ARITHMETIC. 



the next lower, taking in the given num- 

 ber of that denomination, and continue 

 the division. When the divisor is not 

 greater than 12, we proceed as before in 

 short division. 



Examples. 



L. s. d. L. s. d. 



5)84 . . 3 ..9 11)976 . . 13 . . 7 j 

 Ans.16 16 9 Ans.88 15 9^8 



Ib. o~. (hvts. civt. qr. Ib. oz. 

 8)994.. 4.. 8 12)45. .2. .18. .8 



124. .3. .11 3. .3.. 6. .3. .5 4 



When the divisor is greater than 12, 

 the operation is performed by long divi- 



Ejcample. 



L. s. d. 



Divide 8467 .. 16 .. 8 by 659. 



L. s. 



659)8467 .. 16 

 659 



1877 

 1318 

 .559 



20 



659)11196(16 

 659 

 1606 

 3954 

 7652" 

 12 



659)7832(11 

 7249 



d. 

 8(12 



659)2332(| 

 1977 

 .353 



Ans. 12 .. 16 .. llf iff 



In connection with the rule of division, 

 we may notice another kind of Reduc- 

 tion, so called, though Improperly, as by 

 it is meant to bring smaller denomina- 

 tions into larger : as pence into pounds, 

 or drams into hundred weights, &.c ; for 

 which the rule is : divide by the parts of 

 each denomination from that given to the 



highest sought : the remainders, if any, 

 will be of the same name as the quantity 

 from which they were reduced. 



Examples. 



1. In 415684 farthings, how mawy 

 pounds sterling. 



4)415684 

 12)103921 

 2,0)866.0-1 

 Ans. /. 433 .. U .. 1 



2. How many pounds troy are there i 

 6789J dwts. 



2,0)6789,0 

 12)3394 - 10 



2827. 10.. 10 



Ib. 

 Ans. 282 



oz. 

 10 



dwts. 

 10. 



Before we conclude this article we may 

 observe, that, in computations which re- 

 quire several steps, it is often immaterial 

 what course we follow. Some methods 

 may be preferable to others, in point of 

 ease and brevity ; but they all lead to the 

 same conclusion. In addition or subtrac- 

 tion, we may take the articles in any order. 

 When several numbers are to be multipli- 

 ed together, we may take the factors in 

 any order, or we may arrange them into 

 several classes ; find the product of each 

 class, and then multiply the products to- 

 gether. When a number is to be divided 

 by several others, we may take the divi- 

 sors in any order, or we may multiply 

 them into one another, and divide by the 

 product; or we may multiply them into 

 several parcels, and divide by the pro- 

 ducts successively. Finally, when multi- 

 plication and division are both required, 

 we may begin with either; and when 

 both are repeatedly necessary, we may 

 collect the multipliers into one product, 

 and the divisors into another; or we may 

 collect them into parcels, or use them 

 singly ; and that in any order. To begin 

 with multiplication is generally the better 

 mode, as this order preserves the account 

 as clear as possible from fractions. 



We have hitherto given the most ready 

 and direct method of proving the forego- 

 ing examples, but there is another, which 

 is very generally used, called " casting 

 out the 9's," which depends on this prin- 

 ciple : That if any number be divided by 

 9, the remainder is equal to the remainder 



