392 Mr. V. A. Bailey on the Mental Multiplication 



After practising this method half-a-dozen times with 

 numbers similar to those given in the example one becomes 

 capable of dealing easily with products like 



2490731x7615429. 



It is not very difficult after a little practice to add up 

 mentally a series like 27 + 56 4-49 + 18, and in time one can 

 do it as easily as one normally does the series 



3 + 7 + 9 + 4+8 + 5 say. 



As an instance where the method has an exceptional 

 advantage over ordinary multiplication we can take the 

 product 2307103405 x 60802040105. 



In less than two minutes we find mentally that the answer 

 is 140276593757192057525. 



It takes decidedly longer to do by the ordinary process. Of 

 course in a general case the difference will not be as great. 



Suppose it is required to evaluate a product only as far as 

 the first n significant figures. The rule for this is : start 

 the process with the right-hand digit on the slip under the 

 (n+l)th digit from the left of the multiplicand. For 

 example, to get 24968 x 4352 as far as the first 5 significant 

 figures we start thus :— 2 4 9 6 8 



|2534| . 



This gives 108660200, in which we can be sure only of the 

 first five figures. 



The transition from accurate to approximate and abbre- 

 viated multiplication is done quite naturally by this method 

 and involves learning only one rule. 



The use of an ordinary 12-inch slide-rule is equivalent to 

 the determination of the first 3 significant figures in products 

 of numbers like 534 and 869. 



534 



If we would proceed for 534 x 869 by starting at i 96g i 



we arrive at an answer 463500 while the exact result is 

 164046. This is as near as w r e can get on a slide-rule, so in 

 the absence of such an instrument the method just cited is a 

 good substitute. 



The reversed process, which enables one to perform mental 

 long division, is not so easily carried out, but with some 

 practice the method is not much more troublesome than 

 ordinary long division. 



The difficulties that arise are exactly the same as those 

 that arise for anyone learning ordinary long division for the 



