Transcript GCSE Mathematics - Rawlins Academy VLE

GCSE Mathematics
Ratio & Proportion
Aims
• To simplify ratios
• To write ratios in unitary form
• To compare ratios and fractions
What is a Ratio
• What is a ratio?
Notation
2:3
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.
Maps
• For example scales on a map
1:2000
Scale Models
Scale models 1:25
Recipes
If you had a
recipe that used
100g of margarine
to 250g of flour,
the ratio of
margarine to flour
is 100 : 250.
Ratios
There are a few ways of expressing
ratios.
Simplest
Form
Unitary
Form
Equivalent
Form
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.
Question
• Write down the ratio 100 : 250 in its
simplest form.
÷ 50
100
:
250
2
:
5
÷ 50
Question
• Write down a ratio that is equivalent to
2:5
Question
• Write down the ratio 2 : ½ in its
simplest form.
x2
2
:
½
2x 2
:
:
2x½
4
1
x2
Question
• Write down the ratio 1.1 : 0.2 in its
simplest form.
x10
1.1
:
1.1 x 10
:
:
11
0.2
0.2 x 10
2
x10
Unitary Form
Ratios expressed in unitary form are
either of the form
1:n
Or
n:1
In these cases n may be a fraction or a
decimal
Unitary Form
Write the ratio 6 : 10 in the form 1 : n
This side needs
to be 1
÷6
6
:
10
6÷6
:
:
10 ÷ 6
1
1.6
÷6
Unitary Form
Write the ratio 6 : 10 in the form n : 1
This side needs
to be 1
÷ 10
6
:
10
6 ÷ 10
:
:
10 ÷ 10
0.6
1
÷ 10
Question
• Write the ratio 40 : 10
1. In its simplest form
2. In the form 1 : n
Solutions
Write the ratio 40 : 10
In its simplest form
4:1
Divide both
sides by 10
In the form 1 : n
Divide both
sides by 40
1 : 0.25