Divide and Multiply by Five ... Fast

July 26, 2007

Aside from manipulating the GMAT's favorite numbers (72, 64, etc.), one of the calculations you'll do most often when working through GMAT problems is dividing and multiplying by five. It's common in the real world, too. As with most common calculations, there's a better way to do them than long division or traditional multiplication.

For both division and multiplication, the key concept here is that 5 is simply 10 divided by 2. So, anywhere you see a 5 in an equation, you can substitute (10/2). You won't always want to do that, but in some cases, I guarantee you that working with 10s and 2s is preferable to working with 5s.

Using that trick, consider multiplying 36 and 5. (If you automatically know that, work through the example with a less common number, like 47.) Using the trick outlined above, 36(5) = 36(10/2). You now have two options: you can multiply 36 and 10 and then divide by 2, or divide 36 by 2 and then multiply by 10. Either way, both steps are quite simple.

Dividing by 5 works the same way, only backwards. If you're dividing 175 by 5, that's the same as simplifying the fraction 175/5. As we've seen, 5 = 10/2, so 175/5 = 175/(10/2). That's a bit ugly until you divide the fraction, leaving you with 175(2/10). Now, instead of factoring out 175 or doing long division, you can use the steps I showed you with multiplication. Either multiply 175 by 2 and then divide by 10, or divide 175 by 10 and then multiply by 2. In this case, the latter is probably easier.

Once you start experimenting with this approach, you'll find that--like all mental math tricks--sometimes it saves you a lot of time, and other times it doesn't help much at all. That's why it's important that you spend the time (before the test is 48 hours away!) to try out the method on a variety of numbers and get a sense of when it will work best for you.

Jeff Sackmann is a GMAT tutor based in New York City. He has created many resources for GMAT preparation, including the popular GMAT Math Bible and GMAT Verbal Bible, as well as 1,800 practice GMAT math questions.

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