Making (Some) Multiplication Easier

As long-time readers know, I'm always on the lookout for arithmetic shortcuts. My favorites are those that make you think, but still help you do the work faster. You can see several mental math techniques I've previously shared on the site here.

I recently found a list of "10 Easy Arithmetic Tricks" at a site called The List Universe. Some of them overlap with earlier articles of mine, while others aren't all that relevant to the GMAT. One caught my eye, though.

I'll let the article speak for itself:

If you have a large number to multiply and one of the numbers is even, you can easily subdivide to get to the answer:

32 x 125, is the same as:
16 x 250 is the same as:
8 x 500 is the same as:
4 x 1000 = 4,000

How Does It Work?

When you're dealing with big numbers, it's often a good idea to break them down to factors. (Prime factors are smallest, but it isn't always necessary to go all the way down to prime factors.)

So, 32 x 125 is the same as:

(2 x 2 x 2 x 2 x 2) x (5 x 5 x 5)

That isn't much easier, but if you rearrange some of the terms, there are plenty of steps you can do quickly:

(2 x 5) x (2 x 5) x (2 x 5) x 2 x 2
= 10 x 10 x 10 x 2 x 2
= 1,000 x 4 = 4,000

In the trick above, you can save time by breaking one of the numbers down a little bit, rather than going straight to the prime factors. So the process looks like this:

32 x 125
= (16 x 2) x 125
= 16 x 250
= (8 x 2) x 250
= 8 x 500
= (4 x 2) x 500
= 4 x 1,000
= 4,000

Putting It In Practice

As you can tell, there are a lot of ways to handle a question like this. The idea isn't to always work through in the single optimal way, but to have a number of options so that you never have to do multiplication the long way.

Even though it may take longer in the beginning, it's good practice to force yourself to find arithmetic shortcuts for every multiplication problem you encounter. On the GMAT, the numbers almost always give you an opportunity like this. It's up to you to take advantage of it.

About the author: Jeff Sackmann has written many GMAT preparation books, including the popular Total GMAT Math, Total GMAT Verbal, and GMAT 111. He has also created explanations for problems in The Official Guide, as well as 1,800 practice GMAT math questions.

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