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!

categories

Middle School

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

Lesson Plan - Get It!

Audio:

The number 123 is what percentage of 456? Whoa!

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? Discuss with a parent or teacher other locations in the real world where you can find 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:

 

  • 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:

 

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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