Scale both parts
If the ratio is 2:3, multiplying by 4 gives 8:12.
Both parts must be scaled by the same amount.
Year 6
Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
Find missing values in simple ratio situations using multiplication and division facts.
Lesson overview
Ratio and proportion
A ratio compares two linked quantities. If one part changes by multiplying or dividing, the other part changes by the same scale factor.
Find the scale factor
If 3 apples match 12 oranges, the scale factor from 3 to 12 is 4.
| Original | New |
|---|---|
| 3 | 12 |
| x4 | x4 |
Use the known part to find the missing part.
Worked example
In a recipe, flour to sugar is 2:3. If there are 10 cups of flour, how much sugar is needed?
| Flour | Sugar |
|---|---|
| 2 | 3 |
| 10 | ? |
- 2 has become 10, so the scale factor is 5.
- Multiply the sugar part by 5 as well.
- 3 x 5 = 15.
- So 15 cups of sugar are needed.
Try it
Find the scale factor first, then apply it to the other part.
Question 1
2:3 scaled by 4 becomes:
Question 2
If 3 apples match 12 oranges, the scale factor is:
Question 3
In the ratio 5:2, if the first part becomes 20, the second part becomes:
| First | Second |
|---|---|
| 5 | 2 |
| 20 | ? |
Question 4
Which pair is in the same ratio as 2:3?
Question 5
Flour to sugar is 2:3. If flour is 6, sugar is:
Common mistakes
Watch for these when working through the lesson.
- Changing only one part of the ratio.
- Using addition instead of multiplication for scaling.
- Reading the ratio parts in the wrong order.
Related topics
These ideas fit closely with this lesson.
- Solve problems involving percentages and comparison.
- Solve problems involving unequal sharing and grouping.