MATHS-0580
AUTUMN
ADEYEMO
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AUTUMN 2024/2025 SESSION
Objectives
At the end of the lesson, learners will be able to:
Demonstrate an understanding
of ratio
Divide a quantity in a given ratio
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AUTUMN 2024/2025 SESSION
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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AUTUMN 2024/2025 SESSION
Ratio
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AUTUMN 2024/2025 SESSION
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
AUTUMN 2024/2025 SESSION
Simplifying two and three part ratios
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AUTUMN 2024/2025 SESSION
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
AUTUMN 2024/2025 SESSION
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
4:5
÷4
= 1 : 1.25
The ratio of boys to girls in 9G is:
÷5
5:7
÷5
= 1 : 1.4
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AUTUMN 2024/2025 SESSION
Finding the missing number in a ratio
The ratio of boys to girls in year 10
of a particular school is 6 : 7.
If there are 72 boys in the year,
how many girls are there?
We can work this out by finding the
missing number from the ratio.
6:7
× 12
× 12
72 : ?
To do this divide 72 by 6. This tells us that the number of
boys in the year has increased by a factor of 12.
The number of girls will have increased by the same amount.
From this we know there are 7 × 12 = 84 girls in the year.
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AUTUMN 2024/2025 SESSION
Finding the missing number in a ratio
In the new image, the ratio of the height to the width must
remain the same.
Can you find a ratio that is equivalent to 3 : 5, but
with the second part equal to 37.5?
height : width
× 7.5
3:5
× 7.5
? : 37.5
The height of the new
photo is: 3 × 7.5 = 22.5.
If the enlarged photo is 37.5 cm wide, the height is 22.5 cm.
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AUTUMN 2024/2025 SESSION
Dividing in a given ratio
A ratio is made up of parts. The ratio 2 : 3 can also be written
as 2 parts : 3 parts. This gives a total of: 2 + 3 = 5 parts.
How would you divide £40 in the ratio 2 : 3?
Divide £40 by the total number of
parts: £40 ÷ 5 = £8.
2 parts = 2 × 8 = £16.
3 parts = 3 × 8 = £24.
The money would be split £16 : £24.
How can you check if your answer is accurate?
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AUTUMN 2024/2025 SESSION
Dividing in a given ratio
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AUTUMN 2024/2025 SESSION