Scaling in a Ratio (SQA National 5 Applications of Mathematics): Revision Note

Scaling in a ratio

What is an equivalent ratio?

• Equivalent ratios are two ratios that represent the same proportion of quantities within a whole

  • E.g. The ratio 5 : 10 is equivalent to 20 : 40

• Equivalent ratios are frequently used when the values involved take on a real-life meaning

  • A cake recipe involves flour and butter being mixed in the ratio 3 : 2

    • 3 g of flour and 2 g of butter would not lead to a very big cake

    • An equivalent ratio of 300 : 200 gives a more realistic 300 g of flour and 200 g of butter

  • The distance on the map and in real-life is in the ratio 1 : 1000

    • 1 cm on the map is 1000 cm in real life

How do I find an equivalent ratio?

• You can find an equivalent ratio by multiplying (or dividing) each part of the ratio by the same value

  • E.g. Multiply each part of the ratio 2 : 3 : 7 by 4 to find an equivalent ratio of 8 : 12 : 28

  • Ratios can be scaled up or down to suit the context of a question

• The size of each part in the ratio, relative to the others, is still the same

  • The actual values in the equivalent ratio may be more meaningful in the context of the situation

How do I find a missing value in a ratio?

• There are two ways to find missing values

  • Suppose you have two equivalent ratios

    • 2 : 5 and 7 : ?

• You can find missing values by finding the scale factor from one ratio to the other

  • e.g. find what you need to multiply 2 by to get 7

    • 7 ÷ 2 = 3.5

  • Multiply the other quantity by this

    • 5 × 3.5 = 17.5

  • The equivalent ratio is 7 : 17.5

• You can also find missing values by finding the scale factor from one quantity in a ratio to the other

  • e.g. find what you need to multiply 2 by to get 5

    • 5 ÷ 2 = 2.5

  • Multiply the quantity in the other ratio by this

    • 7 × 2.5 = 17.5

  • The equivalent ratio is 7 : 17.5