§ XI. ADDITION OF COMPOUND NUMBERS.

ART. 101. ADDITION of Compound Numbers is the process of finding the amount of two or more compound numbers.

ENGLISH MONEY.

Ex. 1. Paid a London tailor 7£. 13s. 6d. 2far. for a coat; 2£. 17s. 9d. 1far. for a vest; 3£. 8s. 3d. 3far. for pantaloons; 9£. 11s. 8d. 3far. for a surtout; what was the amount of the bill? Ans. 23£. 11s. 4d. 1far:

OPERATION.

1

£. S.

d. far.

7 13 6

2

2 17

9

3

8 3

3

9

11

8

3

Having written units of the same denomination in the same column, we find the sum of farthings in the right-hand column to be 9 farthings, equal to 2d. and 1far. We write the lfar. ùnder the column of farthings, and carry the 2d. to the column of pence; the sum of which is 28d., equal to 2s. 4d. We write the 4d. under the column of pence, and carry the 2s. to the column of shillings; the sum of which is 51s., equal to 2£. 11s. Having written the 11s. under the column of shillings, we carry the 2£. to the column of pounds, and find the whole amount to be 23£. 11s. 4d. 1far.

Ans. 23 11 4 1

The same result can be arrived at by reducing the numbers as they are added in their respective columns. Thus, in working the example, we can, beginning with farthings, add in this way: 3far. and 3far. are 6far., equal to 1d. 2far., and 1far. are 1d. 3far., and 2far. are 1d. 5far., equal 2d. 1far. Writing the lfar. under the column of farthings, carry the 2d. to the column of pence; add 2d. (carried) and 8d. are 10d., and 3d. are 13d., equal to 1s. 1d., and 9d. are 1s. 10d., and 6d. are 1s. 16d., equal to 2s. 4d. Writing the 4d. under the column of pence, carry the 2s. to the column of shillings; add 2s. (carried) and 11s. are 13s., and 8s. are 21s., equal to 1£. 1s., and 17s. are 1£. 18s., and 13s. are 1£. 31s., equal to 2£. 11s. Writing 11s. under the column of shillings, carry the 2£. to the column of pounds, and so find the whole amount to be, as before, 23£. 11s. 4d. 1far.

Thus the adding of compound numbers is like that of simple numbers, except in carrying; which difference holds also in subtracting, multiplying, and dividing of compound numbers.

QUESTIONS. Art. 101. What is addition of compound numbers? How do you arrange compound numbers for addition? Why? What is the difference between addition of compound and addition of simple numbers?

RULE. Write all the given numbers so that units of the same denomination may stand in the same column.

Add as in addition of simple numbers; and carry, from column to column, one for as many units as i takes of the denomination added to make a unit of the denomination next higher.

PROOF. The proof is the same as in addition of simple numbers.

NOTE. The sum of the signs, in circular motion, must always be divided by 12, and the remainder only be written down, as in Ex. 26.

§ XII. SUBTRACTION OF COMPOUND NUMBERS. ART. 102. SUBTRACTION of Compound Numbers is the process of finding the difference between two compound numbers.

ENGLISH MONEY.

Ex. 1. From 87£. 9s. 6d. 3far., take 52£. 11s. 7d. 1far. Ans. 34£. 17s. 11d. 2far.

QUESTIONS. Art. 102. What is subtraction of compound numbers? How do you arrange the numbers for subtraction ?