Puzzling Percentages

Contributor: Briana Pincherri. Lesson ID: 11411

What percentage of math problems and everyday situations require figuring out a percentage? You will encounter them, and you will solve 100% of them after working through this lesson and its videos!


Ratios, Rates, Percentages, and Proportions

learning style
personality style
Lion, Otter
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

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  • The number 123 is what percentage of 456?


  • 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.

Word You See: Math Symbol It Typically Means to Use:
of x (multiply)
is = (equal)


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:

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

Part (Is) = % Number
Whole (Of)   100


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:

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

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