Solving a Proportion Problem
A Ratio and a Proportion
Ratio: The relationship in quantity, amount, or size
between two or more things. Typically expressed
as a quotient of two mathematical expressions (i.e.
A FRACTION). For example:
a
b
Proportion: An equation that equates two ratios (i.e. TWO
EQUAL FRACTIONS). For example:
a
b

c
d
Proportional
Two variables or quantities are proportional if a
change in one is always accompanied by a change
in the other. These variables/quantities always
have a constant ratio (scale factor).
Example- If y is proportional to x and k is the
constant ratio (scale factor), then the
following holds:
𝑦 = 𝑘𝑥
Note: If y = 0, then x = 0. Thus, all proportional
relations must contain the point (0,0).
Example
Is the relation below proportional?
x
y
2
3
4
10
8
12
9
15
No. There is not a constant ratio between the
quantities:
2
4
≠ .
3
10
Every relation is not proportional.
Using a Table to solve a Proportion
Question
Toby uses seven tubes of toothpaste every
ten months. How many tubes would he
use in 5 years?
5 years = 5x12 = 60 months
x6
Months
Tubes
10
7
60
?
42
42 Tubes
x6
Using an Equation to solve a Proportion
Question
Toby uses seven tubes of toothpaste every
ten months. How long would it take him to
use 100 tubes?
Tubes
Months
7 100

10
x
10 100 7
142.86 Months
You learned
this method
in middle
school. Can
you
prove/justify
that it
works?
Using a Diagram to solve a Proportion
Question
One more way to organize your work for 2-99
15
7.83 = x
÷ 1.8
x 1.8
6
0
y = 27
20
14.1
10.8
x 1.8
36