*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

subject

Math

learning style

Visual

personality style

Lion, Otter

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

- 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?

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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