share an amount in a given ratio: 1. ADD the numbers in the ratio to find the total number of parts. 2. DIVIDE the amount by the total number of parts to find the value of ONE part. 3. MULTIPLY to find each share. Every question in this section is these same three steps.

Sally and Bob

Sally and Bob sell their car for $9000 and share it in the ratio 2 : 1. Total parts: 2 + 1 = 3 One part: $9000 ÷ 3 = $3000 Sally: $3000 × 2 = $6000 Bob: $3000 × 1 = $3000 Always CHECK by adding the shares: $6000 + $3000 = $9000. ✓

Each share as a fraction

A ratio also tells you what fraction each person gets. In the ratio 4 : 5 there are 4 + 5 = 9 parts in all. So the first share is 4/9 of the total and the second is 5/9. That is a quick way to check a share is sensible before you calculate it.

Simplify first

Brad paid $80 and Lola paid $40 for a painting, and they sell it for $630. You could use the ratio 80 : 40 — but then one part is $630 ÷ 120 = $5.25, and the arithmetic gets ugly. Simplify 80 : 40 to 2 : 1 first. Now one part is $630 ÷ 3 = $210, so Brad gets $420 and Lola gets $210. Same answer, no calculator needed.

Worked examples

Share $9000 in the ratio 2 : 1

  1. Total parts: 2 + 1 = 3.
  2. One part: 9000 ÷ 3 = 3000.
  3. Shares: 3000 × 2 = 6000 and 3000 × 1 = 3000.

Answer: $6000 and $3000

Share $45 between Ethan and Julie in 1 : 4

  1. Total parts: 1 + 4 = 5.
  2. One part: 45 ÷ 5 = 9.
  3. Ethan: 9 × 1 = 9. Julie: 9 × 4 = 36.

Answer: $9 and $36

An electricity bill of $72 in the ratio 5 : 4

  1. Total parts: 5 + 4 = 9.
  2. One part: 72 ÷ 9 = 8.
  3. Raine: 8 × 5 = 40. Abella: 8 × 4 = 32.

Answer: $40 and $32

A choir of 35 with girls : boys = 4 : 3

  1. Total parts: 4 + 3 = 7.
  2. One part: 35 ÷ 7 = 5.
  3. Boys: 5 × 3 = 15.

Answer: 15 boys, which is 3/7 of the choir

Simplify before you share: $630 in 80 : 40

  1. 80 : 40 simplifies to 2 : 1.
  2. Total parts: 2 + 1 = 3.
  3. One part: 630 ÷ 3 = 210.
  4. Brad: 210 × 2 = 420. Lola: 210 × 1 = 210.

Answer: $420 and $210

Checking a share

  1. Add the two shares back together.
  2. 420 + 210 = 630, the amount you started with.

Answer: The shares are correct

Where you see this in real life

  • Housemates splitting a bill in proportion to how long each stayed. The ratio decides who owes what.
  • Business partners sharing profit in the ratio they invested. Put in twice as much, take out twice as much.

Key words

Share
split an amount into parts of a given size
Parts
the numbers in the ratio, added to give the whole
Value of one part
the amount divided by the total number of parts
Twice as much
two times as much — a ratio of 2 : 1
Conjecture
a sensible guess you then test
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