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.

£.

OPERATION.
8.

ENGLISH MONEY.

Ex. 1. From 87£. 9s. 6d. 3far., take 52£. 11s. 7d. 1far. Ans. 34£. 17s. 11d. 2far. Having placed the less number under the greater, farthings under farthings, pence under pence, &c., we begin with the farthings, thus: 1 far. from 3 far. leaves 2 far., which we set under the Rem. 34 17 11 2 column of farthings. As we cannot

d. far Min. 87 9 6 3 Sub. 52 11 7 1

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

take 7d. from 6d., we add 12d. 1s. to the 6d., making 18d., and then subtract the 7d. from it, and set the remainder, Ild., under the column of pence. We then add 1s. = 12d. to the 11s. in the subtrahend, making 12s., to compensate for the 12d. we added to the 6d. in the minuend. (Art. 30.) Again, since we cannot take 128. from 98., we add 20s. = 1£. to the 9s., making 29s., from which we take the 12s., and set the remainder, 178., under the column of shillings. Having added 1£. 20s. to the 52£., to compensate for the 208. added to the 98. in the minuend, we subtract the pounds as in subtraction of simple numbers, and obtain 34£. for the remainder, and as the result complete, 34£. 17s. 11d. 2far.

RULE. Write the less compound number under the greater, so that units of the same denomination shall stand in the same column. Subtract as in subtraction of simple numbers.

If any number in the subtrahend is larger than that above it, add to the upper number as many units as make one of the next higher denomination before subtracting, and carry one to the next lower number before subtracting it.

PROOF. - The proof is the same as in simple subtraction.

QUESTIONS. What do you do when the upper number is smaller than the lower? How many do you carry to the next denomination? What is the rule for subtraction? The proof?

NOTE.-In Circular Measure, the minuend is sometimes less than the subtrahend, as in Ex. 29, in which case it must be increased by 12 sigus.

ART. 103.

To find the time between two different dates.

Ex. 1. What is the difference of time between October 16th 1852, and August 9th, 1854 ? Ans. 1y. 9mo. 23da.

FIRST OPERATION.
y.

Min. 1854

mo. da.

7

9

Sub. 1852

Rem.

1 9

SECOND OPERATION.

9

16

23

Commencing with January, the first month in the year, and counting the months and days in the later date up to August 9th, we find that 7mo. and 9 da. have elapsed; and counting the months and days in the earlier date, up to October 16th, we find that 9mo. and 16da. have elapsed. We, therefore, write the numbers for subtraction as in the first operation. The same result, however, could be obtained, as some prefer, by reckoning the number of the given months instead of the number of months that have elapsed since the beginning of the year, and writing the numbers as in the second operation; -written either way,

Min. 1854 8
Sub. 1852 10

Rem.

1 9

9

16

23

The earlier date being placed under the later, is subtracted, as by the preceding rule.

NOTE. - In finding the difference between two dates, and in computing interest for less than a month, 30 days are considered a month. In legal transactions, a month is reckoned from any day in one month to the same day of the following month.

EXAMPLES FOR PRACTICE.

2. What is the time from March 21st, 1853, to Jan. 6th, 1857 ? Ans. 3y. 9m. 15da. 3. A note was given Nov. 15th, 1852, and paid April 25th, 1857; how long was it on interest? Ans. 4y. 5mo. 10da. 4. John Quincy Adams was born at Braintree, Mass., July 11th, 1767, and died at Washington, D. C., Feb. 23, 1848; to what age did he live? Ans. 80y. 7mo. 12da. 5. Andrew Jackson was born at Waxaw, S. C., March 15th, 1767, and died at Nashville, Tenn., June 8th, 1845; at what age did he die? Ans. 78y. 2mo. 23da.

QUESTIONS. Art. 103. From what period do you count the months and days in preparing dates for subtraction? How do you arrange the dates for subtraction? How subtract? How many days are considered a month in business transactions? What is the second method of preparing dates for subtraction?