ARITHMETIC. 



The following examples will furnish 

 he learner with practice. 



1. 21 ells of Holland, at'Ts. 8$d.per ell. 



Jlns. L8 .. 1 .. 10. 



2. 35 firkins of butter, at 155. 3$d. per 

 firkin. jj ns . L26 .. 15 .. 2 



3. 75 Ib. of nutmegs, at 7s. 2$d. per lb. 



Ans. L27 .. 2 .. 2. 



4. 37 yards of tabby, at 9s. 7d. per yard. 



Jlns. L\7 .. 14 .. 7. 



5. 97 cwt. of cheese, at II. 5s. 3d. per 

 cwt. ^ n5 . 122 ..9 .. 3. 



6. 43 dozen of candles, at 6s. 4d. jftcr 

 doz - ^zs. 13 .. 12 .. 4. 



7. 127 #. of bohea tea, at 12s. 3d. per 

 lb - Jlns. L77 .. 15 .. 9. 



8. 135 gallons of rum, at 7s. 5d. per gal- 

 lo- Jlns. 50 .. 1 .. 3. 



9. 74 ells of diaper, at 1*. 4$il.per ell 



Jlns. L5 .. 1 .. 9. 



The use of multiplication is to compute 

 the amount of any number of equal arti- 

 cles, either in respect of measure, weight, 

 value, or any other consideration. The 

 multiplicand expresses how much is to 

 be reckoned for each article, and the 

 multiplier expresses how many times that 

 is to be reckoned. As the multiplier 

 points out the number of articles to be 

 added, it is always an abstract number, 

 and has no reference to any value or mea- 

 sure whatever. It is therefore quite im- 

 proper to attempt the multiplication of 

 shillings by shillings, or to consider the 

 multiplier as expressive of any denomi- 

 nation. The roost common instances, in 

 which the practice of this operation is 

 required, are to find the amount of any 

 number of parcels, to find the value of 

 any number of articles, to find the weight 

 or measure of a number of articles, &c. 

 This computation for changing any sum 

 of money, weight or measure, into a dif- 

 ferent kind, is called Reduction. When 

 the quantity given is expressed in differ- 

 ent denominations, we reduce the highest 

 to the next lower, and add thereto the 

 given number of that denomination ; and 

 proceed in like manner till we have re- 

 duced it to the lowest denomination. 



Ex. Reduce 581. 4s. 2$d. into farthings. 

 58 .. 4 .. 2i 



20 

 1164 s- shillings in 58 .. 4. 



13970 =s pence in L58 ., 4 .. 2. 



4 



Ans. 55882 = farthings in 58 .. 4 .. 2 



DIVISION. 



In division two numbers are given, and 

 it is required to find how often the for- 

 mer contains the latter. Thus it may be 

 asked how often 21 contains 7, and the 

 answer is exactly 3 times. The former 

 given number (21) is called the dividend ; 

 the latter (7) the divisor ; and the num- 

 ber required (3) the quotient. It fre- 

 quently happens that the division cannot 

 be completed exactly without fractions. 

 Thus it may be asked, how often 8 is con- 

 tained in 19 ? the answer is, twice, and 

 the remainder of 3. This operation con- 

 sists in subtracting the divisor from the 

 dividend, and again from the remainder, 

 as often as it can be done, and reckoning 

 the number of subtractions. As this ope- 

 ration, performed at large, would be very 

 tedious, when the quotient is a high num- 

 ber, it is proper to shorten it by every 

 convenient method ; and, for this purpose, 

 we may multiply the divisor by any num- 

 ber, whose product is not greater' than 

 the dividend, and so subtract it twice or 

 thrice, or oftener, at the same time. The 

 best way is, to multiply it by the greatest 

 number that does not raise the product 

 too high, and that number is also the 

 quotient. For example, to divide 45 by 

 7, we inquire what is the greatest multi- 

 plier for 7, that does not give a product 

 above 45; and we shall find that it is 6 ; 

 and 6 times 7 is 42, which, subtracted 

 from 45, leaves a remainder of 3. There- 

 fore 7 may be subtracted 6 times from 45; 

 or, which is the same thing, 45 divided 

 by 7, gives a quotient of 6, and a remain- 

 der of 3. If the divisor do not exceed 12, 

 we readily find the highest multiplier 

 that can be used from the multiplication 

 table. If it exceed 12, we may try any 

 multiplier that we think will answer. If 

 the product be greater than the dividend, 

 the multiplier is too great ; and if the re- 

 mainder, after the product is subtracted 

 from the dividend, be greater than the 

 divisor, the multiplier is too small. In 

 either of these cases we must try another. 

 But the attentive learner, after some prac- 

 tice, will generally hit on the right multi- 

 plier at first. If the divisor be contained 

 oftener than ten times in the dividend, 

 the operation requires as many steps as 

 there are figures in the quotient. For 

 instance, if the quotient be greater than 

 100, but less than 1000, it requires three 

 steps. 



