Multiplication Tricks: Mental Math I

Are you a random-intuitive-creative individual trapped in a logical-sequential-analytical world? So what if you were born with a tendency to over-utilize the right hemisphere of your brain. I mean, is that your fault? The cold hard fact is that you still have to make it through some fairly left-leaning academic subjects, and I'm not talking politics. How would you like to multiply 43 x 47 in your head faster than Napoleon Dynamite can reach for his TI-84. Here are a few multiplication tips & tricks that will give you an edge in basic multiplication, boost your confidence, and help you move beyond math to really important things!

As a foundation for these techniques you need to memorize the squared integers up to 30.

In elementary through college math these simple computations come up again and again and again. Instead of rummaging around in your backpack for a buried calculator, pulling these facts out of your mind will save you a surprising amount of frustration and time.

By squared integers I mean 1 x 1, 2 x 2, 3 x 3, 4 x 4 etc...Memorize them all the way up to 30 x 30 so you can say the answers in your sleep. Writing these problems out by hand on a piece of paper and repeating the products out loud will help cement them into your gray matter.

For the larger squares such as 18 x 18 or 26 x 26, multiplying the unit digits will give you a nice little memory jog as to the product of each squared pair. For example, for 18 x 18, the 8 x 8 = 64 and so I know the answer will have a 4 in the units position - in this case 324. Multiplying 26 x 26, will give 6 x 6 = 36 for the units multiplication, and therefore a 6 in the units position - in this case 676.

Enough of the boring stuff. In algebra we know that (x + 1)(x - 1) = x² - 1. Just trust me - Ok? This may not be the most scintillating fact you've ever come across in your life, but to the left-brainer this is almost nirvana. What this means is that if you take a product such as 19 x 21, to find the answer you just square the number between the two (20) and subtract one. So 19 x 21 = 20 x 20 - 1 = 399. How about 24 x 26 - that would be 25 x 25 - 1 = 624. And 29 x 31 = 30 x 30 - 1 = 899.

You can see that if you have the basic squares memorized, you can speedily find answers to numerous multiplication problems by simply subtracting 1 from the answer in your head. The exciting news is that this is just the tip of the iceberg. OK, OK, so maybe this idea won't allow you to solve the world's economic troubles, but, you can take this concept and expand it to solve dozens of other multiplication problems in your mind. "How do we do that?", you say. You'll just have to read Mental Math II.