Home > Proportion > Dividing into a given ratio

## Dividing into a given ratio

To divide a quantity into a given ratio we need to calculate the multiplier that takes us from the number of parts to the required amount.

### When we have the total

When we know the total amount that we have, we can calculate the multiplier from the  number of parts to the quantity by dividing the total amount by the total number of parts.

So multiplier = (Total amount)$\div$(Total number of parts)

Examples

Split $90 into the ratio 2:3:5 Total amount =$90

Total number of parts = $2+3+5=10$

So multiplier = $\frac{90}{10}=9$

Answer is $2 \times 9:3 \times 9:5 \times 9$

= $18:$27:\$45

Mac is making a potion that will put warts on the noses of the girls she knows.  It uses ground frogs legs, eel jelly and spiders eyes in the ratio of 5:3:4.  She wishes to make 500g of the potion.  How much does she need of each ingredient?

Multiplier = (Total amount)$\div$(Total number of parts) = $\frac{500}{12}=41.667$

So multiply each number of parts by 41.667

She needs 208.33g of ground frogs legs, 125g of eel jelly and 166.67g of spider’s eyes.

### When we know the amount of a portion

When we the know the amount of a portion, we can calculate the multiplier by dividing the portion amount by the number of parts of that portion.

In short the multiplier = (Portion amount)$\div$(Portion parts)

Examples

An alloy is made up of metals A and B in the ratio of 3:5.

If there is 39kg of metel A how much is there of metal B?

Multiplier = (Portion amount)$\div$(Portion parts) = $\frac{39}{3}=13$, since we know the details of A.

So there are $5 \times 13 = 65kg$ of metal B

JiG has this strange idea that one day she will be able to fly and decides that if she can learn to run faster she might be able to fly sooner.  Her running program consistes of running and walking and standing in the ratio of 4:2:1.  If she plans to run for 30 minutes, how long will she be out for altogether?

Multiplier = (Portion amount)$\div$(Portion parts) =$\frac{30}{4}=7.5$, since we have the information for running.

Walking will be 15 minutes (we multiplied 2 by 7.5)

Standing will be 7.5 minutes.

In total she will be out 52.5 minutes.