Ratios and Rates

UK Secondary (7-11)

Dividing a Quantity into a Given Ratio I

Lesson

Ratios tell us about the relative sizes of two or more values. They are often used in everyday life, whether it's for dividing up money, betting odds, cooking or mixing cement! So knowing how to apply your knowledge about ratios is really important. Remember that the order that the words are written in the question correspond to the order of the values in the ratio so don't jumble them around.

You need to know!

- How to calculate the total number of parts (by adding all the numbers in the ratio).

- How to calculate what one part is worth (by dividing a value by the total number of parts) and

- How to calculate what each share of the ratio is worth (by multiplying what one part is worth with each number in the ratio)

Question: How many parts are in the ratio $4:15$4:15?

Do: To work this out, we add $4+15$4+15. So there are $19$19 parts in total.

It doesn't matter how many parts there are to the ratio, we just keep adding them up to get the total number of parts.

Question: What is the total number of parts in the ratio $6:1:9:4$6:1:9:4?

Think: $6+1+9+4=20$6+1+9+4=20

Do: That means the total number of parts is $20$20.

Once you can calculate the total number of parts, we can use it to divide up quantities in a given ratio.

**Evaluate:** $20$20 is divided up into two parts, $A$`A` and $B$`B`, in the ratio $2:3$2:3.

a) What is the value of A?

b) What is the value of B?

Let's look at another example.

**Evaluate: **$30$30 is divided into $3$3 parts, $A$`A`, $B$`B` and $C$`C`, in the ratio $5:3:2$5:3:2.

a) Find the value of A.

b) Find the value of B.

c) Find the value of C.

Neil and Dave bought a scratch ticket that cost $\$10$$10. They won $\$100000$$100000. If they share the winnings in the same ratio as they contributed and they contributed to the price of the ticket in the ratio $7:3$7:3:

a) How much should Neil receive of the prize?

b) How much should Dave receive of the prize?

The length of a garden bed is split up into three sections for beans, turnips and parsley respectively in the ratio $6:7:63$6:7:63. If the total length of the garden bed is 19 metres:

a) What is the length of the side for beans?

b) What is the length of the side for turnips?

c) What is the length of the side for parsley?