83. IF we wish to subtract £15 13s. 10d. from £20 5s. 8d., we proceed as follows:

OPERATION.

£ S. d. 20 5 8 15 13 10 4 11 10

We place the numbers of the subtrahend directly under the numbers of the same denomination in the minuend, and draw a line underneath. Commencing with the pence, we see that we cannot subtract 10d. from 8d.; we therefore increase the 8d. by 12d. making 20d.; then subtracting 10d. from the 20d., we have the difference 10d., which we write under the column of pence. Having added 12d. to the minuend, we must equally increase the subtrahend, which we do by

adding ls. (the same as the 12d.,) to the 13s., making 14s. This cannot be subtracted from 5s. ; we therefore increase the 5s. by 20s., making 25s. Now, subtracting 14s. from 25s. we have 11s., which we write under the column of shillings. Before subtracting the pounds, we add £1 to £15 to compensate for the 20s. added to the 5s., and then say £16 from £20 leaves £4.

NOTE. It will be seen that this process is similar to that in the "shorter and more practical" example of simple subtraction, (ART. 12.) But the preceding subtraction might be also performed as in the second example of simple subtraction.

Hence, we have this general

RULE.

I. Place the less number under the greater, so that the same denominations may stand under each other; draw a line below them.

II. Begin at the right, and subtract each number in the lower line from the one directly above it, and set the remainder below.

III. If any number in the lower line is greater than the one above it, add so many to the upper number as make one of the next higher denomination; then subtract the lower number from the upper one thus increased, and set down the remainder. Carry 1, expressing the increase of the upper line, to the next number in the lower line; after which subtract this number from the one above it, as before; and thus proceed till all the numbers are subtracted.

PROOF.

If the work be right, the difference added to the subtrahend will equal the minuend; as in simple subtraction.

1. Bought 20 yards of broadcloth for £18 5s. 3d., 30 pounds of feathers for £8 2s. 4d., 100 yards carpeting for

£45 17s. 8d., 10 pieces of cotton cloth for £8 18s. 1d., 50 yards of calico for £2 0s. 10d. What was the cost of the whole? Ans. £83 4s. 2d.

2. Bought four hogsheads of sugar, weighing as follows 1st weighed 8cwt. 1qr. 231b. 10oz.; 2d weighed 9cwt. 2qr. Olb. 3oz.; 3d weighed 10cwt. Oqr. Olb. 8oz.; 4th weighed 8cwt. 3qr. 271b. How much did the four weigh? Ans. 36cwt. 3qr. 23lb. 5oz.

3. A man owns three farms; the first contains 69 acres, 3 roods, 10 rods; the second contains 100 acres, 5 rods; the third contains 150 acres, 2 roods. How many acres are there in all? Ans. 320A. 1R. 15P.

4. Suppose a note given August 3d, 1838, to be paid November 10th, 1843. How long was the note on interest, if we count 30 days to the month? and how long if the time is accurately computed? 1st Ans. 5yr. 3mo. 7da. 2d Ans. 1925 days.

5. A person buys 15cwt. 3qr. 2016. of sugar, and sells 10cwt. Oqr. 11lb. How much remains unsold?

Ans. 5cwt. 3qr. 9lb.

6. From a piece of cloth containing 37yd. 3qr. 2n., there has been taken at one time 6yd. 1qr., at another time 10yd. 3qr. 3na. How much then remains? Ans. 20yd. 2qr. 3na.

7. From a pile of wood containing 100 cords, I sold at one time 10C. 100S. ft., at another time I sold 18C. 59S.ft. How many cords remain unsold? Ans. 70C. 97 S. ft.

8. A farmer raises 100bu. 3pk. 2qt. of wheat from one field, 87bu. 1pk. 1qt. 1pt. from another field; he sells 53bu. to one person, and 37bu. 2pk. 1qt. to another person. How many bushels has he remaining? Ans. 97bu. 2pk. 2qt. 1pt.

9. Bought 5 loads of coal. The first weighed 2056 pounds, the second weighed 2250, the third weighed 2240,