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How to Simplify Expressions Involving Decimals

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  • 0:01 A Decimal Expression
  • 1:30 How to Simplify
  • 2:40 Example 1
  • 3:52 Example 2
  • 4:37 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you should be able to take any expression involving decimals and simplify it. You'll learn what to look for and what things you can combine.

A Decimal Expression

Decimals are everywhere. Decimals are the numbers with a decimal point. You find them in stores when you go shopping. Almost every single price tag that you look at will have a decimal number on it. You might buy a candy bar for $0.69 or $1.29. Both of these are decimal numbers. Do you see the decimal point in both of them?

In math and in real life, when you are working with decimal numbers, you will come across an expression that you can simplify. Simplifying means combining your like terms. Your like terms are the terms that have a common variable. For example 4.3x and 2.7x are like terms. So are 6.1x^2 and 8.7x^2. However, 4.3x and 6.1x^2 are not like terms. This is because the variable and its exponent must be the same for them to be like terms. The number attached to the variable does not have to be the same.

For example, when you need to calculate the total cost of your shopping trip, the expression you get can be simplified. If x stands for the sales tax, your expression might be something like this:

12.99x + 4.59x + 24.99x

How to Simplify

This expression can be simplified because you have like terms that can be combined together. When you combine your like terms, you perform the operation between the terms that are alike. For our expression, we see that we can add together the decimal numbers 12.99, 4.59, and 24.99.

After combining our like terms, we find our total of the numbers, and then we write this total with the variable. So 12.99x + 4.59x + 24.99x becomes 42.57x. See how we wrote our total for the numbers and then we wrote the variable again? This is what simplifying is. When we have a simplifying problem, this is all we have to do. If you see other symbols in the problem, like parentheses, then, of course, you would do them first, following your order of operations. And, if you have more than one variable, you would combine the terms with one variable, and then you would combine the terms of the other variables separately. Your answer will have one term for each variable.

Let's look at a couple of examples.

Example 1

Simplify:

4.3x + 2.7x - 8.5y + 32.7y

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