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never knew anything of arithmetic would do, had he to count a quantity of anything.
But here we have a different notation for every article or quantity we may have under our consideration ; there are notations for money, for time, for weight, and for
But let not the learner be disheartened; the requisite knowledge is easily acquired. By referring to the arithmetical tables at the beginning of the book, he will perceive the different notations necessary for him to use. Nor is it necessary that he should even learn them by rote; the few sums set down for practice, will be arranged as the tables are inserted in the book, and by carefully working the examples and referring to the tables, they will be sufficiently impressed upon the mind.
For in this as in any other science, our object ought to be to inform the reason, and keep the memory clear of incumbrance; to thoroughly understand the theory, and to be able to apply it when necessary; and when the necessity ceases, to have the mind disengaged, and at once to be able to employ it upon any other subject it may be necessary for us to take into consideration.
Add together the following sums of money, £43 6s. 9 d., £64 175. 10 d., £86 158. 3 d., and £76 14s. 94d.
In the above sum you perceive an £ written to denote the pounds, an s the shillings, and a d the pence; the half-pennies and farthings being written as in mixed numbers, in the same line as the pence. To work it you place the different sums in a column—the pounds under pounds, shillings under shillings, pence under pence, and farthings under farthings. You then commence to add at the lowest denomination-viz. farthings, and from your knowledge of fractions you know that half-pennies are two-fourths, and also that when the denominators are the same, we have but to add the numerators together.
And now you must observe the notation that we use in reckoning our money. Should our farthings exceed four, for every four we count one penny; and should there be any over, we write that sum under our farthings, and carry the pence to the pence. We then count up the pence; and if they exceed twelve, we write such remainder --that is, the sum left after extracting the twelves—under the pence, carrying one for each twelve we may have had, to the shillings; we then count up the shillings, and after extracting the twenties, we write the remainder under the shillings, and carry one for each twenty we may have had, to the pounds; pounds being the highest amount in which we keep accounts of money, are reckoned by tens, as in Simple Addition. You now know what I intended to convey when I spoke of notation; for here in one sum are four, each differing from the other; four, twelve, twenty, and ten.
4 farthings make id. 12 pence make 1s.
20 shillings make £1. and pounds are added, as in Simple Addition, by carrying the tens.
In adding the example, I find, by ad- £. s. d. ding the farthings, that there are nine.
43 6 91 Now this nine I do not write, but know
64 17 101
86 15 31 ing nine farthings to be twopence farthing,
76 14 98 I write down , or one farthing, and carry
271 14 91 two to the pence, which I find make 33; I do not write 33 pence, but I find that it makes two shillings and nine pence; I therefore write down the 9 under the pence, and carry two to the shillings, which, when added, make fifty-four; now as I know fifty-four shillings to be two pounds fourteen shillings, I write the sum of 14 shillings under the shillings, and carry two to the pounds, which I add as numbers are added in Simple Addition. Should you have to add sums having fractions expressed by longer terms, find a common denominator, then add your numerators together ; if their amount exceed the denominator, reduce it to a mixed number, writing the fraction under the fractions, and carrying the whole number to the pence. Should you not be able to determine at a glance how many shillings there are in the amount of your pence, divide by twelve, carrying the quotient to the shillings, and writing the remainder under the pence. In like manner when your shillings are added, divide the amount by twenty, carrying the quotient to the pounds, and writing the remainder under the shillings.
Exercise (1.) Add together the following sums : £64 19s. 8 d.; £6 17s. 6 d.; £79 14s. 7 d. ; £18 178. 1 d.; £16 14s. 2 d.; and £13 19s. 54d. € d.
£ s. d. (2.) Add 27 16 41 (3.) Add 14 5 4 19 17 31
17 16 2 16 19
29 7 6 0 13 47
107 3 81 29 16 7
14 19 113
£ s. d. (4.) Add 907 16 41
£ d. (5.) Add 794 19 2
416 17 98 976 14 11
0 13 71 19 17 48
309 17 63 714 19 33 763 14 6
(6.) A merchant purchased goods to the amount of £678 14s. 61d. ; paid for packing £1 4s. 2d.; for case 168. 4d.; for porterage, £1 48. 03d.; for freight,
4 Os. 6 d.; for booking, 9 d.; how much did he pay altogether?
Answers to Addition of Money.
2 83 (2.) 94 5 51
(4.) 2321 19 4.
ADDITION OF WEIGHTS AND MEASURES
A silversmith bought the following articles, viz. a silver tankard, weighing 5 oz. 11 dwt. 4 gr.; four silver plates, weighing 1 lb.7 oz. 19 dwt. 21 gr.; a ladle, weighing 3 dwts. and 6 grs. ; and a candlestick, which weighed 6 lbs. 5 oz. 7 dwt. 3 gr.; what was the entire weight of the several articles ? Having written the articles in a
lb. oz. dwt. gr. column, and each under its proper
0 5 11
19 head, we commence to add the
0 0 3 6 grains, which we find are 34 : now
3 as twenty-four grains Troy make
10 one pennyweight, I write 10 under the grains, and carry one to the dwts. which I find are thirty-two; twenty dwts, make one ounce, I therefore write 12 under the dwts., and carry one to the ounces, which I find to be eighteen ; now twelve ounces make one pound, I therefore write the overplus 6 under the ounces, carrying one to the pounds, which are added and written as in whole numbers.
lb. Ex. (1.) Add 5 2 15 22 (2.) Add 6 3 4 6 17
8 4 6 8 13
9 7 3 19 14
ADDITION OF APOTHECARIES' WEIGHT.