# Guess and Check: One & Two Operation Problems with Positive Decimals

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• 0:01 Decimal Problems
• 2:20 Check the Guess
• 2:55 Refine and Repeat
• 3:52 Example
• 5:48 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.

In this video lesson, you will learn how to use your guessing skills in finding the correct answer to a decimal problem. Learn how you can refine your guess to make an even better guess and get closer to finding your answer.

## Decimal Problems

In this video lesson, we're going to talk about decimal problems. Decimals are numbers that have a decimal point. Specifically, we'll talk about problems that only require one or two steps to solve. These types of problems look like these:

8.1x = 12.15

2x - 8.9 = 20.52

You may already be familiar with some methods to solve these types of problems. But after watching this video lesson, you will have an additional method to add to your problem solving tool box. The more tools or methods you have, the better off you will be when you are given a random problem, whether it be in school, on a game show, or for work.

The method that you will learn in this video lesson is called the guess and check method. That's right; you'll be making educated guesses to come up with an answer. You will then check that answer to see if it is the right one. Then, you will modify your guess to get even closer to the right answer. You repeat this process until you have arrived at the only correct answer there is.

Let's take our first problem to see how you can use the guess and check method. Our problem is 8.1x = 12.15. We begin by making a first guess. We will need to use our heads a bit and apply some common sense here. We see that we have an 8.1 multiplied by our variable. Our variable x is the number that we are looking for.

So, we are looking for a number that when multiplied by 8.1 will give us 12.15. We know that 8.1 is close to 8. We also know that 8 * 1 = 8 and 8 * 2 = 16. So, this tells us that most likely our answer will be between 1 and 2. We can begin by trying 1.2.

## Check the Guess

We have guessed 1.2 for the answer. So, now we need to check this guess. To check our guess, we plug our guess into the problem for x, and then we calculate to see if our guess gives us the answer we're looking for. We plug 1.2 into our variable to see what it gives us. 8.1 * 1.2 = 9.72. Okay, it equals 9.72. That's not what we want; we want it to equal 12.15.

## Refine and Repeat

Because our guess did not give us what we want, we now need to refine our guess. We see that our first guess of 1.2 gave us a number that is lower than the 12.15 that we wanted. This tells us that we need to make another guess that is higher than 1.2. The rule here is that if our guess gives us an answer that is lower, then we need to increase the value of our guess.

If our guess gives us an answer that is higher, then we need to lower the value of our guess. We now repeat the whole guess and check process for our next guess. Let's try 1.5. Plugging this in, we get 8.1 * 1.5 = 12.15. Is this the solution we want? It is! This tells us that our correct answer is 1.5, and we are done!

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