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Ratios & Proportions
Text 4.2
• Ratio – is a comparison of two numbers
• Ratios can be written 3 ways:
– 3 to 2
– 3:2
– 3
2
• Proportion – a statement that says two
ratios are equal.
Example Question 1
• Sam wants to paint a small picket fence
in his back yard.
• He has 2 different colours of paint, red
and yellow.
• He wants to do a pattern of three red
pickets and then two yellow pickets per
panel.
• Like this:
Fill in the missing pieces into your table
Add another column to the table:
Ratio
red to yellow
Add another column to the table:
Ratio:
red to yellow
6
4
10
9
6
15
12
8
20
What would the ratio be in five panels? Six?
Ratio:
red to yellow
5
6
6
4
10
9
6
15
12
8
20
Add this information to your table
Compare the ratios from the table to
the first ratio. What can you conclude?
Write the conclusion down.
Suppose you had 24 red pickets.
a) By what number are you multiplying the
original number of red pickets?
b) How many yellow pickets do you have?
Let’s form a proportion, can you find the
fourth number?
3
2

27
?
18
This is called a “between”
relationship because we can find
the relationship between ratios.
?
3 12

4 16
Find the unknown:
(across the equal sign)
6 48

2 16
?
Find the unknown:
(across the equal sign)
2 6

5 15
?
Between, find the unknown
(across the equal sign)
?
40:60
= 2:3
Between, find the unknown
(across the equal sign)
4:5:3 = ?8:10:6
This is called a “within” relationship,
because we need to find the
relationship within the ratio.
?
6 15

2 5
Within, find the unknown:
?
6 10

3 5
Within, find the unknown
?
2:16
= 5:40
Within, find the unknown
1? 2.5

2 5
Within, find the unknown
1:5 =
?
1.5:
7.5
Example #2
Jasmine has a recipe for fruit punch that
requires 1 cup of grape juice to be
mixed with 3 cup of cranberry juice.
How many cups of grape juice does
jasmine need for 12 cups of cranberry
juice?
How many cups of grape juice does
jasmine need for 12 cups of cranberry
juice?
Let’s make a ratio:
1 cup grape juice : 3 cups cranberry juice.
Or 1:3
How many cups of grape juice does
jasmine need for 12 cups of cranberry
juice?
1 4?

3 12
Suppose Jasmine wants to make 60 cups
of punch for the party. How many cups
of juice of each type will she need?
Let’s look at the ratio of grape juice and
total cups of juice.
?
1 15

4 60
Please work on pg 165-166
# 1-5
a)
1:2
b)
3:5
c)
5:2
d)
3:1
e)
2:3
f)
5:5 or 1:1
8
4
or
38 19
13
38
17
38
21
38
6:8 or 3:4
8:4 or 2:1
4:6 or 2:3
40
2
1
0
16
1.5
6
1.6
7.5
20.25
5
6
36
9
1
7