Joe Pagano

Teach Your Kids Arithmetic - Subtraction Shortcuts



Posted: Monday, November 13, 2006

by Joe Pagano
Math by Joe

As students, we become comfortable with what we learn first. Of the four arithmetic operations of addition, subtraction, multiplication, and division, we learn to add first and for this reason are most comfortable with addition. If we apply the principle of thinking in terms of what we are most comfortable with, then subtraction need not be a difficult operation to master. Consequently, by applying addition principles to subtraction, we find our shortcut to mastery of this operation.

Addition is the first pillar of arithmetic magic. Once this operation is mastered, all others can be conquered. The reason for this is inherent in the nature and interrelationship of the four arithmetic operations. You see addition and subtraction are inverse operations of one another. This interrelationship imputes a connection between these two procedures. What this means is that we can master one through the mastery of the other. Moreover, multiplication can be mastered through addition, since multiplication is repeated addition; similarly, division via multiplication or subtraction, since division is repeated subtraction as well as the inverse operation of multiplication. Thus why fret with mastering four distinct arithmetic operations when we can think of mastering one and then using shortcuts and derivative principles to master the others?

Such is the case with subtraction. If you have read my book Arithmetic Magic then you learned how to master subtraction through addition. In this work, I show you how to handle subtraction problems like 106 - 53. Rather than do a subtraction, you can think of "adding up" from 53 to 106. Another way of thinking about 106 - 53 is what is missing from 53 to make 106? This is the same principle that is taught to cashiers to make change, before, of course, the newer cash registers came out that do this for them. What cashiers would do is count up from the 53 to the 106. Thus we count from 53 to 60 to get 7. Then we count from 60 to 100 to get 40 more. So far we have counted 7 + 40 or 47 total. The final step is to count from 100 to 106 which is 6 more. As a result, we have 47 + 6 or 53 as our total. Thus 106 - 53 is 53. Let us take one more example to show how nicely this shortcut works. Take 96 - 49. Rather than fumble with this, it’s simple if we add up from 49 to 96 as thus: 49 to 50 makes 1; 50 to 96 makes 46; and 1 + 46 is equal to 47. So 96 - 49 is 47.

If you apply this subtraction shortcut regularly, you will never have a problem with this operation again. This method works with more complicated examples as well as you can easily verify. Try to teach this method to your kids and have them practice with a few examples. In addition to the good mental workout they will get, their arithmetic skills will soar to new heights. And there’s nothing better than seeing those A’s on their report cards.

See more at my cool math site Cool Math Sites Arithmetic Magic
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