and Division of Large Numbers. 393 



first time. These difficulties disappear in the mental method 

 with practice, as they do in the other. 



Let us take as an example 7102983-^578. This time we 

 use the slip o£ paper to write the answer on, backwards, as 

 will be seen. 



Start with the right end of the blank slip under the 5 in 

 578, thus : 57 8 



IZZD 





and under the 5 write the obvious first figure in the answer, 

 namely 1. Then subtract 1x5 from the 7 in the dividend 

 leaving 2, which together with the 1 in the dividend forms 

 21 for the next stage. 



Now move the slip one figure to the right, thus : 



578 



CIZIl 



14 

 The process is 21 — 1 x 7 = 14 ; -v- =2 and 4 over. 



Write down 2 on the slip under the 5, while the 4 

 together with the in the dividend forms 40 for the next 

 stage. 



Again move the slip one figure, thus : — 573 



21 



18 

 and perform the process 40 — 1x8 — 2x7 = 18; — =3 and 



3 over. . ° 



On trial, however, it will be found that the 3 is too high, 



IS 



so we will take -=- =2 and 8 over. 



5 



Write down 2 on the slip under the 5, while the 8 

 together with the 2 in the dividend forms 82 for the next 

 stage. 



The next position of the slip is 



578 



32lL 



Perform the process 82-2x8-2x7=52; y«9 and 

 7 over (since 10 is inadmissible as a digit). 



For the next stage we have 79 and the position 



578 

 I 9221 I . 



