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6th-8th Grade Math: Practice & Review55 chapters | 468 lessons

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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.

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 4.3*x* and 2.7*x* are like terms. So are 6.1*x*^2 and 8.7*x*^2. However, 4.3*x* and 6.1*x*^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:

12.99*x* + 4.59*x* + 24.99*x*

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 12.99*x* + 4.59*x* + 24.99*x* becomes 42.57*x*. 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.

Simplify:

4.3*x* + 2.7*x* - 8.5*y* + 32.7*y*

In this problem, we see that we have two variables, an *x* and a *y*. So, we combine our terms with *x* together, and we combine our terms with *y* together. Essentially, we have two mini problems in this one problem. We have 4.3*x* + 2.7*x* for the *x* terms and we have -8.5*y* + 32.7*y* for the *y* terms. Notice how I've included the negative sign with the 8.5. You have to be careful that you keep the negative sign with those numbers that are negative. Evaluating our two mini problems, we get 4.3*x* + 2.7*x* = 7*x* and -8.5*y* + 32.7*y* = 24.2*y*. Our problem then simplifies to 4.3*x* + 2.7*x* - 8.5*y* + 32.7*y* = 7*x* + 24.2*y*, and we are done!

Simplify:

2(1.1*x* + 3.4*x*)

In this problem, we see a set of parentheses. We always follow our order of operations. So, we tackle the parentheses first. We add 1.1*x* to 3.4*x*. We get 2(1.1*x* + 3.4*x*) = 2(4.5*x*). Then, we multiply the 2 by the 4.5*x*. We get 2(4.5*x*) = 9*x*, and we are done!

Let's review what we've learned. **Decimals** are the numbers with a decimal point. **Simplifying** means combining your like terms. When you see an expression with decimals in them, and you see that some terms share a common variable with the same exponent, then you can go ahead and simplify the expression by combining those terms. If you have more than one variable, your simplified problem will have one term for each variable.

After reviewing this lesson, you should have the ability to:

- Define decimals and simplifying
- Explain how to simplify expressions with decimals

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6th-8th Grade Math: Practice & Review55 chapters | 468 lessons

- Inequalities with Decimals 5:36
- Converting Decimals to Mixed Numbers 5:44
- Converting Repeating Decimals into Fractions 7:06
- Adding and Subtracting Decimals: Examples & Word Problems 6:53
- Multiplying and Dividing Decimals: Examples & Word Problems 5:29
- How to Estimate with Decimals to Solve Math Problems 8:51
- Estimating Sums, Differences & Products of Decimals 5:53
- Solving Problems Using Decimal Numbers 6:57
- Estimation: One & Two Operation Problems with Positive Decimals 5:31
- Guess and Check: One & Two Operation Problems with Positive Decimals 6:47
- Look for a Pattern: One & Two Operation Problems with Positive Decimals 7:10
- Solving Multi-Step Inequalities with Decimals 8:01
- Maps with Decimal Distances 4:17
- How to Simplify Expressions Involving Decimals 5:04
- Go to 6th-8th Grade Math: Operations with Decimals

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