Understanding Percentages

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Introduction and Video

In this video lesson, we'll introduce the basics for understanding percentages. We'll define what percentages are, how they are used to represent ratios, and how to write them. We'll also discuss the connection between fractions, decimals, and percentages.

Lesson Notes for Understanding Percentages

Let's look at the details of the lesson including what percentages are, how they are used to represent ratios, and how to write them.

What is a Percent?

A percent is a numerical value that is accompanied by a symbol, typically a slanted line with two circles, which is placed after the number.
This symbol signifies that the number represents a specific part-to-total ratio, where the total is always considered to be 100.
It is important to note that the symbol itself can be interpreted as meaning "per 100" or "out of 100".

Understanding Percentages. Definition of percent as a ratio out of 100.

Interpreting Percentages

The term "percent" can be translated as "per 100" or "out of 100".
For instance, if we encounter the percentage 20%, it can be interpreted as 20 per 100 or 20 out of 100.

Representing Percentages

Percentages can be represented in various forms, including fractions and decimals.
For example, the percentage 85% can also be expressed as the fraction 85/100 or the decimal 0.85.
Similarly, if we have a ratio of 85 out of 100, we can conveniently write it as 85%.

Understanding Percentages. Example of representing 85 out of 100 as a fraction, decimal, and percent.

Calculations with Percent

When it comes to performing calculations involving percentages, it is important to convert them into fractions or decimals before proceeding.
Let's consider a scenario where we need to solve a problem that involves multiplying 25% by eight. In order to obtain an accurate result, we must first convert the percentage to a fraction (25/100) or decimal (0.25). Then the fraction or decimal can be multiplied by eight to find the solution.

Summary and Practice

In this video lesson, we learned that percentages serve as a representation of ratios out of 100. We also learned that percentages can be converted to fractions and decimals which is important for solving math problems with percentages.

Try this practice activity to see what you learned. Click on the correct answers.

Video Transcript

In this video lesson, we're going to learn about percent. Now, you've probably seen a percent before. It's a number written with a symbol after it. And that symbol looks like a slanted line with two circles. But what exactly does that symbol represent? So a percent is a type of part to total ratio where the total is 100. So we can recognize a percent by the symbol, but we can also think of that symbol as meaning per 100 or out of 100.

So the word percent translates to per 100 or out of 100. So if we see this 20%, we can think of it as 20 per 100 or 20 out of 100. Here's another example. 85 out of 100 teenagers have cell phones. There's many different ways that we can represent that 85 out of 100. And we've been learning about ratios. So we can set this up as a fraction as 85 over 100. Or we could translate that to a decimal as 85 hundredths, 0.85.

But now we know that out of 100 can also be used as a percent. So 85 out of 100 can be written as 85%. As we move forward with our lessons, we're going to learn how to solve all different types of problems that have percent. But it's very important to remember that when we do calculations with percent, we have to convert it to a fraction or decimal first.

So if you see a problem like this 25% times eight, we can't solve it in this format. We have to convert that percent to a fraction or decimal. So we could do 25 over 100 times eight, that would be okay. Or we could do zero point 25 times eight and set it up as a decimal. That would also be okay.

So now you've learned what a percent is. It's a way of representing a ratio that's out of 100. And when we do calculations with percent, we have to convert it to a fraction or a decimal.

Related Standard: Common Core 6.RP.A.3, 7.RP.A.3

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