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Ratio
A ratio compares the sizes of parts
or quantities to each other.
What is the ratio of red counters
to blue counters?
red : blue
For every three red counters there is
one blue counter. This means that
the ratio is 3 : 1.
=9:3
=3:1
Is this ratio the same as the ratio of blue counters to
red counters?
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Red to blue ratio
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Ratio
In this example, what is the
ratio of red counters to
blue counters?
For every twelve red counters
there are eight blue counters.
red : blue
Is it possible to simplify
this ratio?
= 12 : 8
÷4
÷4
= 3:2
By finding the highest common factor of these numbers,
we can see that for every three red counters there are
two blue counters.
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Simplifying ratios
Ratios can be simplified like fractions by dividing each part
by the highest common factor.
For example,
÷7
21 : 35
÷7
÷ 16
=3:5
64 : 16
÷ 16
=4:1
For a three-part ratio, all three parts must be divided by the
same number.
For example,
÷3
÷3
=2:4:3
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8 : 24 : 10
6 : 12 : 9
÷2
÷2
= 4 : 12 : 5
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Simplifying two and three part ratios
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Equivalent ratio spider diagrams
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Simplifying ratios with units
When a ratio is expressed in different
units, we must write the ratio in the
same units before simplifying.
For example, simplify the ratio
90¢ : $3.
The first step to take is to write the
ratio using the same units.
Once the units are the same we
don’t need to write them in the ratio.
When the ratio is simplified, add the
units back in.
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90 ¢ : 300 ¢
90 : 300
÷ 30
÷ 30
= 3 : 10
= 3 ¢ : 10 ¢
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Simplifying ratios with units
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Simplifying ratios containing decimals
When a ratio is expressed using decimals we can
simplify it by writing it in whole-number form.
For example, simplify the
ratio 0.8 cm : 2 cm.
We can write this ratio in
whole-number form by
multiplying both parts by 10.
0.8 : 2
× 10
× 10
= 8 : 20
Once the ratio is in whole
number form, apply
simplification if this is possible.
÷4
÷4
=2:5
= 2 cm : 5 cm
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Simplifying ratios containing fractions
We can apply a similar principle when dealing with
ratios involving fractions.
For example, calculate the ratio
in whole number form.
We can write this ratio in
whole-number form by
multiplying both parts by 3.
Use simplification methods
wherever possible to reduce
the ratio to its simplest form.
2
3
m : 4m
2
3
:4
×3
×3
= 2 : 12
÷2
÷2
=1:6
= 1m : 6m
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Comparing ratios
We can compare ratios by writing them in the form 1 : m
or m : 1, where m is any number.
The ratio 5 : 8 can be
written in the form 1 : m by
dividing both parts of the
ratio by 5.
The ratio 5 : 8 can be
written in the form m : 1
by dividing both parts of
the ratio by 8.
5:8
5:8
÷5
÷5
= 1 : 1.6
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÷8
÷8
= 0.625 : 1
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Comparing ratios
The ratio of boys to girls in class 9P is 4 : 5. The ratio of
boys to girls in class 9G is 5 : 7.
Which class has the higher proportion of girls?
The ratio of boys to girls in 9P is:
4:5
÷4
÷4
= 1 : 1.25
The ratio of boys to girls in 9G is:
5:7
÷5
÷5
= 1 : 1.4
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