Example 1
Simplify the ratio 6:9.
- Look for a number that divides both parts.
- Both 6 and 9 divide by 3.
- 6 divided by 3 = 2 and 9 divided by 3 = 3
So: 6:9 simplifies to 2:3.
Back to National 3
Topic
Ratio
Ratio compares amounts. It is used for sharing, mixing drinks, recipes, and comparing groups.
Topic explanation
A ratio such as 2:3 means there are 2 parts of one thing for every 3 parts of another thing. The parts show how the amounts compare.
To share £30 in the ratio 2:3, add the parts first: 2 + 3 = 5 parts. One part is £30 divided by 5, which is £6.
Ratios can be simplified like fractions. For example, 10:15 simplifies to 2:3 because both parts can be divided by 5.
Quick methods
- Simplify
- Divide each part of the ratio by the same number.
- Share an amount
- Add the parts, find one part, then build each share.
- Scale up
- Multiply every part of the ratio by the same number.
- Check your answer
- The final parts should add to the total amount given.
Worked examples
Example 2
Share £35.00 in the ratio 2:5.
- Add the ratio parts: 2 + 5 = 7 parts
- Find one part: £35.00 divided by 7 = £5.00.
- First share: 2 × £5.00 = £10.00. Second share: 5 × £5.00 = £25.00
So: The shares are £10.00 and £25.00.
Example 3
A drink uses juice and water in the ratio 1:4. How much water is needed for 750 ml of juice?
- The juice part is 1 and the water part is 4.
- If 1 part is 750 ml, multiply by 4 to find the water.
- 750 ml × 4 = 3000 ml
So: 3000 ml of water is needed.