3.2.7

Two Ratios

Test yourself

Dealing With More Than One Ratio

You can scale up ratios by multiplying or dividing each part by the same number.

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Example

  • On a farm, the ratio of cows to sheep is 6 : 5. The ratio of sheep to pigs is 2 : 1. The total number of cows, sheep and pigs on the farm is 189. How many sheep are there on the farm?
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Example

  • Scale up the first ratio by 2 and the second ratio by 5 to get:
    • cows : sheep = 12 : 10, sheep : pigs = 10 : 5
    • So cows : sheep : pigs = 12 : 10 : 5.
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Example

  • Add up the number of parts and divide the total quantity by this number to get the value for each part:
    • Number of parts = 12 + 10 + 5 = 27
    • Value per part = 189 ÷ 27 = 7
    • Sheep is 10 parts so total number of sheep is 7 × 10 = 70.

Ratios

A ratio a : b means that for each 'a' of one thing there are 'b' of another. For example, if the ratio of boys to girls in a class is 3 : 4 that means that for every 3 boys there are 4 girls.

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Reducing a ratio

  • To reduce a ratio to a simpler form divide all parts by the same number.
  • It is in its simplest form if all parts are whole numbers and there are no more common factors left to divide by.
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Fractions and decimals

  • If a ratio contains decimals or fractions, multiply to get rid of them before simplifying the ratio.
  • If a ratio has mixed units convert both to the smaller unit and simplify.
  • Then remove the units from the ratio.
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Mixed unit ratios

  • If a ratio has mixed units convert both to the smaller unit and simplify.
  • Once both are using the same unit you can remove the units from the ratio.
    • 4.6kg : 2300g is the same as 4600g : 2300g
    • We can remove the unit and simplify to get 2:1
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Ratios as Linear Functions

  • See above for how you can convert from a ratio it a linear function.

Jump to other topics

1Number

1.1Using Numbers

1.2Fractions, Decimals & Percentages

1.3Powers & Roots

1.4Accuracy

2Algebra

2.1Introduction to Algebra

2.2Manipulating Algebra

2.3Proofs & Functions

2.4Straight Line Graphs

2.5Common Graphs

2.6Transformations & Tangents

2.7Properties of Graphs

2.8Solving Equations

2.9Inequalities

2.10Sequences

3Ratio

4Geometry

4.1Introduction to Geometry

4.2Triangles & Quadrilaterals

4.3Transformations

4.4Circle Basics

4.5Circle Theorems

4.6Measurements & Units

4.7Calculating Area

4.8Triangle Formulae

4.93D Shapes

4.10Vectors

5Probability

6Statistics

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