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 decimal2. "is" to "="3. "of" to " "4. Unknown to "x"

Then, solve the equation.

Finding the Part...

60 = 24.40

Examples:Find

40% of 60

20% of 90

.20 90 = 18

Write a mathematical sentence

Write a mathematical sentence

Click

Click

X = .10 88

What is 10% of 88?

Write a mathematical sentence

X = 8.8

Try these:

Find 12% of 70 What is 40% of 28?

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

Steps1. Set up the proportion as shown.

2. Substitute given values into the proportion.

3. Solve the proportion.

is

of

%

100=

Note: You can use this box to solve many problems involving percents!

Note: Try to find the numbers that are attached to the words/symbols: is, of, or percent.

Example: What is 25% of 400?

Steps1. Set up the proportion.

2. Substitute.

3. Solve.

is

of

%

100=

What is 25% of 400?

25

100400

?

Click on each box to see if you substituted correctly.

400 x 25 = 100w10,000 = 100w10,000/100 = w100 = w Click

Example: What is 32% of 300?

Steps1. Set up the proportion.

2. Substitute.

3. Solve.

is

of

%

100=

32

100300

?

Click on each box to see if you substituted correctly.

300 x 32 = 100w9,600 = 100w9600/100 = w96 = w

What is 32% of 300?

Click

Try it: What is 20% of 180?

Steps1. Set up the proportion.

2. Substitute.

3. Solve.

is

of

%

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 equation2. Setting up a proportion

40% of what number is 50?

.40 X = 50

X = 50 .40

X = 125

Try This:

100 is 20% of what number?

100 = .20 x

100 = x .20

x = 500

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...

What percent of 80 is 24?

x 80 = 24

X = 24 80

X = .30

X = 30%

Remember, you can solve this by:1. Translating into an equation2. Setting up a proportion

60 is what percent of 15?

60 = X 15

60 = X15

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?