Equivalent ratios keep the same multiplier
The ratio 6 : 9 can be simplified because both parts share a common factor of 3.
A ratio is simplified only when the parts have no common factor greater than 1.
Year 8
Ratio scaling, simplifying and sharing in a ratio
Simplify ratios, scale them up and down, and share quantities using ratio parts with clear multiplicative reasoning.
Lesson overview
Number - ratio and multiplicative reasoning
Ratio compares one amount with another. If the multiplier is the same for both parts, the ratio stays equivalent. That helps us simplify, scale recipes and divide a total into parts. The key is to think multiplicatively rather than additively.
Scaling uses the same multiplication on both parts
If orange to blue paint is 2 : 5, then a larger mix could be 4 : 10 or 6 : 15.
Multiply or divide both parts by the same number to keep the ratio equivalent.
Sharing in a ratio starts with total parts
To share 48 in the ratio 1 : 3, first count the total number of parts.
Find one part first, then build each share from that unit.
Worked example
Share 70 pounds in the ratio 2 : 5.
- Add the ratio parts: 2 + 5 = 7.
- Divide the total by 7 to find one part.
- One part is 10.
- Multiply by 2 and by 5 to get the two shares: 20 and 50.
Try it
Decide whether the task is about simplifying, scaling or sharing before you calculate.
Question 1
Which ratio is equivalent to 3 : 4?
Question 2
Simplify 8 : 20.
Question 3
A recipe uses flour and butter in the ratio 5 : 2. If flour is 15 cups, how much butter is needed?
Question 4
Share 36 pounds in the ratio 1 : 2.
Question 5
Which statement is correct?
| Ratio | Equivalent ratio |
|---|---|
| 2 : 3 | 4 : 6 |
| 5 : 7 | 10 : 14 |
Common mistakes
Watch for these when working through the lesson.
- Adding the same amount to both parts instead of using the same multiplier.
- Forgetting to add the ratio parts before sharing a total.
- Simplifying only one side of the ratio.
Related topics
These ideas fit closely with this lesson.
- Percentages of amounts without a calculator.
- Rounding to significant figures.
- Expand single brackets.