5 Tips for Faster Mental Division (Part 1)

Have you ever wished you could divide numbers quickly and easily in your head? Believe it or not, you can! Over the next two weeks, we'll be learning my top 5 tips to help you become a mental division maestro.

Jason Marshall, PhD,
July 27, 2013
Episode #163

Page 2 of 2

...check if you can simplify the problem before you start doing any division. In particular, if the number you're dividing into (aka, the dividend) and the number you're dividing by (aka, the divisor) are both even, you should start by dividing both by 2. For example, in the problem 164 / 26, start by dividing both the top and bottom by 2 to obtain the simplified (but otherwise identical) problem 82 / 13. Why is that helpful? Simply because it's almost always easier to work with smaller numbers.

But that's not the only way a division problem can be simplified. In a problem like 93 / 27, the dividend and divisor are not both even numbers—so we can't simplify the problem by dividing both by 2. But both are divisible by 3 (in other words, 3 is a factor of both 93 and 27). Which means that in this case we can divide both the dividend and divisor by 3 to obtain the simplified problem 31 / 9.

The quick and dirty tip here is to always look for factors common to both the dividend and the divisor, and then to divide both by each common factor before you do anything else.

Tip #3: Multiply Before Dividing

There are times in life when doing the opposite of what you should be doing is bad. But there are other times when it's actually very, very good. This is one of those times because when it comes to mental division, it turns out that it's often helpful to multiply instead.

Like many mental math tricks before it, this one relies upon the fact that dividing by 10 (or 100, or any other power of 10) is easy—just move the decimal point one position to the left for each power of 10. And since it's so easy to divide by powers of 10, we should strive to do it as often as possible—even when we're supposed to be doing something like dividing a number by 5. But how can we possibly do that? We use the fact that 5 = 10 / 2.

For example, let's imagine you're back working in your coffee shop and you've decided to calculate the average amount of money you make each day of a 5-day work week. In other words, you need to divide the total amount of money you bring in over those 5-days—let's say it's $1,677—and divide it by 5. But instead of calculating $1,677 / 5, let's use the fact that 5 = 10 / 2 to turn this problem into $1,677 / (10 / 2). Using what we've learned about how to divide fractions (remember invert and multiply?), we see that this is the same as $1,677 × 2 / 10. In other words, we've managed to turn a hard problem of mentally dividing by 5 into two simple problems. First, multiply $1,677 by 2 to get $3,354. And second, divide the result by 10 to find that the average income for each day of the week is $3,354 / 10 = $335.40.

Does this trick only work for division by 5? No! You can use the same idea to turn division by 20 into multiplication by 5 followed by division by 100, or division by 25 into multiplication by 4 followed by division by 100, and lots and lots of other things, too. And when combined with today's first tip about making approximations, this trick becomes even more powerful. Just remember to stop and think before you start working on a problem, and you'll often see that there's a much easier way to the solution.

Wrap Up

Okay, that's all the math we have time for today. Of course, those are only 3 of my top 5 tips for faster mental division. So be sure to check back next time to learn the last—and most powerful—pair of tips!

Be sure to check out my mental math audiobook called The Math Dude’s 5 Tips to Mastering Mental MathAnd for even more math goodness, check out my book The Math Dude’s Quick and Dirty Guide to Algebra.

Remember to become a fan of the Math Dude on Facebook where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too. Finally, please send your math questions my way via FacebookTwitter, or email at mathdude@quickanddirtytips.com.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Mental division image from Shutterstock.


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