Mental Math: Multiply By Nine (and other numbers too!)

August 06, 2007

If you've read many of the articles on this site, you know how passionately I feel about avoiding traditional calculation methods. Here's a way to multiply large numbers (or any numbers, really) by 9, without setting up multi-digit multiplication problems. You'll save time, too.

Since 9 is the same as (10-1), you can substitute the latter term anywhere you see a 9:

23(9) = 23(10 - 1)

Presumably, you can multiply 23 times 10 quite rapidly, and 23 times 1 even faster:

23(10 - 1) = 230 - 23 = 207

This is very similar to the method I introduced a while back for percents. And like the method for percents, you can use it for numbers other than 9, too. The idea is: if you're multiplying by a number that is the sum or difference between two easier numbers, you can turn that one multiplication problem into 2. For instance:

19(8) = 19(10 - 2) = 190 - 38 = 152

27(11) = 27(10 + 1) = 270 + 27 = 297

25(15) = 25(10 + 5) = 250 + 125 = 375

20(99) = 20(100 - 1) = 2000 - 20 = 1980

Try it on some other multiplication problems yourself! With a bit of practice, you'll get through calculations like these much more quickly than before.

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

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