MATHEMATICS 13 



by the addition of the separate figures which compose 

 them. 



Let us suppose that the number 2063 has to be multi- 

 plied 345 times; that means, either that the number 

 2063 has to be added to itself 345 times, or that the 

 number 345 has to be added to itself 2063 times, the 

 result of either process being of course the same. This 

 tedious process of addition is avoided by the device of 

 multiplication : 



Thus 2063 

 multiplied by 345 



produces 711735 



In this way we quickly arrive at the result of adding 

 2063 together, first 5 times, then 40 times, and lastly 300 

 times. If we wish to test the first process, we must see 

 that 2063 added together five times produces the same 

 result as the multiplication of that sum by the number 

 5, thus : 



2063 



2063 



2063 



2063 



2063 



10315 



In obtaining the same result by multiplying, we see 

 by the multiplication table just referred to, that 5 

 times 3 are 15. We therefore set 5 down at the 



