Introduction to Ratios
One way to express a rate is as a ratio. It is a way of comparing quantities. It is very similar to a fraction.
Example What is the ratio of students in this class who typically ride the bus compared to those that do
not?
In another grade 9 class, the ratio of riding the bus to not riding the bus is 16:13.
How many students ride the bus? How many students do not?
How many students are there?
What percentage of the class ride the bus?
Equivalent ratios represent the same proportion. We write equivalent ratios by multiplying or dividing both
terms in the ratio by the same number.
Write equivalent ratios for:
11:12
14:10
Examine the diagram below.
What is the ratio of cats to dogs?
Suppose the dogs and cats got into a fight. How many cats would each dog have to fight?
We can often solve for an unknown value in 2 equivalent ratios. There are a few methods for finding this
unknown value.
a)
2 : 5  10 : x
b) 4: 8 = x : 20
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c) 5 : 60 = 35 : x
We can use ratios to solve many problems. Note that many of these problems could be solved using unit
rates as well.
Example 1
The instructions on an outboard motor are to mix gas and engine oil in a ratio of 20:1. How many mL of
engine oil must be added to 5 L of gas? (There are ______________mL in 1L.)
Example 2
A wheelchair ramp should have a ratio of height to length (often called rise to run) of 1 : 12. If a wheelchair
ramp needs to be 4 feet high, how long should it be?
Example 3
In 2002, the ratio of male to female doctors in Canada was 7 : 3 . If there were 72 female doctors in a city
at that time, how many male doctors were there?
Example 4
A recipe with 3 eggs with feed 5 people. How many eggs would be required to make a recipe that feeds 20
people?
Example 5
Suppose Mary earns $75 working for 5 hours. How much would she earn in a 40 hour week?
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