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Kevin has edited encyclopedias, taught history, and has an MA in Islamic law/finance. He has since founded his own financial advice firm, Newton Analytical.

Have you ever had to figure out the answer to a quick math problem? Sure, you can use your calculator on your phone, but what if that's out of battery life? In this lesson, we'll learn how to do mental math for multiplication and division.

Why Use Mental Math?

Do you always have a calculator on you? Fine, chances are you do have a phone around you most of the time, but do you really feel like pulling it out, unlocking it and tapping in the problem every time? Wouldn't it be nice to just be able to do that sort of thing in your head? Better yet, I bet you'd feel really smart being able to do math just like that.

Being able to do mental math, or math done in your head, has many advantages. No, I probably can't sell you on the idea of 'needing to find an answer when you don't have a calculator' that much anymore with the popularity of smartphones, but everyone wants to look smarter. Also, learning the basics of mental math will help you build abilities and confidence in math as a whole. Oh, and you do know that those cell phones eventually run out of battery life, right?

Mental Multiplication

If you're going to do mental math, then the single fastest way to mess something up is to forget about the unit places. There is a big difference between 7 times 10 and 7 times 100. Let's face it, those extra zeros can be intimidating. Therefore, when doing mental math with multiplication and division, you can do something that you otherwise couldn't do with adding or subtracting numbers in your head. You can ignore the unit places for a minute. Note that I said for a minute! Take the problem 70 times 100. Now, you could mentally multiply a bunch of numbers by zero, but why make it harder on yourself? Simply count the number of zeros, and then multiply the non-zero numbers. Then, tack the number of zeros on at the end and you get the answer: 7,000.

That sort of trick is useful for problems where you have nice round numbers, but what about numbers that are a bit trickier. Let's say that you had to multiply 71 by 99. That already looks like less fun, doesn't it? Sometimes, it's good enough to just get it close. As such, you can do some quick adjustments. There's really not a big difference between 99 and 100, so you can go up to 100 and get 7,100 easily. If you are just trying to get a rough idea, that gives you a very good approximation.

However, if you need to be exact, all is not lost! Go back to 71 times 99. Now, if you wanted to, you could set up the problem in your head and multiply the ones and then the tens, and then add everything together. However, if you're like me, that's a lot of work. I'd much rather just multiply 71 by 100. It's easier, right? Sure, but it's not exact. So, what do you do? Well, you just subtract 71 from 7,100. After all, all you're doing is taking away one occurrence of the number. By the way, the answer is 7,029.

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So, what about division? For that, I've got two quick strategies. First, try to find something that will get you to a number that is easy to divide by. For example, if you've got to multiply by 8, try dividing by 2 three times. Likewise, for dividing by 20, you can just divide by 2 and then by 10. On the other hand, you could split the dividend into two chunks. Say that you've got to find out what 354 divided by 6 is. Before you pull your hair out, break it up into 300 and 54. 300 / 6 = 50, while 54 / 6 = 9. Add 50 and 9, and you get the answer.

Examples

Let's try out another multiplication problem to make sure we get all the concepts. Say that you were going to multiply 980 by 130. Those are some pretty big numbers. However, let's knock those zeros off first - just remember you took two off! Now, you've got 98 * 13. That could just be 100 * 13, with 13 subtracted twice, right? I like that idea better. That means we have 1,274. However, we've still got those two zeros, so tack them on the back. That means we have 127,400.

So, what about division? Take 186 divided by 4. What's the first thing you need to do? You could simply divide it by 2 twice, giving you 93 first and then 46.5. But, what about that other way? 100 / 4 = 25, while 86 / 4 = 21.5. Add the two together and you get 46.5.

Lesson Summary

In this lesson, we look at how to use mental math to solve both multiplication and division problems. To do either of them, it does require a certain amount of mental flexibility, but once you know what to do, you can easily do it. For multiplication, don't be afraid to come back to the zeros, nor should you worry about rounding only to subtract out extras. In division, feel free to break up either the divisor or the dividend into smaller pieces.

Vocabulary & Definition

mental math

Mental math is math completed in your head.

Learning Outcomes

After viewing this lesson, you should be able to do these tasks:

Summarize the mental math tricks for multiplying and dividing

Use the strategies discussed in this lesson to correctly compute multiplication and division problems in your head

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