Sharing in a Ratio

Grade 4

The idea — dividing into parts

When you share an amount in a ratio, you're splitting it into groups of different sizes. The ratio tells you how many equal parts each person (or group) gets.

The method has three steps: find the total number of parts, work out the value of one part, then multiply up for each share. Get those three steps clear and the rest follows.

The three-step method

Step 1 — Add the ratio parts to find the total. Step 2 — Divide the amount by that total to get one part. Step 3 — Multiply each ratio number by one part.

Worked example

EXAMPLE

Share £120 between Ali and Beth in the ratio 3:5.

Step 1: total parts = 3 + 5 = 8. Step 2: one part = £120 ÷ 8 = £15. Step 3: Ali gets 3 × £15 = £45; Beth gets 5 × £15 = £75. Quick check: £45 + £75 = £120 ✓. Ali gets £45 and Beth gets £75.

When only one share is given

Some questions give you one person's share and ask for another's. Find the value of one part from the share you know, then work out the rest from there.

EXAMPLE

Carl and Donna share prize money in the ratio 2:7. Carl receives £18. How much does Donna receive?

Carl's share is 2 parts = £18, so one part = £18 ÷ 2 = £9. Donna gets 7 parts: 7 × £9 =£63.

Don't be tempted to add the ratio and divide into the total straight away when you don't know the total — you don't have it yet. Work from the share you're given to find one part first.

Try this one

The ratio of red to blue to yellow sweets in a bag is 4 : 5 : 1.

There are 60 sweets in total.

(a) How many blue sweets are there? [2]

(b) What fraction of the sweets are yellow? Give your answer in its simplest form. [1]

Nova's hint:

This is a three-part ratio problem combined with fractions of an amount.

Ask yourself: 'How many total parts are there, and what is one part worth?' Once you have one part, multiply by the relevant number of parts for each colour.

Try to Solve it with Nova?