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How to Estimate Quotients

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  • 0:01 What are Quotients?
  • 0:49 Estimating Easy Problems
  • 3:27 Estimating…
  • 6:14 Estimating Very…
  • 8:20 Lesson Summary
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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.

What Are Quotients?

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.

Estimating Easy Problems

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.

Estimating Intermediate Problems

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.

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