Sharing in a Ratio

In a Nutshell

To share an amount in a ratio, find the total number of parts, work out what one part is worth, then multiply.

Sharing in a ratio is a three-step process:

  1. Add the parts of the ratio to get the total parts.
  2. Divide the amount by the total parts to find the value of one part.
  3. Multiply each side of the ratio by the value of one part.
One part=Total amountSum of ratio parts\text{One part} = \frac{\text{Total amount}}{\text{Sum of ratio parts}}

The bar model below shows this visually. Enter a total to see how the amount is shared.

Sharing in a ratio by dealing A pile of coins is dealt out in ratio groups to collection boxes. Watch the dealing to see that sharing in a ratio is repeated fair dealing.
Problem:

Press Deal to watch coins being dealt out in ratio groups. Notice how the dealing repeats until every coin is allocated. Try different problems to see the pattern.

Watch it work

Question: Share £60 in the ratio 3:23 : 2.

Have a go

Q1. Share 40 sweets in the ratio 3:53 : 5.

Q2. Share £72 in the ratio 5:45 : 4.

Q3. Share 120 marbles in the ratio 1:2:31 : 2 : 3.

Q4. Share £200 in the ratio 7:37 : 3.

Q5. Two friends share £45 in the ratio 2:72 : 7. How much does the person with the larger share get?