The Percent The Percent ProportionProportion

Let’s start with what Let’s start with what you know:you know:

What is the definition of a ratio?A ratio is a comparison of 2 or more numbers.

What is a proportion?

A proportion is an equation containing 2 equivalent ratios.

PercentPercent

What is the definition of percent?

Percent is a ratio where the 2nd number is 100. So, a number out of 100 is another way of defining percent.

The Percent ProportionThe Percent Proportion

%

100=

IS

OF

(Part)

Whole

Many percent problems can be solved using this proportion. Let’s look at some examples.

Take a look at the 3 different types of percent proportion problems below:

1.What is 60% of 80?

2.What percent of 75 is 15?

3.12 is 55% of what number?

%/100 = is/of

1. What is 60% of 80?1. What is 60% of 80?

Using the percent proportion, we see in this problem that we know a) the percent and

b) the “of”. We always know that we have the number 100. So, the part we are missing is the “is”.

So: 60 = x Cross multiply to solve.

100 80 100x = 60 • 80 or 4800

Solve for x and you get x = 48.

2. 2. What percent of 75 is What percent of 75 is 15?15?

Set up your proportion for this problem.

What are the 3 parts you know?

So x = 15

100 75

Solve this by cross multiplying.

3. 3. 12 is 55% of what 12 is 55% of what number?number?

What 3 parts do we know?

Set up your proportion and solve by cross-multiplying.

(Round to the nearest 100ths place)

Let’s try some Let’s try some applicationsapplications

Example 1.

Mark sells appliances. He earns 8% commission on sales. If he sells $4000 worth of appliances, how much commission does he make?

Example 2Example 2

Ryan was practicing his free throws. He made 27 out of 40 shots. What was his free throw percentage?

Example 3:Example 3:

The value of gold today is 180% of its value three years ago. If a gold chain was worth $90 three years ago, what is it worth today?

Let’s ReviewLet’s Review

*A percent is a number out of 100.*The percent proportion is the % over 100 set equal to “is” over “of”. (or the part over the whole)

*We will be given 3 of the 4 parts of the proportion to set it up.

*Cross multiply and divide to solve.