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



The usual process gives 79 — 2 x 8 — 9 x 7 = 0, so that at the 

 following stage our process gives us 8 — 72= —64, which 

 plainly is inadmissible on account of its negative sign. 

 Hsnce we must return to the stage just two before the last 



52 52 



where we put -£■ =9 and 7 t)ver, and instead we try — =8 



and 12 over. 



Thus the next slip position is 573 



I 822T1. 



The process is 129-2x8-8x7 = 57; ^-=8 and 17 over 



(as 9 and 12 over is abandoned on trial). 



We have now found the integral part of the answer to be 



12288, written on the slip as | 88221 | . If it is desired to 



obtain the fractional part in decimal form, it is only neces- 

 sary to continue the above process, adding zeroes to the 

 dividend as wanted. 



But if the " remainder" is required then one proceeds as 

 follows : — carrying on from the last stage we have as a new 

 slip position 678 



88221 



and the usual process is 178 — 8x8 — 8x7 = 58 ; then put 



— =0 and 58 over *. 

 5 



The next stage is 



and 583-8x8-0x7 = 519. 



As soon as all the figures in the dividend are used up we 

 stop, and the final figure 519 is the required remainder. 



This process for getting the remainder is seen to be justi- 

 fiable, if we begin the mental multiplication of 578 by 12288 

 and add 519 simultaneously. 



As it is not easy to explain the method of mental division 

 fully with one example, another is given in tabular form 

 (p. 395> 



In learning these mental methods it may be advisable at 

 first to perforin part of the calculation on paper, or to write 

 down the " carry over." But it is astonishing how soon one 

 can drop these crutches. 



N 

 * At each stage put -p = and N over, but otherwise proceed as usual. 



