Teach Your Kids Arithmetic - Multiplication Shortcuts Part II
Posted: Sunday, May 08, 2011
by Joe Pagano
Math by Joe
Did you ever watch an illusionist pull off one of those amazing mind-blowers in which a rabbit appears out of a seeming empty hat? Or one in which, a previously torn piece of paper with unique writing on it is miraculously restored whole? These mind-bending illusions might really seem like magic but there is a trick behind every one. Similarly with math, multiplying lightning fast might seem like an illusion, but there really is a trick behind it. With various shortcut techniques, some of which will be outlined here, you too can seem like a mathematical illusionist.
Yet most people will never get that chance because they fall deficient in the ability to reckon with numbers. The need to have such a facility is certainly not an overstatement, as the one who is fast with numbers, is the one deemed a fast thinker, and the one who ultimately achieves success. If you doubt these assertions, just survey the rich and famous and the very wealthy: to a man, all are quick thinkers and will be found to be very comfortable with numbers and their inherent calculations.
To be fast with numbers, and indeed comfortable with their intrinsic nature, one need only learn the secrets of the trade. Learning how to multiply fast only requires that one look differently at numbers, more from a piecewise analysis, and learn to break products down into manageable parts. What is meant by this can be seen with specific examples.
Let us take the specific number 9. We can put multiplications by 9 into a separate class, and by making such classes, we form a partition essentially of the different possible multiplications of numbers. By doing this, we break all multiplications down into different sets, and thus simplify the approach to doing such calculations.
Getting back to multiplication by 9, we can view 9 as 1 off from 10. Now multiplying any number by 10 is easy: we merely attach a 0 to the end of the number. Thus 10 x 98 is 980. Now multiplying this number by 9 is almost as easy, since we can write 9 as (10 - 1). Thus 9 x 98 is actually (10 - 1)*98. With a simple application of thedistributive property, we have10*98 - 1*98. Thus 9*98 is 980 - 98. To make this subtraction easy we write 98 as 100 - 2. Thus 980 - 98 is 980 - 100 + 2 (remember the double negative is a positive) and we have the result, which is 882.
This amazing method can be used with any number times 9. Let's do another: 9*36. This is 360 - 36, which is 360 - 30 - 6, which is 330 - 6 or 324. Notice how we are breaking down the subtraction to make the result more easily obtainable. Let's try another: 9*321. This is 3210 - 321, which is 3210 - 300 - 20 - 1, which is 2910 - 20 - 1, which is 2890 - 1, which is 2889. Pretty cool, no?
With this little trick, you can now multiply any number by 9 and get the result quite easily. With a little more partitioning of numbers into classes, and some more tricks, you will son look like the master illusionist we mentioned at the beginning of this article; only you won't be pulling a rabbit out the hat but rather a number out of the air. Have fun with this knowledge.
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