ARITHMETIC 



MULTIPLICATION. 



In multiplication two numbers are 

 given, and it is required to find how 

 much the first amounts to, when reckon- 

 ed as many times as there are units in the 

 second. Thus 8 multiplied by 5, or 5 

 times 8, is 40. The given numbers (8 and 

 5) are called factors; the first (8) the 

 multiplicand; the second (5) the multi- 

 plier ; and the amount (40) the product. 

 This operation is nothing else than addi- 

 tion of the same number several times re- 

 peated. If we mark 8 five times under 

 each other, and add them, the sum is 40 : 

 but as this kind of addition is of frequent 

 and extensive use, in order to shorten the 

 operation, we mark down the number 

 only once, and conceive it to be repeated 

 as often as there are units in the multipli- 

 er. For this purpose, the learner must 

 be thoroughly acquainted with the follow- 

 ing multiplication table, which is com- 

 posed by adding each digit 12 times. 



TABLE. 



In this table the multiplicand figures 

 are in the upper horizontal row ; the 

 multipliers are in the left hand column, 

 and the products will be found under the 

 multiplicand, and in the same row with 

 the multiplier; thus 9 times 11 are 99 ; 

 and 99 will be found in the column under 

 the 11, and in the same horizontal row 

 with the 9, among the multipliers. 



If both factors be under 12, the table 

 exhibits the product at once. If the mul- 



tiplier only be under 12, we begin at the 

 unit place, and multiply the figures in 

 their order, carrying the tens to the 

 higher place, as in addition. 



Example. 



76859 multiplied by 4 



4 



Ans. 307436 



or, 76859 added 4 times. 

 76859 

 76859 

 76859 

 Ans. 307436 the same as before. 



If the multiplier be 10, we annex a cy- 

 pher to the multiplicand. If the multi- 

 plier be 100, we annex two cyphers ; and 

 so on. The reason is obvious, from the 

 use of cyphers in notation. If the multi- 

 plier be any digit, with one or more cy- 

 phers on the right hand, we multiply by 

 the figure, and annex an equal number of 

 cyphers to the product. 



Thus, if it be required to multiply by 

 60, we first multiply by 6, and then annex 

 a cypher. It is the same thing as to add 

 the multiplicand 60 times ; and this might 

 be done by writing the account at large, 

 dividing the column into 10 parts of 6 

 lines, finding the sum of each part, and 

 adding these ten sums together. If the 

 multiplier consist of several significant 

 figures, we multiply separately by each, 

 and add the products. It is the same as 

 if we divided a long account of Addition 

 into parts corresponding to the figures of 

 the multiplier. 



Example. 



To multiply 7329 by 365 



7329 7329 7329 



5 60 300 



36645 439740 2198700 



36645 = 5 times.. 



439740 = 60 times. 



2198700 = 300 times. 



2675085 = 365 times. 



It is obvious that 5 times the multiph 

 cand added to 60 times, and to 300 times, 

 the same must amount to the product re- 

 quired. In practice, we place the pro- 

 ducts at once under each other; and as 

 the cyphers arising from the higher places 



