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COMPOUND ADDITION.

COMPOUND ADDITION is the adding together of Compound Numbers.

RULE.-1. Write down the given numbers in such a way that those of the same kind or denomination may stand directly below one another-pounds under pounds, shillings under shillings, &c.

2. Add the numbers in the lowest denomination, and find how many of the next higher denomination are contained in the amount. Carry the quotient to the next column, marking any remainder below the column just added.

3. Add the numbers of the next denomination in the same way, including what has been brought from the previous column, and so on, till all the denominations have been added. The highest denomination is added as in Simple Addition.

Example 1.-Add together the following sums-£31, 12s. 7 d., £73, 14s. 8 d., £69, 17s. 5 d., £87, 15s. 64d., and £37, 12s. 3 d.

£ S. d. 31 12 71 73 14 8 69 17 53 87 15 61 37 12 31 £300 12

71/

Here, after writing down £ s. d., place the pounds under £, the shillings under s., and the pence with the farthings under d.; and draw a line under the figures. Beginning with the farthings, we have first, or 2 farthings, then 1, 3, 2, 2— in all, 10 farthings. These are converted to pence, and make 23d.; put down the, and carry This being added, 2d. to the pence column. makes 31 pence, or 2 shillings and 7 pence: write the 7 under the pence, and carry the 2 to the unit row of shillings; adding it, we have 2, 2, 5, 7, 4, and 2—in all, 22: then, going to the next column, the figures in which are all tens, we say 22 and 10 are 32, then 42, 52, 62, 72-in all, 72 shillings, which, being converted to pounds, make £3, 12s.; 12, therefore, is written under the shillings, and 3 carried to the pounds, which are now added, and the amount put down as in Simple Addition.

NOTE. In adding the shilling column, the following is the most convenient method:-Add the unit row of shillings as already described in the foregoing example, it amounts to 22; mark the last figure, 2, below the unit row, and carrying the tens, 2, to the tens' row, add it also: then halve the amount (that is, divide it by 2); if 1 remains after halving, mark 1 below the tens' row, and carry the half to the pounds. If nothing remains on halving, carry the half to the pounds, but without marking anything below the tens' row of shillings. In the present example, the tens' row amounts to 7, which, being halved, makes 3, and 1 over; therefore mark the 1 below the tens row of shillings, and carry 3 to the pounds.

The halving of the tens' row of shillings is merely a short way of dividing the amount of the shillings by 20, to convert them to pounds.

Example 2.-Add together 3 tons 7 cwts.

qrs. 17 lbs. 5 oz.; 7 tons 3 cwts. 2 qrs. 13 lbs.; 8 tons 12 cwts. 3 qrs. 4 lbs. 7 oz.; 6 tons 17 cwts. 2 qrs. 10 lbs. 9 oz.; 12 tons 9 cwts. 2 qrs. 18 lbs. 13 oz.

207

tons. cuts. qrs.

lbs.

3

7 2

17

5

7

3 2

13

8

12

3

6

17

2

10

12

9

2

18

38 11 1

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9

13

2

Here having written down in a line the marks for tons, hundredweights, quarters, pounds, and ounces, write each quantity under its proper name, and draw a line under all. Commencing to add at the ounces, we find there are 34; now, 16 ounces being a pound, 34 oz. are equal to 2 lbs. and 2 oz.: put down the 2 oz. under the ounces, and carry the 2 lbs. to the pound column. Adding this column, there are 64 lbs., which, being converted to quarters, gives 2 qrs. and 8 lbs. over; the 8 lbs. are written under the pounds, and the 2 qrs. carried to the column of quarters. This being added, gives 13; and 13 qrs. converted to cwts., give 3 cwts. and 1 qr.; put down 1 under the qrs., and carry 3 to the cwts. Adding these, we find there are 51 cwts., which, being converted to tons, give 2 tons, and 11 cwts. over; write 11 under the cwts., and carry 2 to the tons. These are now added, and their amount put down as in Simple Addition.

All compound quantities being added on the same principles as the above, it is unnecessary to give examples of the addition of the other weights and measures.

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Miscellaneous Exercises.

1. Bought a pair of boots for 18s. 6d., a pair of hat for 13s. 8d., and a pair of gloves for 2s. 3d. I expend altogether?

shoes for 7s. 6d., How much did Ans. £2, 1s. 11d.

2. Paid for tea 5s. 6d., for sugar 3s. 4d., for coffee 2s. 4d., for butter 3s. 6d., for cheese 5s. 3d., for beef 12s. 4d. How much did all come to? Ans. £1, 12s. 3d.

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3. A shopkeeper owes the following sums: -To A, £7, 15s. 91d.; to B, £8, 15s. 6d. ; to C, £27, 13s. 44d.; to D, £35, 10s. 4d.; to E, £29, 3s. 104d.; to F, £18, 12s. 5d. What is the amount of his debts ? Ans. £127, 11s. 34d.

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4. A family is owing £3, 7s. 4d. to the baker, £4, 15s. 94d. to the butcher, £4, 13s. 34d. to the grocer, £1, 8s. 3d. to the shoemaker, £6, 14s. Sd. to the tailor, £8, 13s. 74d. to the draper. How much money will it require to pay off these debts?

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Ans. £29, 12s. 114d. 5. A butcher supplied a family with 64 lbs. of beef on Monday, 4 lbs. on Tuesday, 7 lbs. on Wednesday, 8 lbs. on Thursday, 62 lbs. on Friday, and 10 lbs. on Saturday. What did the week's supply amount to? Ans. 433 lbs., or 3 st. 13 lbs.

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6. A grocer sold 7 lbs. 6 oz. tea on Monday, 9 lbs. 10 oz. on Tuesday, 5 lbs. 12 oz. on Wednesday, 14 lbs. 9 oz. on Thursday, 10 lbs. 3 oz. on Friday, and 18 lbs. 5 oz. on Saturday. How much was the week's sale? Ans. 65 lbs. 13 oz. 7. A tea-merchant buys 6 chests of tea. No. 1 weighs 3 qrs. 12 lbs.; No. 2, 3 qrs. 17 lbs.; No. 3, 1 cwt. 7 lbs. ; No. 4, 1 cwt. 1 qr.; No. 5, 3 qrs. 23 lbs.; and No. 6, 3 qrs. 13 lbs. What is the total weight? Ans. 5 cwts. 3 qrs. 16 lbs.

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8. What is the weight of 5 hhds. sugar? No. 1 weighing 15 cwts. 3 qrs. 13 lbs.; No. 2, 13 cwts. 2 qrs. 7 lbs.; No. 3, 17 cwts. 1 qr. 18 lbs.; No. 4, 14 cwts. 3 qrs. 15 lbs.; and No. 5, 16 cwts. 1 qr. 13 lbs. Ans. 78 cwts. O qrs. 10 lbs.

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9. A silversmith sold a gentleman silver-plate as follows:-Dishes, 7 lbs. 6 oz. 7 dwts.; plates, 5 lbs. 9 oz. 12 dwts.; spoons, 2 lbs. 6 oz. 13 dwts.; a tea-service weighing 4 lbs. 7 oz. 4 dwts. What was the total weight? Ans. 20 lbs. 5 oz. 16 dwts. 10. A draper bought 6 ends cloth: the first contained 37 yds. 3 qrs., 2 nails; the second, 28 yds. 2 qrs. 3 nails; the third, 43 yds. 3 qrs. 1 nail; the fourth, 37 yds. qrs.; the fifth, 47 yds. 1 qr. 2 nails; the sixth, 39 yds. and 3 nails. How many yards are in all? Ans. 234 yds. 1 qr. 3 nails. 11. A hop-merchant bought 5 bags of hops, of which the first weighed 2 cwts. 3 qrs. 13 lbs.; the the third, 2 cwts. 3 qrs. 5 lbs. ; the the fifth, 2 cwts. 3 qrs. 17 lbs. whole ?

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second, 2 cwts. 3 qrs. 11 lbs. ; fourth, 2 cwts. 3 qrs. 12 lbs. ; What is the weight of the Ans. 14 cwts. 1 qr. 2 lbs.

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