VUB Mini Notes
Percent Notes
Name_____________________
Page one
The word percent means per one hundred. We use the % sign to indicate percent.
You need to be comfortable switching from percent, to decimal, to a reduced fraction.
Likewise you need to be comfortable switching from a decimal, to reduced fraction, to
a percent.
To change a % to a decimal, do the following.
 Move the decimal point two places to the left.
 Then drop the % sign.
To change a % to a fraction, do the following.
 Put the number over 100 and reduce each fraction if possible.
 Always drop the % sign.
To change a decimal to a percent, do the following.
 Move the decimal point two places to the right.
 Always add the % sign.
To change a fraction to a percent, do the following.
 Divide the denominator into the numerator.
 Add a decimal.
 Add two or more zeros to change the fraction to a decimal.
 To change the decimal to a percent, move the decimal point two places to the right
and add the % sign.
For the following problems we started with a percent. Next step was to change the percent to
a decimal and then write a fraction with a denominator of 100 and last step is write a reduced
fraction if possible.
75%  .75 
75
3

100 4
106%  1.06 
106 53

100 50
1
125
1
12 %  12.5%  .125 

2
1000 8
VUB Mini Notes
Percent Notes
Name_____________________
Page two
There are some key words you should know when working with percent.
The word “of” means multiplication and the word “is” means equal.
Ratio
 A ratio is a comparison of two things.
Proportions
 A proportion is two ratios set equal to each other.
 Cross multiply and solve for the given variable.
 When you cross multiply, rewrite the problem and draw an x,
then follow the straight lines to write the equation.
Variables
 Variables are letters that represent different values depending on the problem.
Various letters are used in the problems. Please make sure you are using the same
variable as is used in the problem.
Now let’s look at the example below.
What is 8% of 20?
is
%

of
100
In the proportion above, we do not know the number in the “is” position.
So write a variable there, such as x.
We do know the number in the “of” position is 20 and we know the percent is 8.
Now fill this information into the proportion above.
x
8

20
100
Cross multiply and we get
So we write
100x  8  20
100x  160
100
160
x 
100
100
x  1 .6
VUB Mini Notes
Percent Notes
Name_____________________
Page three
The second method to solve this problem is to use the key words of and is.
Again the word “of” means multiplication and the word “is” means equal.
What is 8% of 20?
x  .0820
x  1.6
What is 34% of 50?
Fill in the information from the problem in the following formula for the first method.
is
%

of
100
x
34

50
100
Cross multiply and we get the following.
100x  34  50
100x  1700
100
1700
x 
100
100
x  17
The second method to solve this problem is to use the key words of and is.
Again the word “of” means multiplication and the word “is” means equal.
What is 34% of 50?
x  .3450
x  17
VUB Mini Notes
Percent Notes
Name_____________________
Page four
What percent of 40 is 32?
Fill in the information from the problem in the following formula.
is
%

of
100
32
p

40
100
40p  32  100
40p  3200
40
3200
p 
40
40
p  80
So the answer is 80%.
Since we are solving for p this is the answer written as a percent.
What percent of 40 is 32?
32  d40
32
40
 d
40
40
.8  d or
d  .8 the decimal value
or
80% as a percent
Try the following.
What is 52% of 80?
What percent of 125 is 25?