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Maths Gcse Aqa Foundation

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    7 主题
  4. Tree-Diagrams-And-Combined-Probability Aqa Foundation
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  5. Simple-Probability-Diagrams Aqa Foundation
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  6. Transformations Aqa Foundation
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  7. Vectors Aqa Foundation
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  19. Direct-And-Inverse-Proportion Aqa Foundation
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  20. Ratio-Problem-Solving Aqa Foundation
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  21. Sequences Aqa Foundation
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  28. Forming-And-Solving-Equations Aqa Foundation
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  34. Introduction Aqa Foundation
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Exam code:8300

Equivalent ratios

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

    • E.g. 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

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

  • Finding an equivalent ratio is similar to finding equivalent fractions

    • However it is crucial to remember that 1 : 4 is not equivalent to 1 fourth

  • In questions you will be given information that will allow you to find the multiplier

    • The information may be about the one part of the ratio, or it may be about the whole 

    • You can then use this to find the other parts of the equivalent ratio and answer the question

Examiner Tips and Tricks

  • Writing down what you are doing to each part of the ratio helps show your working and makes it easier to keep track of what you are doing.

    • E.g.

table row space A colon B space row space 3 colon 4 space row cell table row cell cross times 5 end cell downwards arrow end table end cell space space space cell table row downwards arrow cell cross times 5 end cell end table end cell row space 15 colon 20 space end table

Worked Example

The ratio of cabbage leaves eaten by two rabbits, Alfred and Bob, is 7 : 5.

(a) Write down an equivalent ratio that would involve a total of 48 cabbage leaves being eaten.

We have information about the whole so first add up the parts of the ratio to find how many parts make the whole

7 + 5 = 12

We require a total of 48 so divide this by 12 to find the multiplier

48 ÷ 12 = 4

Answer the question by multiplying each part of the ratio by this multiplier

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