Three Types of Percent
Problems
Day 2
Remember, percents are "parts of a whole".
The part is the numerator and the whole is the
denominator.
17% means 17 parts per 100 or
We are going to solve problems involving percents.
There are 3 types of problems:
1. Find the part What number is 54% of 34?
2. Find the whole 4 is 60% of what number?
3. Find the percent 18 is what percent of 28?
Two words that will occur in these types of problems
are "is" and "of".
These words have specific meanings in math.
"Is" means equals (=)
"Of" means multiply
To solve a percent problem, translate the words into an
equation.
Change the following:
1. Percent into a decimal
2. "is" to "="
3. "of" to " "
4. Unknown to "x"
Then, solve the equation.
Finding the Part...
Examples:
Find
Change the percent to a decimal and
multiply.
40% of 60
.40
60 = 24
Click
20% of 90
.20
90 =Click
18
Another Method:
You can also solve percent problems by setting up a
proportion.
Since percents are parts of a whole, you can create the
following proportion:
When figuring out which is the "part" and which is the
"whole", remember that you take a percent of the whole
and the answer is the part. In other words, the whole is
with the word "of" and the part is with the word "is".
Proportion Method
Steps
1. Set up the proportion as shown. is
of
=
%
100
Note: You can use this box to solve many problems
involving percents!
2. Substitute given values into the proportion.
Note: Try to find the numbers that are attached to the
words/symbols: is, of, or percent.
3. Solve the proportion.
Example: What is 25% of 400?
is
Steps
1. Set up the proportion.
of
2. Substitute.
What is 25% of 400?
3. Solve.
400 x 25 = 100w
10,000 = 100w
10,000/100 = w
100 = w
Click
?
400
=
25
%
100
100
Click on each box to see if
you substituted correctly.
Example: What is 32% of 300?
Steps
1. Set up the proportion.
is
?
of
300
=
32
%
100
100
Click on each box to see if
you substituted correctly.
2. Substitute.
What is 32% of 300?
300 x 32 = 9600
3. Solve. 9,600 ÷ 100 = 96
is
of
=
Click
%
100
Try it: What is 20% of 180?
is
Steps
1. Set up the proportion.
of
2. Substitute.
3. Solve.
=
%
100
12 Find 30% of 45
14 Find the greater value.
A
20% of 16
B
10% of 90
C
25% of 40
D
100% of 7
15 Find the greater value.
A
2% of 1000
B
5% of 500
C
10% of 300
D
15% of 100
16 Identify any values that are equal.
A
What is 40% of 80?
B
60% of 70
C
25% of 128
D
200% of 16
Finding the Whole...
Remember, you can solve this by:
1. Translating into an equation
2. Setting up a proportion
40% of what number is 50?
.40
X = 50
X = 50
.40
50 x 100 = 5000
5000 ÷ 40 = 125
X = 125
is
50
of
?
=
40
%
100
100
Try This:
100 is 20% of what number?
100 = .20
100 = x
.20
x = 500
x
17 56 is 70% of what?
18 12% of what number is 6?
19 65% of what number is 10?
20 27 is 150% of what number?
21 1% of what number is 12?
Finding the Percent...
Remember, you can solve this by:
1. Translating into an equation
2. Setting up a proportion
What percent of 80 is 24?
x 80 = 24
X = 24
80
X = .30
X = 30%
60 is what percent of 15?
60 = X 15
60 = X
15
4=X
400% = X
22 What percent of 3 is 12?
23 30 is what percent of 36?
25 2 is what percent of 1?
You have just studied three different types of percent
problems.
Try all 3 types:
24 is 40% of what number?
42 is what percent of 840?
What is 30% of 45?
27 Find the largest value.
A
What is 50% of 50?
B
What number is 45% of 60?
C
30 is 60% of what number?
D
25% of what number is 150?
28 Find the greatest percentage value.
A
What percent of 30 is 18?
B
60 is what percent of 90?
C
What percent of 70 is 210?
D
1,000 is what percent of 100?
30 8 is what percent of 28?
32 Find 27% of 54.
33 23 is what percent of 200?
34 What percent is 35 of 20?