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3rd-5th Grade Math: Practice & Review37 chapters | 251 lessons

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Lesson Transcript

Instructor:
*Artem Cheprasov*

It may seem crazy to think you can quickly estimate the answer to something like 81,837/95 but by the end of this lesson, you'll be able to easily estimate quotients of simple and more difficult division problems. After the lesson, test your new knowledge with practice examples.

You might feel nervous if I asked you to estimate the quotient of 49,348 divided by 726. But you shouldn't! The problem isn't really that hard. In fact, it's probably much easier to get the answer than you might guess. Remember, we're estimating. We don't care about an exact answer; we just want to be close to the real answer.

This lesson will show you how to estimate quotients through easy, intermediate and more challenging division problems. But before we start, let's review the definition for quotient. A **quotient** is the answer you get after dividing one number by another. So, in a problem like 10 / 5 = 2, the quotient is 2.

Let me prove to you that you can estimate a quotient pretty easily by using **compatible numbers**, which are numbers that are close to the numbers in question, yet can divide one another easily.

For example, the numbers 134 and 7 are not compatible numbers under any scenario because we can't divide them very easily. The answer to 134/7 is a messy 19.14. We want whole numbers as our answer instead since they're much easier to handle. A whole number is a number with no fraction or decimal. So, 50, 60 and 2 are whole numbers; 50.3, 60.4, 2.98 are not.

Unlike 134 and 7, the numbers 100 and 20 are compatible numbers because they can be easily divided to get an answer of 5, from 100/20.

Let's apply the concept of compatible numbers to a simple problem where we can estimate quotients.

Estimate the answer to the following problem: 84/9.

Hmm. How can we possibly solve this and estimate the correct answer? Well, let's think about this. We have two numbers: 84 and 9. Do we know of any number that is close to 84 that can be easily divided by 9?

What about 81? 81 can be divided by 9 to get an answer of 9. That's it, 9 is our estimate. And if you get a calculator or puzzle out 84/9, you'd get 9.33, which just proves our estimate was spot on.

Estimate the answer now to 36/5. Pause the video now to try this problem on your own.

Ready? Ok, again, 36 cannot be divided by 5 very cleanly. Meaning, the real answer won't be a whole number. So, to get an easy answer we need to think of a number close to 36 that can be easily divided by 5. Well, our options are 35 or 40. Since 35 is the closest number, we divide 35 by 5 to get an answer of 7.

Ok, so those were kind of easy. But I had to show you them because those 'easy' problems serve as a very important foundation to solving more difficult ones.

Let's go back to our intro problem of 49,348 divided by 726. How in the world are we going to estimate the answer to this one? Well, it's actually just as easy as before. 49,348 is a messy number. Why don't we just round it down to 49,000? We can always change this number later if we need to.

Now our problem is 49,000/726. That's better, but it's still messy. Can we clean up the 726 a bit? Again, let's just round it down to 700 for now. We can always change it later if we need to. 49,000/700 is a much cleaner problem to deal with. However, those are still some pretty big numbers! I don't like that. That's too hard for my brain to handle. So, why don't we cross out all the zeroes in the smaller number, 700, and the equivalent number of zeroes from the bigger number. Since 700 has two zeroes, we take away two zeroes from each number to get ourselves a much easier problem of 490/7.

Now here's an important trick. We only divide the nonzero digits together so as long as the numerator remains larger than the denominator when dividing these digits. In this case, this means we disregard the 0 in 490 to get 49/7. If you divide 49/7, what do you get? 7. Next, put the same number of zeroes that we disregarded after your answer. This means we put one 0 after 7 to get an answer of 70. 70 is our estimate to 49,348 divided by 726.

To recap, our original problem was 49,348 divided by 726. Our compatible numbers turned out to be 49,000 and 700 because dividing these two numbers gives us a whole number of 70.

Let me give you another problem and a slightly different approach to it using what you already know. Estimate the answer to 369,938 divided by 56,938. Wow! My head is totally spinning. But you already have enough in your brainbox to solve this one!

Let's see what we can do: 369,938 is close to 370,000, but I don't know of any numbers that divide 37 very well so what about rounding it down to 360,000? Disregard the zeroes for now. Do you know of any numbers that divided 36 very well? I can think of one, a 6!

56,938 is closer to 55,000 than it is to 60,000, but I don't care. To estimate using compatible numbers, I need that easy 6! So, I round 56,938 to 60,000 instead. Now the problem is 360,000/60,000. But I imagine it as 36/6 by disregarding the zeroes. And the answer to that is an easy 6. How many more zeroes does 360,000 have than 60,000? None! Both have the same number of zeroes. This means I don't attach any zeroes to 6. My answer and estimate is roughly 6.

What is the real answer to 369,938 divided by 56938? About 6.5. It turns out my estimate was pretty close!

Estimating quotients isn't that hard so long as you use compatible numbers! A **quotient** is the answer you get after dividing one number by another, and **compatible numbers** are numbers that are close to the numbers in question yet can divide one another easily.

For example, if the problem is 21/5, it's best to round these numbers to ones that are easier to deal with like 20 and 5. 20 divided by 5 is 4, and so the estimate to this problem would be 4.

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3rd-5th Grade Math: Practice & Review37 chapters | 251 lessons

- How to Round Whole Numbers 6:03
- Rounding Numbers to the Nearest 1000, 10,000 & 100,000 7:04
- Estimating a Difference by Rounding 4:57
- How to Use Front-End Estimation 5:26
- Rounding Decimals & Finding the Missing Digit 6:50
- Estimating the Sum & Difference Between Two Decimals 5:12
- How to Round Mixed Numbers 3:20
- How to Estimate Products
- How to Estimate Quotients 8:57
- Go to Estimation & Rounding

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