gcse mathematics ratio & proportion. aims to simplify ratios to write ratios in unitary form to...
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GCSE Mathematics
Ratio & Proportion
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Aims
• To simplify ratios• To write ratios in unitary form• To compare ratios and fractions
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What is a Ratio
• What is a ratio?
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Notation
This is read as 2 to 3.It means that for every 2 units of the first quantity there are 3 units of the second.
2 : 3
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Maps
• For example scales on a map 1:2000
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Scale Models
Scale models 1:25
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Recipes
If you had a recipe that used 100g of margarine to 250g of flour, the ratio of margarine to flour is 100 : 250.
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Ratios
There are a few ways of expressing ratios.
Simplest Form
Unitary Form
Equivalent Form
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Simplest Form
• If a ratio is in its simplest form the numbers do not share a common factor.
• The numbers are whole numbers. • Simplifying ratios is similar to
simplifying fractions.
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Question
• Write down the ratio 100 : 250 in its simplest form.
:2 5
:100 250÷ 50 ÷ 50
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Question
• Write down a ratio that is equivalent to
2 : 5
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Question
• Write down the ratio 2 : ½ in its simplest form.
:2x 2 2 x ½
:2 ½ x2 x2
:4 1
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Question
• Write down the ratio 1.1 : 0.2 in its simplest form.
:1.1 x 10 0.2 x 10
:1.1 0.2x10 x10
:11 2
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Unitary Form
Ratios expressed in unitary form are either of the form
1 : nOr
n : 1In these cases n may be a fraction or a decimal
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Unitary Form
Write the ratio 6 : 10 in the form 1 : n
:6 ÷ 6 10 ÷ 6
:6 10÷ 6 ÷ 6
:1
This side needs to be 1
61 .
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Unitary Form
Write the ratio 6 : 10 in the form n : 1
:6 ÷ 10 10 ÷ 10
:6 10÷ 10 ÷ 10
:0.6 1
This side needs to be 1
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Question
• Write the ratio 40 : 10 1. In its simplest form
2. In the form 1 : n
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Solutions
Write the ratio 40 : 10 In its simplest form
4 : 1
In the form 1 : n 1 : 0.25
Divide both sides by 10
Divide both sides by 40