Download ratio and proportion

WJEC MATHEMATICS
INTERMEDIATE
NUMBER
RATIO AND PROPORTION
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Contents
Simplifying Ratio
Simplifying Scale Ratio
Sharing in a given Ratio
Reverse Ratio
Recipes
Proportion
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
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Understanding Ratio
Ratio shows the proportion between two things. It is represented by
two numbers separated by :
2: 3
The above ratio shows that for every 2 of object A there is three of
object B
Simplifying Ratio
Simplifying Ratio is extremely similar to simplifying fractions. Make
sure you understand that process in the 'Equivalent Fractions'
booklet.
Consider the following ratio
24: 36
To simplify this ratio, we need to understand what we can divide 24
and 36 by. They are both even so we can divide them both by 2.
12: 18
Again, these are both even numbers. So divide them both by 2.
6: 9
This time, we cannot divide both numbers by 2. However, both
numbers are in the 3 times table so divide them both by 3.
2: 3
This is now fully simplified.
Exercise N25
Simplify the following ratios
a. 20:35
d. 80:100
b. 20:24
e. 64:56
c. 36:40
f. 49:56
g. 81:63
h. 99:66
i. 12:17
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Simplifying Scale Ratio
You may be required to simplify a ratio that involve different units
Before simplifying make sure both
sides are in the SAME UNITS
Example 1
Simplify the following
500𝑔: 3𝑘𝑔
The first step is to get the units the same. To answer these questions
you will need to know your units and conversions. You can find these
in the booklet 'Metric and Imperial Units & Conversions'
500: 3000
There is now no need to write the units as the units are the same.
Divide both numbers by 100:
5: 30
Divide both numbers by 5
1: 6
Example 2
Simplify
30 𝑠𝑒𝑐𝑠 ∶ 3 𝑚𝑖𝑛𝑠
Putting them both into seconds
30: 180
3: 18
1: 6
Exercise N26
a. 5kg:500g
c. 2mins:40secs
b. 5m:150cm
d. 3litres:600ml
e. 5km:900m
f. 8kg:1.6kg
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Sharing in a given ratio
Very commonly, you are given an amount and instructed to share it
in a given ratio.
Example
Share £49 in the ratio 5:2
Total amount
to share out
£7
The PURSES
Method
This means we will give 5
purses to one person and 2
purses to another
£7
£7
£7
£7
£7
£7
We have 7 purses and £49 to share equally between them so we
need to put £7 in each one
So we now know how much each person gets by adding the
amounts on each side
£35: £14
After completing a few of these questions you won't need to draw
purses. The next page shows the same question with the workings
shown that you would need to show in an exam.
5
Share £49 in the ratio 5:2
5+2=7 (Total purses)
49 ÷ 7 = £7 (Each Purse)
£7 × 5: £7 × 2
£35 : £14
Exercise N27
1. Share £63 in the ratio 7:2
2. Share £56 in the ratio 4:3
3. Share £80 in the ratio 3:1
4. Share £135 in the ratio 3:2
5. Share £147 in the ratio 4:2:1
6. Share £520 in the ratio 5:2:1
7. Share £445 in the ratio 5:3:2
Reverse Ratio
For some questions, you won't be given the total, but the value of a
proportion from the ratio.
When an amount is shared in the ratio 2:3 the largest share is £24.
How much was shared in total?
Consider the purses for this question
£8
£8
£8
£8
£8
These three purses must add
to £24
Total amount shared = £8 + £8 + £8 + £8 +£8 = 40
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Exam Questions N13
1.
2.
3.
4.
5.
6.
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Recipes
You may be given the recipe for making food for a number of people
and use proportion to increase the ingredients for more people.
Example
The ingredients for 12 cakes are as follows:
300g flour
180g butter
150g sugar
2 eggs
How much is needed of each of the above ingredients for 30 cakes.
There's nothing we can multiply 12 by to get 30, so we need to work
out the amount of ingredients needed for a smaller amount first.
Working out the ingredients for 6 works because it's easy to get from
12 to 6 (÷ 2) and easy to get from 6 to 30 (×5)
6 cakes
150g flour
90g butter
75g sugar
1 egg
30 cakes
750g flour
450g butter
375 sugar
5 eggs
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Exam Questions N14
1.
2.
9
3.
4.
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Proportion
Here's an example question
It takes 3 men 6 days to dig 4 gardens. How long will it take 24 men
to dig 12 gardens?
Begin by putting the information in a table. This makes it easier to
see.
Men
Time (Days)
Gardens
3
6
4
24
?
12
If the same three men dig twelve gardens, it will take 3 times as long.
So if the amount of men did not change we can fill in the middle row
of the table
Men
Time (Days)
Gardens
3
6
4
3
18
12
24
?
12
This time we will keep the number of gardens the same, but we have
24 men working (This is 8 times as many). So they should be able to
complete the job 8 times as fast. To calculate the number of days,
we divide 18 by 8.
Men
3
3
24
Time (Days)
6
18
2.25
Gardens
4
12
12
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Exercise N28
1. It takes 6 workers 2 days to build 4 cars. How many days does it
take 4 workers to build 8 cars?
2. It takes 4 men 12 days to dig 1 hole. How many days will it take 6
men to dig 3 holes?
3. It takes 15 Robots 6 days working 5 hours a day to complete a
job. How many days will it take 25 robots, working 6 hours a day, to
complete the same job?
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