=

Next, adding up the column of shillings, together with the 1 s. which we reserved, we find the amount to be 23 s 1.3s. Setting the 3s. under its own column, we add the 1£. with the other pounds, and, finding the amount to be 41 £., we write it down, and the work is done.

Ans. 41 £. 3 s. 6 d.

Note. It will be recollected, that, to reduce a lower into a higher denomination, we divide by the number which it takes of the lower to make one of the higher denomination. In addition, this is usually called carrying for that number: thus, between pence and shillings, we carry for 12, and between shillings and pounds, for 20, &c.

The above process may be given in the form of a general RULE for the Addition of Compound Numbers:

I. Write the numbers to be added so that those of the same denomination may stand directly under each other.

II. Add together the numbers in the column of the lowest denomination, and carry for that number which it takes of the same to make one of the next higher denomination Proceed in this manner with all the denominations, till you come to the last, whose amount is written as in simple numbers.

Proof. The same as in addition of simple numbers.

EXAMPLES FOR PRACTICE.

Bought a silver tankard, weighing 2 lb. 3 oz., a silver cup, weighing 3 oz. 10 pwt., and a silver thimble, weighing 2 pwt. 13 grs.; what was the weight of the whole?

A man bought 5 loads of hay, weighing as follows, viz. 23 cwt. ( = 1 T. 3 cwt.) 2 qrs. 17 lb.; 21 cwt. 1 qr. 16 lb. ; 19 cwt. 0 qr. 24 lb.; 24 cwt. 3 qrs.; 11 cwt. 0 qr. 1lb.; how many tons in the whole?

There are four pieces of cloth, which measure as follows, viz. 36 yds. 2 qrs. 1 na.; 18 yds. 1 qr. 2 na.; 46 yds. 3 qrs. 3 na.; 12 yds. 0 qr. 2 na.; how many yards in the whole ?

There are 3 fields, which measure as follows, viz. 17 A. 3 r. 16 p.; 28 A. 5 r. 18 p.; 11 A. 0 r. 25 p.; how much land in the three fields?

A merchant bought two casks of brandy, containing as follows, viz. 70 gal. 3 qts.; 67 gal. 1 qt.; how many hogsheads, of 63 gal. each, in the whole ?

SUBTRACTION

OF COMPOUND NUMBERS.

39. 1. A boy bought a knife for 9 cents, and sold it for 17 cents; how much did he gain by the bargain?

2. A boy bought a slate for 2 s. 6 d., and a book for 3 s. 6 d., how much more was the cost of the book than of the slate? 3. A boy owed his playmate 2 s.; he paid him 1 s. 6 d. ; how much did he then owe him?

4. Bought two books; the price of one was 4 s. 6 d., the price of the other 3 s. 9 d.; what was the difference of their costs?

5. A boy lent 5 s. 3 d.; he received in payment 2 s. 6 d.; how much was then due ?

6. A man has a bottle of wine containing 2 gallons and 3 quarts; after turning out 3 quarts, how much remained? 7. How much is 4 gal. less 3 gal. ? 4 gal. 4 gal.1 qt.? 4 gal. -1 gal. 1 qt.? 4 gal. 4 gal. 1 gal. 3 qts.? 4 gal. 2 gal. 3 qis.?

1 gal. 3 qts.?

8. How much is 1 ft.

(less) 6 in.? 1 ft.

(less) 2 qts.? 1 gal. 2 qts.? 4 gal. 1 qt.

8 in.? 6 ft.

9. What is the difference between 4 £. 6 s. and 1£. 8 s. ? 10. How much is 3£. (less) 1 s.? 3£. - 2 s.? 3£.

3 s.? 3£.

5£. 8. s?

-

15 s. 3. 4 s. -2£. 6 s.? 10£. 4 s.

11. A man bought a horse for 30£. 4 s. 8., and a cow for 5£. 14 s. 6 d. ; what is the difference of their costs?

.;

OPERATION.

£. S. d.

Minuend, 30 4 8
Subtrahend, 5

14 6

Ans. 24 10 2

As the two numbers are large, it will be convenient to write them down, the less under the greater, pence under pence, shillings under shillings, &c. We may now take 6 d. from 8 d., and there will remain 2 d. Proceeding to the shillings, we cannot take 14 s. from 4 s., but we may borrow, as in simple numbers, 1 from the pounds, 20 s., which joined to the 4 s. makes 24 s., from which taking 14 s. leaves 10 s., which we set down. We must now carry 1 to the 5£., making 6£., which taken from 30£. leaves 24€., and the work is done. Note. The most convenient way in borrowing is, to sub

H*

=

tract me subtrahend from the figure borrowed, and add the difference to the minuend. Thus, in the above example, 14 from 20 leaves 6, and 4 is 10.

The process in the foregoing example may be presented in the form of a RULE for the Subtraction of Compound Numbers.

I. Write down the sums or quantities, the less under the greater, placing those numbers which are of the same denomination directly under each other.

II. Beginning with the least denomination, take successively the lower number in each denomination from the upper, and write the remainder underneath, as in subtraction of simple, numbers.

III. If the lower number of any denomination be greater than the upper, borrow as many units as make one of the next higher denomination, subtract the lower number therefrom, and to the remainder add the upper number, remembering always to add 1 to the next higher denomination for that which you borrowed.

Proof. Add the remainder and the subtrahend together, as in subtraction of simple numbers; if the work be right, the amount will be equal to the minuend.

EXAMPLES FOR PRACTICE.

1. A merchant sold goods to the amount of 136 £.7 s. 61 d., and received in payment 50£. 10 s. 4d; how much remained due ? Ans. 85. 17 s. 12 d. 2. A man bought a farm for 1256 £. 10 s., and, in selling it, lost 87£. 10 s. 6 d.; how much did he sell it for? Ans. 1168£. 19 s. 6 d. 3. A man bought a horse for 27£. and a pair of oxen for 19. 12 s. 8 d.; how much was the horse valued more than the oxen?

4. A merchant drew from a hogshead of molasses, at one time, 13 gal. 3 qts. ; at another time, 5 gal. 2 qts. 1 pt.; what quantity was there left? Ans. 43 gal. 2 qts. 1 pt. 5. A pipe of brandy, containing 118 gal. sprang a leak, when it was found only 97 gal. 3 qts. 1 pt. remained in the cask; how much was the leakage?

6. There was a silver tankard which weighed 3 lb. 4 oz. ; the lid alone weighed 5 oz. 7 pwt. 13 grs.; how much did the tankard weigh without the lid ?