To share an amount in a ratio, add the ratio numbers to count the parts, divide the amount by that count to get one part, then multiply. This appears in money, mixtures, ages and angle questions, and it is the base for every later lesson in ratio and proportional reasoning.
What does a ratio actually tell you?
A ratio such as 3:5 says that for every 3 units the first share gets, the second share gets 5. It does not say how big the units are. The total decides that.
Picture the amount cut into equal slices. The first person takes 3 slices and the second takes 5, so the whole amount is 8 slices. Once you know the size of one slice, every share follows.
How to share an amount, step by step
- Add the ratio numbers to find the total number of parts.
- Divide the amount by the number of parts to find one part.
- Multiply one part by each ratio number to get each share.
- Check that the shares add up to the original amount.
Worked example
Share RM480 between Hana and Ravi in the ratio 3:5.
Step 1, parts: 3 + 5 = 8 parts.
Step 2, one part: 480 ÷ 8 = 60, so one part is RM60.
Step 3, shares: Hana gets 3 × 60 = RM180. Ravi gets 5 × 60 = RM300.
Check: 180 + 300 = 480. The shares are also in the ratio 180:300 = 3:5 after dividing both by 60.
The mistake to watch for
A common slip is to divide the whole amount by each ratio number.
Mistaken working: 480 ÷ 3 = 160 and 480 ÷ 5 = 96.
The two “shares” add up to 256, not 480, so they cannot be right.
The error is that 480 is the amount for all 8 parts, not for 3 parts or 5 parts. Divide by the sum of the ratio numbers first. The check step catches this at once, which is why it is worth the ten seconds.
Check yourself
Try these on paper, then open each answer.
1. Share 350 g of flour in the ratio 2:3:2.
Show answer
Parts: 2 + 3 + 2 = 7. One part: 350 ÷ 7 = 50 g.
Shares: 2 × 50 = 100 g, 3 × 50 = 150 g, 2 × 50 = 100 g.
100 g, 150 g, 100 g. Check: 100 + 150 + 100 = 350.
2. Two parcels have masses in the ratio 4:1 and a total mass of 65 kg. Find the heavier mass.
Show answer
Parts: 4 + 1 = 5. One part: 65 ÷ 5 = 13 kg.
Heavier parcel: 4 × 13 = 52 kg. Lighter parcel: 13 kg. Check: 52 + 13 = 65.
3. Two friends share money in the ratio 7:4. The larger share is RM54 more than the smaller. Find the total.
Show answer
The difference is 7 − 4 = 3 parts, and 3 parts = RM54, so one part = RM18.
Total parts: 7 + 4 = 11, so the total is 11 × 18 = RM198.
Check: shares are 7 × 18 = RM126 and 4 × 18 = RM72. The difference is 126 − 72 = 54, and 126 + 72 = 198.
Where this leads next
Next, see how the same idea works when units differ in scaling a recipe with mixed units. The non-calculator working trainer helps you practise the division steps without losing accuracy.
Some students can do these steps alone yet stall when a problem gives a difference instead of a total. Our teachers look for exactly that pattern in online one-to-one Mathematics tuition.