COMPOUND ADDITION. COMPOUND ADDITION, is the adding of the parts of integers, such as shillings, pence, farthings, ounces, &c. called different denominations. RULES. 1. Place like parts under each other, viz. farthings under farthings, pence nuder pence &c. 2. Begin at the lowest parts, and carry according to the value of an unit of the next superiour denomination; viz. for every 4 in the sum of farthings carry 1 t the column of pence, and for every 12 in the sum of pence carry 1 to the column of shill gs, &c. Proceed in this manner with each column, till you come to the last, which is the same as Simple Addition. The reason of this rule is plain, from the table of coin following N. B. If you carry at 20, 30, 40 60, or any just number of tens, as in adding shillings, degrees, poles. (or roods) minutes, seconds, &c. proceed with the column of units as in addition of integers, and from the sum of the column of tens carry 1 for every 2, or 1 for every 3, &c. according as 20, (or two tens) 30, (or three ten-) &c. make an unit of the next superiour denomination. The reason is evident as in the following operations. 1. What is the sum of £78. 17s 1d.-£16. 78. 5d.-and of 19s. 6d. when added together? £3. OPERATION. £. S. d. 78 17 1 16 7 5 3 19 6 Sum, 99 4 Having, according to rule 1, placed like parts under each other, I begin with the pence column, and say 6 and 5 make 11, and 1 makes 12. the sum of the parts, or numbers. Now, as 12 of this denomination make one of the next higher, or, agreeably to the pence table, 12 pence make one shilling. I inquire how often 12 is contained in 12, the sum of the first column, or that of peace, and 0 finding it to be once, and nothing over, I set down O under the column of peace, and carry one to that of shillings, to be adjod to the second column. saying, 1 I carry to 9 makes 10, and 7 are 17, and 7 are 24; and because in shillings we carry at a just naaber of tens, viz. at 20, I set down 4 my right hand figure, below, in the place of units, as die rected in the rule, and carry 2 tens to the place of teus; thus: 2 tens, collected out of the units, and 1 ten, make 3 tens, and 1 makes 4 tens, or 2 twenties; and because 2 teus, or 1 tweaty, nake an unit in the next lace, viz. that of pounds, I carry my 2 twenty shillings, or 2 pounds, to the place of pounds, which, being integers, are added as taught in Simple Addition. For the readier despatch in casting up pence, the learner is requested to commit to memory the following PENCE TABLE. 3. d 1 0 Pence. 12 20 30 3 40 1 8 2 6 345 4 2 5 이 5 10 6 8 6 50 60 70 are 80 9 2 4 16 8 EXPLANATION. Read the table thus: 12 pence are one shilling; 20 peuce are 1 shilling and 8 pence; 30 pence are 2 shillings and 6 pence; 40 pence are 3 smugs and 4 pence, &c. PROOF. Compound Addition may be proved several ways, as is shewn in Simple Addition. Thos~ 1. Merchants, and men of business, nsually add each column, first upwards and then downwards, and if both sums agree, the work is allowed to be right. 2. By casting out the nines. If the items are of different denominations, as pounds, shillings, pence, &c. you must begin with the highest denomination, and after casting out the 9's, reduce the excess to the next inferiour denomination, and then casting out the 9's, reduce the excess to the next inferior denomination. Proceed in like manner with this and all the other wer denominations, placing the last excess at the top of the cross; then. in like manner, cst the 9's out of the total, placing the exc s the f ot of the cross, and if the figures at the foot and top be the same, the work may be presumed to be right. First, I begin with the pounds, and say 4+8=12=1 +2=3, and 3+5=8, and 8+5=13=1+3=4; a d the exces. 4. reduced to shillings is 4×20=80=8, and 8+1=9=0; then 7+1=8, and 8+8=16=1+6=7; and the excess. 7, reduced to pence; i- 7× 12=84=8+4=12=1+2=3, and 3+1=4. and 3+7=1i=1+1=2; and the Xess, 2. dared to farthings, is 2×4=8, and 8+1=9=0, and+2=2. So this 2, being the excess of the items, I place at the top of the cross, and proceed to cast the 9's out of the total, saying 14. 4=5,and the excess, 5, reduced to shillings, is 5×20=100=1, and 1 +1=2, and 2+6=8; and this excess, 8, reduced to pence, is 8×12 =96=6, and 6+5=11=2; and this excess, 2, reduced to farthings, is 2X4=8, and 8+3=11=1+1=2; which excess, 2, 1 place at the foot of the cross, and because it is the same with the figure at the top, I conclude the work is right. 5. A person dying, left for the use of his widow £4000; to each of his four sons £4256; to each of his five daughters £3678; to each of his six near relations £245: what was his estate? Ans. £40,884. 6. A gentleman, on a journey, summing up his expenses, wanted to know the entire amount of his charges since his departure from home, which was on the 1st of April, 1821. The first day he pays for breakfast, for oats, for his horse, Second day, for shoeing his horse, 0 3 0 1 0 1 0 1 0 2 9 7. Suppose I owe one person £5 4s 6d.-another £7 11s. 9d.another £4.7s. 5d.-another £7 8s. 4d-another £8 Os. Od —and another £9 7s. 6d. how much do i owe in all, to these several perBons? Ans. 2. OF TROY WEIGHT. By Troy Weight are weighed gold, silver, jewels, amber, electuazies, and liquors. TABLE. NOTE. 1 avoirdupois is equal to 14oz. 11pwts. 15grs. Troy. 21 18 EXAMPLES. 20. 1 02. prts. grs. 48 11 18 42 10 14 40 9 16 36 22. 14. 13 12 In adding this example, I begin with the grains, and say 13 and 4 make 17, and one ten on the left make 27, which being above 24, I dot, and go on with the excess, 3, saying 3 and 2 make 5, and two tens, or 20, on the left, make 25; where I again dot, and proceed with the excess, 1, saying, 1 and 20 make 21, and 8 make 29; where I dot, and go on with the excess, 5, saying 5 and one 10 on the left hand make 36. I set down the excess, 12, and carry away 4 for the dots to the pennyweights. In adding up the pennyweights you carry at 20, which, therefore, are added like shillings. In the ounces you carry at 12, which are added as pence. The pounds are integers, and as such, therefore, you must carry according to the value of the higher denomination. Some men of business add the grains as integers, and setting down the sum on a separate paper, divide by 24, and then placing the remainder, as the excess, under the grains, and carry the quotient to the penny weights. By avoirdupois weight are weighed butter, cheese, rosin, wax, pitch, tallow, hay, flax, beef, brass, iron, steel, tin, copper, and all kinds of metals, except gold and silver; groceries, such as tea, sugar, bread, and all things of a coarse nature. gers, and then divide the sum by 16 or 28, setting down the remainder as the excess, and carry the quotient. APOTHECARIES WEIGHT. By this weight, apothecaries compound their medicines, their pound being the same as the pound froy, but differently, divided; yet they buy and sell their drugs by Avoirdupois. |