Puzzling Percentages

Lesson Plan - Get It!

Audio:

• How often do you see a percent sign?

They are all around us in everyday life, from percentages off at the department store to grades in your classes, and so many other places.

• Can you think of anywhere else you see percentages?

Percentage problems often read like these:

• What percent of 30 is 10?
• 20 is 15% of what number?
• What number is 12% of 60?

As you can see, there are three different things you can solve for in a percentage problem. You are either looking for the percentage, a part of a number, or the entire number.

To find any one of these, there is some secret decoding you need to know how to do.

Now, there are two ways you can solve percent problems.

• The first is using the information above to "decode" the problem and write it with multiplication and an equal sign.

Here is an example:

• What percent of 30 is 10?

n x 30 = 10

n x ³⁰/₃₀ = ¹⁰/₁₀

n = .33

10 is 33% of 30

Please watch this Percentage word problem video by Math Meeting to see another example solving percentages:

Another method for solving percentage problems is to set up a proportion as follows:

NOTE: The denominator will always be 100 because percent means "per hundred" (as in literally 100).

Here is an example using the proportion method:

• 9 is 15% of what number?

For this method, you first have to decide if 9 should stand for the "part" of a number or the "whole" thing.

In this case, 9 is only 15% of a larger number, so the 9 is just PART of the whole entire number. Therefore, it can be placed into the proportion for the "Part."

⁹/_x = ¹⁵/₁₀₀ ← x was filled in for the whole number because that is what you don't know.

To solve, you will cross multiply. In other words, 9 • (times) 100 = x • (times) 15.

9(100) = 15x ← Multiply the 9 and the 100 to get 900. Then write the equal sign. Finally, multiply the x times the 15 to get 15x.

⁹⁰⁰/₁₅ = ^15x/₁₅ ← Divide both sides by 15 to solve for x.

60 = x ← This means that 9 is 15% of the number 60.

Watch this Video 1-Percent Proportion Problems: Review of 7th Grade Skills video by Morgan Lemmon to see a few percentage problems solved using proportions:

Once you have completed the videos showing each method of solving percent problems, you may go to the Got It? section for some practice.