Percent of a Number
When asked to find a certain percent of a number, you must first change
the percent to a decimal or fraction, and then MULTIPLY that by the
number.
25% of 12
= .25 X 12
(decimal)
OR
= ¼ X 12
(fraction)
=3
So the word “of” can be translated to “multiplied by”
Example 1
Find 40% of 45.
This can be also stated, “What is 40% of 45?
= .40 X 45
You try: Find 20% of 75
Find 135% of 24
What is 135% of 24?
Remember 135% is a number bigger than 1, since it is bigger than 100%
Convert to decimal: 135% = 1.35
135% of 24
=1.35X 24
=32.4
You try this: Find 130% of 10.
6.5 Solving Percent Problems
Example: “10 is 50% of 20”
amount
Amount
(Part)
%
“=“
%
Base
(Percent) (Whole)
base
“times“
Amount = % · Base
Base = Amount/ %
% = Amount/Base
** Note: Must change % to decimal before multiplying. Drop the
% sign and move the decimal point two places to the LEFT. If
there is no decimal place, just start at the % sign.
10 is 50% of 20
10 = 50% · 20
10 = .50 · 20
10 = 10
What good is it to show 10=10? I already know that!
How about this question:
What number is 160% of 15.8?
amount
%
base
Usually, the number before the word, “is” is the amount
and the number after the word “of” is the base.
In this case we are asking for the amount.
Amount = 160% · 15.8 = 1.60 · 15.8 = 25.28
Why is the “Amount” bigger than the base?
14 is what percent of 32?
amount
%
base
Amount
Percent =
Base
amount
%
base
This equation gives you the percent as a decimal value,
though, so you must then convert it to a percent by moving
the decimal place to the RIGHT two places and then putting
a % sign at the end.
14
Percent =
= 0.4375 = 43.75%
32
amount
Amount
Base =
Percent
%
base
31.5 is 33⅓ % of what number?
amount
%
base
How do you write 33⅓ as a decimal? We can’t write it as . 33⅓
This is a special percent. To convert it we first have to change it to a fraction with
denominator 100.
1 33 ⋅ 3 + 1 100
1
100 1
1
3
33 % = 3 =
= 3 =
⋅
= = .3
3
100
100
100
3 100 3
33
If you get a repeating decimal when converting a decimal, it’s better to leave it as
a fraction, so change 33⅓ % to 1/3.
Amount 31.5
3
Base =
=
= 31.5 × = 94.5
1
Percent
1
3
Circle Graphs (or Pie Charts)
A circle graph (aka Pie Chart) is a specialized graph used in statistics
in which the relative proportions of parts of a whole (usually given as
percentages) are shown as different size wedges of a pie. All the
wedges of the pie add up to 100%.
2004 Presidential Election
John Kerry
38%
Preident Bush
62%
According to the pie chart above, find the number of states won by
George W. Bush in the 2004 Presidential Elections.
What are we being asked to find?
Given: Percentage of votes of each candidate.
What is the base?
What is the amount?
You do this:
What % of e-mail
messages are Spam?
Types of E-mail Messages
Other
4%
Work or School
5%
Request ecommerce
16%
Family and
Friends
31%
Spam
?