5 Tips for Faster Mental Multiplication

Ever dreamed of being able to multiply numbers lickety-split…and completely in your head? Wouldn't it be great if you could quickly solve problems like 36 x 25 and 47 x 24? Good news—you can! Keep on reading to find out how.

Tip #1: How to Multiply by Powers of 5

There are times in life when you just get lucky. It turns out that one of those lucky little moments occurs each and every time you need to multiply one number by another number that happens to be a power of 5. For example, let's say you need to find 36 x 5 (which, of course, fits the bill since 5 is the first power of 5). The trick is to recognize the fact that 5 = 10 / 2. Why is that helpful? Because it means that we can find 36 x 5 by instead finding 36 x 10 (which is easy) and then dividing the result by 2. In this case, 36 x 10 = 360, and 360 / 2 = 180. Impressively speedy, right?

Tip #2: How to Square Numbers Ending in 5

Our fun with 5s doesn't end there. We talked about how to square numbers in your head before, but it turns out that things get a whole lot easier when squaring a two-digit number that ends in 5. Here's the trick: Any time you square a two-digit number that ends in 5, the last digits of the answer will be 25 and the digits before that are given by multiplying the first digit of the number by the number that's one greater.
For example, this trick says that the last two digits of 45^2 must be 25, and the digits before that are given by 4 x 5 = 20. So 45^2 = 2,025. How about 75^2? Well, once again we know that the last two digits will be 25 (since they always are for this kind of problem), and the previous digits are given by 7 x 8 (that's the first digit times the number that's one greater). So the answer is 75^2 = 5,625. Fast and easy!

Tip #3: How to Easily Multiply Lots of 9s

The third trick for today has to do with multiplying any number by 9, 99, 999, or any other number that's 1 less than a power of 10. What makes all of these wild 9 numbers special? In a problem like 44 x 9, the trick is to recognize that 44 x 9 = 44 x (10 - 1). The distributive property of multiplication tells us that this is the same as 44 x 10 - 44. And since it's easy to multiply by a power of 10, looking at the problem this way makes it much easier to solve. In particular, it tells us that 44 x 9 = 44 x 10 - 44 = 440 - 44 = 440 - 40 - 4 = 396 (sharp-eyed math fans may notice a trick there related to Math

Tip #4: How to Multiply by Powers of 2

You can use today's fourth tip any time you're multiplying one number by another number that's a power of 2. Which means that any time you're multiplying some number by 2, 4, 8, 16, 32, 64, and so on, this is your ticket to mental math bliss. Instead of going through the usual multiplication process, in this case all you have to do is double the number you're multiplying for each power of 2 in the other number.
For example, the problem 12 x 8 is the same thing as 12 x 2^3 or 12 x 2 x 2 x 2.

Tip #5: How to Double and Halve to Multiply Fast

The previous trick is really just a special case of today's fifth and final (and I think coolest) trick that you can use whenever one of the numbers you're multiplying is even. Let's say you're multiplying 47 x 24. Since 24 is an even number, let's use the idea of doubling and halving to solve this problem quickly.
What do I mean by doubling and halving? Well, the trick is to continually double one number while halving the other. In this case, this means that we turn the problem 47 x 24 into the problem 94 x 12 by simultaneously doubling 47 and halving 24. We can then do the same thing and turn the problem into 188 x 6, and again to get 376 x 3. At this point,

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