SIMPLE DIVISION. 3t 



;;. Divide 3756789275474 by 2. Ans. 1878394637737. 

 4. Divide 12345678900 by 7. Ans. 1763668414^. 



5. Divide 



The reason of this rule is extremely obvious : for the num- 

 bers, that are to be added, are the products of the divisor by eve- 

 ry figure of the quotient separately, and each possesses, by its place, 

 its complete Value ; therefore, the sum of the parts, together with 

 the remainder, must be equal to the 'whole. 



Rule III. Subtract the remainder from the dividend, and 

 what remains will be equal to the product of the divisor and quo- 

 tient ; which may be proved by casting out the nines, as was done 

 in multiplication. 



This rule has been already demonstrated in multiplication. 



To avoid obscurity, I shall give an example, proved according 

 to all the different methods. 



EXAMPLE. 



57)123456789(1419043 123456789 



87* ■ 87 48 



364 9933301 1419043) 123456741(87^0"! 



348* 1 1352344 1 1352344 



48 



• 165 9933301 



..87* 123456789 Proof by Mult. 993330I 



..786 

 ..783^ 



nines. 



. . . . 378 Proof ly cafi'ing out the 



.... 348* 4 is the excess of 9's in the quotient. 



6 ditto - . - - in the divisor. 



309 6 ditto in 4X6, which 



261* is also the excess of 9's in (12345674 1 ) 



the dividend made less by the remainder. 



48* 



123456789 Proof by Add: 



iLion. 



For illustration, we need only refer to the example j except 

 for the proof by addition ; where it may be remarked, that the 

 asterisms shew the numbers to be added, and the dotted Jines 

 'lieir order. / 



