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Gerard Kelly

# Short-Cut Math

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By adding an amount 10 one number and subtracting an equal amount from a second number, the sum of the two numbers remains the same.
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The 370 − 37 is, of course, 37 × (10 − 1) instead of 37 × 9.
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Either way, the answer is the same.
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To multiply 64 by 25, for instance, you can divide 64 by 4 (= 16) and multiply by 100 (just add two zeros), and there’s your answer: 1,600.
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Take 28 × 15, for instance.
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If you halve 28 (= 14) and double 15 (= 30), you change the problem to 14 × 30 which, as you can see, is an easy 420—the same answer you will get by multiplying 28 by 15.
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If you halve 28 (= 14) and double 15 (= 30), you change the problem to 14 × 30 which, as you can see, is an easy 420—the same answer you will get by multiplying 28 by 15.

It’s not always the size of a number that makes it difficult to handle but the KIND of number it is. You know, of course, that it’s much easier to multiply by 10 than by 9 even though 10 is the larger number. However, the “difficult” number 9 can be changed into two “easy” numbers, 10 minus 1, which equal 9. Therefore, to multiply a number by 9, you can multiply by 10 (simply add a zero to the number) and subtract the number, thus: 37 × 9 = 370 − 37 = 333.
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They’re inexpensive, easily carried, never need a battery, and give you a record of what you did so the work can be checked.
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For example, to find the sum of 29 and 36, you can add 1 to 29 and subtract 1 from 36 so that the problem becomes 30 + 35; you can see at once that the answer is 65.
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You can apply the same principle to multiplying.
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As you work with short-cuts, you will probably see other ways of calculating faster and easier.
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Discovering methods of your own can add new excitement to your journey through this corner of the magic world of numbers.
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And don’t forget those old reliables, pencil and paper.
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Examples are given under each short-cut to demonstrate how it works.
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The steps are used where needed for additional clarity and are followed by a “Short way” indicating how the method would actually be used.
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If you can do ordinary arithmetic, you will have no trouble in using these methods.
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After that, study whatever methods are of special interest to you.
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The best approach is to concentrate on the methods you can use in your daily work or the ones you would like to learn just for the fun of knowing them.
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This book contains about 150 short-cuts that provide faster, easier ways to add, subtract, multiply and divide.
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You can apply them at school, home, shop, or office to save time and trouble.
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