SiMPtt MULTIPLICATION. %% 



uie you are multiplying by, and carrying for the tens, a.'j 

 in addition^ 



3. Add all the lines together^ and their sum is the 

 product. 



Method 



Rule i. Cast the nines out of the two factx>rs, as in addition^ 

 and set down the remainder. 



2. Multiply the two remainders together, and if the excess of 

 nines in their product is equal to the excess of nines m the total 

 product, the answer is right. 



EXAMPLE. 



42T5 3=:exces3of 9's in the multiplicand. 

 878 5s=ditto in the multiplier. 



33720 

 29505 

 33720 



3 70G770 6:±ditto ill the product srescess of 9's in 3 X 



Demonstration OFTHE Rule. Let M and /^T be the number 

 of 9's in the faciors to be multiplied, and a and h "^^vhat remains , 

 then M^a and N^h vnW be the numbers themselves, and their 



product is Mx iV-f- M-^b^ NXa-^-axh-, but tlie three first of 

 these products are each a precise number of 9's, because one of 

 their factors is so : therefore, these being cast away, there re- 

 mains only <2 X ^ ; and if the 9's are also cast out of this, the 

 excess is the excess of 9's in the total product ; but a and h are 

 the excesses in the fectors themselves, and i^X^ their product j 

 therefore the rule is tree. (^ E. D. 



This method is Eable to the same incon?enIence with that in 

 addition. 



Multiplication- may also, very naturally, be proved by division ; 

 for the product being, divided by either of the factors, v.'ili cvi* 

 dendy give the otiier ; but it would have been contrary to good 

 method to have given this rule in the text, becauscT the pupii i*$ 

 supposed, as yet, to be unactjuainted with diyifion. 



