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6th-8th Grade Math: Practice & Review55 chapters | 469 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 will learn how using estimation can help you simplify your problem so that you can solve it much easier. Learn how estimation can help even when you need to solve for a missing variable.

If you were working for a market research company that analyzes data from questionnaires and surveys, then you would eventually have to deal with decimal numbers. **Decimal numbers** are numbers that have a decimal point in them. Say you were working for the company Best Research Company. Your current project requires you to take the data you have and convert it using a formula. Your job is to find the new value for each set of data. Your problems look like these:

4.1 + *x* = 9

2.3*x* - 6.54 = 10.33

*x* - 4.21 = 6.3

Looking at these, you recognize that they are actually decimal problems that require only one or two steps to solve. What you need to do is to solve for the *x* by getting it by itself. To do that, you first look for any addition or subtraction going on with the variable, and then you go ahead and perform the opposite operation to both sides of the equation. Then you look for any multiplication or division going on with the variable and then you perform the opposite operation again to both sides of the equation to get the *x* by itself.

For example, to solve the first problem, you see that your *x* is being added by a 4.1. So you go ahead and subtract the 4.1. You subtract it from both sides because the rule of equality tells you that whatever you do to one side, you have to do to the other. So you get:

4.1 + *x* - 4.1 = 9 - 4.1

Evaluating this, you get:

*x* = 4.9

The new value for this problem is 4.9.

Now, your boss comes in right after you've finished this first problem, and he tells you that you can estimate your answer to make your job easier and quicker. After all, you do have a huge stack of papers in front of you filled with other data that you need to process. Your boss wants to get through as many data points as possible. He knows that estimating the problems will make the process go a lot faster.

To estimate your problems, you pick a place value to round to. Then, you round your numbers to that value, and then you go ahead and solve the problem. To round, you look at the digit to the right of the place value that you are rounding to. If it is 5 or greater, then you round up by 1. If it is less than 5, then you keep the digit.

Your boss tells you that rounding to the nearest whole number will work for this set of data. Other problems though might tell you to round to the first decimal space, second decimal space, or any other place value. But, in your case, you will round to the nearest whole number. That helps you out a lot!

Rounding the first problem to the nearest whole number, you get:

4 + *x* = 9

Solving this, you get:

4 + *x* - 4 = 9 - 4

Which turns into:

*x* = 5

The estimated answer is 5. Comparing your two answers, you see that the estimated answer is not that far off from the actual answer. You feel okay about using the estimated answers.

You proceed with the other two problems, each time rounding to the nearest whole number.

Rounding the second problem to the nearest whole number gives you:

2*x* - 7 = 10

You see that this problem has both subtraction and multiplication. You tackle the subtraction first. You add the 7 to both sides of the equation. You get:

2*x* - 7 + 7 = 10 + 7

This turns into:

2*x* = 17

Now you can go ahead and divide both sides by 2. You get:

2*x*/2 = 17/2.

This gives you an answer of:

*x* = 8.5

The last problem rounded to the nearest whole number gives you:

*x* - 4 = 6

You see that the *x* is being subtracted by a 4. This tells you that you need to add 4 to both sides of the equation. You get:

*x* - 4 + 4 = 6 + 4

Which turns into:

*x* = 10

And you are done with this set of three problems.

As you saw, estimating your problems makes solving your problems easier to do.

Let's review what we've learned. **Decimal numbers** are our numbers that have a decimal point. We can use estimation to solve our one- and two-step decimal problems. It makes solving the problems easier.

To solve our one- and two-step decimal problems, we first look for any addition or subtraction taking place to our variable. If we see some, then we perform the opposite operation to both sides of the equation. Then we look for any multiplication or division going on with our variable. If we see that, then we perform the opposite operation again to both sides of the equation to solve for the variable.

To estimate, we choose a place value to round our decimal numbers to. Then we look at the digit to the right of that place value. If it is 5 or greater, then we round our place value digit up by 1. If it is less than 5, then we keep that place value the same.

Once you have finished looking over this lesson, you should be able to estimate the solution to a one- or two-step decimal problem by rounding.

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6th-8th Grade Math: Practice & Review55 chapters | 469 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
- 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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