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. 



270 



