Download Ratio and Proportion - George Brown College

Ratio and Proportion
• A ratio is a comparison of one number to another.
The order that the ratio is written in matters.
For example, 1 (apple) to 2 (oranges) is not the same as 2 (apples) to 1 (orange).
Note that a fraction is a specific kind of ratio comparing part to a whole.
• Ratios can be written in three different ways:
With a colon
e.g. 5:3
In words
e.g. 5 to 3
As a fraction
5
e.g.
3
• Ratios should be simplified to lowest terms (Just like fractions).
e.g. 6:3 can be simplified to 3:1 by dividing each number in the ratio by 3.
• A proportion is made up of two equal ratios.
For example, 2:3 = 4:6
• Proportions can be solved using cross multiplication.
Example:
3
7
3
7
45
=
=
𝑥
45
𝑥
3x = 45(7)
x=
45(7)
x=
15(7)
3
[Cross multiply. Remember to keep the equal sign between two sides.]
[Divide both sides by 3 to isolate x.]
[Reduce here if you can. (45 and 3 can both be divided by 3).]
1
x = 105
Tutoring and Learning Centre, George Brown College 2013
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Practice Questions:
1. Solve for x.
a)
b)
c)
d)
e)
f)
𝑥
12
3
𝑥
3
𝑥
=
=
9
11
2
11
1
5
=
2
5
10
a) 2:3 = x:18
60
b) 5:3 = 10:x
c) x:2 = 3:4
30
=
5
=
=
2. Solve for x.
𝑥
9
d) 9:12 = x:3
45
e) 18:x = 30:7
𝑥
𝑥
f) 1:2 = x:9
7
Answers:
1
1
1. a) 2
b) 7 2
c) 2
d) 55
2. a) 12
b) 6
c) 1 2
1
1
d) 2 4
Tutoring and Learning Centre, George Brown College 2013
3
4
e) 1 11
f) 1 5
e) 4 5
f) 4 2
1
1
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