Page:Popular Science Monthly Volume 88.djvu/298

 That Mathematical Short Cut

��Short Cuts in Arithmetic

THE principle described by Mr. Shourn in the November issue of the Popular Science Monthly as a "Short Cut in MultipHcation," can be used equally as well in addition, sub- traction and division, with slight varia- tions. To use his figures in

Addition.

974265 = 33 = 6 84337 = 25 = 7

��1058602 = 22

��13 = 4 = 4

��974265 84337

��Subtraction. 33

25

��889928 = 44 =8

If the 33 and 25 were further reduced it would be 7 • from 6, in that case 10 would have to be added to the six, and 1 subtracted from result, as below : 33 = 6 = 16 25 = 7 = 7

9 1

8

Multiplication.

974265 = 33 = 6

84337 = 25 = 7

��42

��82166587305 = 51 = Division.

��In division the division digits are mul- tiplied by those of the quotient and to the result the remainder is added, these must equal the sum of the digits of the dividend :

Dividend = 974265 = 33 = 6 Division = 84337 = 25 = 7 Quotient =1146558 = 27 = 2 1/7 (7 X 2) + 1 = 15 =6 Dividend = 6

— L. E. F.

��Be Sure You're Right

THOSE who read in the November number of the Popular Science Monthly the article entitled "Short-Cut Multiplication Proof" may be inter- ested to know that the principle of the method there discussed may also be ap- plied to the other three fundamental arithmetical processes.

As a simple example suppose we di- vide 25 into 375. Our answer or quo- tient would be 15. Now let us reduce each one of these figures to its lowest terms, which, according to this process, means adding the 2 and 5 in the divisor, making 7. Then 3 plus 7 plus 5 in the dividend equals 15, and 1 plus 5 in the 15 makes 6, the lowest term of our divi- dend; and 1 plus 5 equals 6, the lowest term of our quotient. To prove the problem all that is necessary is to mul- tiply the lowest term of our quotient by the lowest term of our divisor. If our division was correct our answer will be the lowest term of the dividend. That is, in this case (quotient) 6 x (divisor) 7 equals 42 ; and as 4 plus 2 is 6, the same as the lowest term of our dividend, we know that our division was correct.

The following is an illustration of proving substraction :

5721 equals when the digits are added together 15

3545 equals when added 17. and 7

plus 1 equals 8

2176 equals when added 16, and 6

plus 1 equals 7

The same problem in addition would be:

5721 equals 15 equals 6

3545 equals 17 equals 8

14 equals 5 9266 equals 23 equals equals 5

With a little practice one may become very proficient in reducing the numbers to their lowest terms, thus making the process valuable for those who have to check over their own work. Trv it.

— M. A.

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