Algebra2go®
Proportions
Objective 1
Solve Proportion Problems
A proportion is an equation with two ratios!
x =2
The equation 4 3 represents a proportion and
it can be solved using a technique call crossmultiplying. It can also be solved by first
using an LCD to clear the fractions.
Sometimes it may be easier to clear the
fractions, but most students tend to like to
cross-multiply.
Here we will solve the proportion problem
using the cross-multiplication technique.
x =2
4 3
x =2
4 3
3x = 8
x = 83 or 2 2
3
Page 1 of 4
Algebra2go®
Now we will solve the proportion problem
using the clearing fraction or “Kung Fu”
fraction technique.
x =2
LCD=12
12 (
4
)
3
( )
x =
2
12
3
4
3x = 8
x = 83 or 2 2
3
Remember that you can only cross-multiply
across an equals (=) sign and you should
only do this when you have a proportion. Do
not attempt to cross-multiply on the equation
below. It is not a proportion. Use the clearing
fractions technique in this case.
Page 2 of 4
x=3 + 1
2 4 5
19
x= 10
LCD=20
Algebra2go®
Example 1: Solve the proportion.
1
2
x
4
=
2
3
In this problem we will cross-multiply twice
to reach the solution.
1
2
x
4
=
1⋅2 =
2 3
Remember, this is called
“cross-cancelling” and can
only be performed across a
multiplication operation!
1
1⋅2 =
21 3
2
3
Remember, we can only
perform “cross-multiplication”
across an equals sign!
4⋅ x
4⋅ x
4
1 = x
3
1 = 4x
3
1
Here we rewrite 4x as a
fraction by placing it
over 1. This way we can
again cross-multiply.
1 = 12x
12 12
1 = x or x = 1
12
12
Page 3 of 4
Algebra2go®
Example 2: Solve each proportion problem.
x =5
a) 4
8
2 =4
b) 5
x
25 = x
c) 100
4
Answer the following homework questions.
In Exercises 1 - 9, solve each proportion problem. Try not to use a
calculator.
4
1) x = 29
2) 3x = 10
11
1
3) 0.5
1.2 = x
Page 4 of 4
x = 0.15
4) 1.4
3
x = 0.5
5) 0.3
2.5
x = 0.05
6) 12
0.12
7)
6
5
1 = 2
2
3
x
2
8) 3 = 8
x 1
2
9)
1
1
2 = 3
x 14