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GED Math: Quantitative, Arithmetic & Algebraic Problem Solving10 chapters | 73 lessons | 7 flashcard sets

Instructor:
*Betsy Chesnutt*

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Understanding percents can help you quickly determine how much things cost and many other things. In this lesson, you will learn what percents are and how to use the percent formula.

I went to the store yesterday and saw a shirt I really liked. The tag said it cost $37.99, but it was currently on sale for 30% off. I only had $30 with me. Was that enough to purchase the shirt or not? What exactly does a percent represent and how can we use it to calculate the cost of my new shirt?

The word **percent** comes from the Latin words *per centum* which means *by the hundred*, so a percent tells you how many parts you have out of 100 total. For example, if you had a bag full of 100 different colored marbles and I told you that 25% of the marbles in the bag were red, then you would know that exactly 25 of the marbles were red. Similarly, if my shirt cost exactly $100, I would know that 30% of $100 was $30, so the shirt would cost $70 ($100-$30 = $70).

Percents can also be written as fractions or decimals. To convert a percent to a fraction, simply divide it by 100. That means that 30% could be written as 30/100 or 3/10. This could also be written as a decimal (3/10 = 0.3).

Percents are really easy to calculate when you have exactly 100 things, but it's rare for the amount of something to be exactly 100. Percents are still really useful though, and we can use the percent formula to calculate percents of any amount!

To find a percent of any number, you can use the percent formula where:

**Part** = the part of the whole

**Whole** = the total amount that the percent is operating on - also known as the base

**Percent (%)** = the number of parts per 100 - also known as the rate

Let's look at three different examples of how you could use the percent formula.

First, we will look at how to find the part that is a percentage of a whole amount. This is exactly what I needed to do when I wanted to know if I could buy the new shirt. I knew the total amount (the total cost of the shirt - $37.99) and the percent (30%), and needed to find 30% of the whole so I would know how much the shirt would actually cost. To do this, we can cross multiply and solve for the part:

We could round this to $11.40 since you can't pay part of a cent. So, how much will the shirt cost then? If the original price was $37.99 and it is 30% off, we can subtract the part we just found from $37.99 to find the new price:

$37.99 - $11.40 = $26.59

So, I would have enough money to buy the shirt!

To find the whole when you know the part and base, you will have to cross multiply again and then solve for the base. As an example, let's say that you know that 40% of a box full of apples are green and the rest are red. You know that there are exactly 20 green apples, so how many apples are there total in the box?

In this case, 40% is the percent and 20 is the part. Now what is the whole (the total number of apples)?

There are a total of 50 apples in the box. 20 are green, which means that 30 must be red.

Once again, to find the percent if you already know the whole and part, you can use the percent formula, but you must cross multiply and then solve for the percent. Let's try an example. Suppose that in a classroom there are 30 students and 12 of the students are girls. What percent of the students in the class are girls?

30 would be the whole and 12 would be the part, so let's see how to find the percent:

In this class, we have determined that 40% of the total students are girls.

A **percent** tells you how many parts you have out of one hundred. You can use the percent formula to calculate any quantity if you know the other two.

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GED Math: Quantitative, Arithmetic & Algebraic Problem Solving10 chapters | 73 lessons | 7 flashcard sets

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