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. 28. $ XII. SUBTRACTION OF COMPOUND NUMBERS. ART. 102. SUBTRACTION of Compound Numbers is finding the difference between two numbers of different denominations. ENGLISH MONEY. Ex. 1. From 87£. 9s. 6d. 3qr., take 52£. 11s. 7d. 1qr. QUESTIONS. 7 1 1 1 2 Ans. 34 £. 17s. 11d. 2qr. Having placed the less number under the greater, farthings under farthings, pence under pence, &c., we begin with the qrs. or farthings thus: 1qr. from 3qr. leaves 2qr., which we set under the column of qrs. Now, Art. 102. What is subtraction of compound numbers? How do you arrange the numbers for subtraction? as we cannot take 7d. from 6d., we add 12d. = 1s. to the 6d., making 18d., and then subtract the 7d. from it, and set the remainder, 11d., 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 12s. from 9s., we add 20s. 1£. to the 9s., making 29s., from which we take the 12s. and set the remainder, 17s., under the column of shillings. Having added 1£. 20s. to the 52£., to compensate for the 20s. added to the 9s. in the minuend, we subtract the pounds as in subtraction of simple numbers, and obtain 34 £. for the remainder. = = RULE. -1. Write those numbers under each other which are of the same denomination, the less compound number under the greater. 2. Then begin with the lowest denomination, and subtract each lower number from the one above it, and write the difference underneath. 3. If any lower number is larger than the upper, suppose as many to be added to the upper number as would make one of the next higher denomination, then subtract the lower figure, remembering to carry one to the next lower number before subtracting it; and proceed thus till all the numbers are subtracted. PROOF. The proof is the same as in simple subtraction. EXAMPLES FOR PRACTICE. 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 Motion, the minuend is sometimes less than the subtrahend, as in Ex. 29, in which case it must be increased by 12 signs. ART. 103. To find the time between two different dates. Ex. 1. What is the difference of time between October 16th, 1842, and August 9th, 1844 ? Ans. ly. 9mo. 23da. FIRST OPERATION. y. mo. da. Min. 1844 7 9 Sub. 1842 9 16 Rem. 1 9 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 9da. have elapsed; and counting the months and days in the earlier date up to October 16th, we find that 9mo. and 16da. have elapsed. Then, setting down the earlier date under the later, and placing the months and days at the right of the year of each date respectively, as in the example, we subtract the lower number from the upper, and the remainder is the time between the dates. SECOND OPERATION. Min. 1844 8 9 RULE. Set down the earlier date under the later, writing the year of each on the left, next after this the number of months that have elapsed since the beginning of the year, and on the right the day of the month. Then subtract as in the preceding rule. NOTE.-1. A month in legal transactions is reckoned from any day in one month to the same day of the following month; but in computing interest for less time than a month, and in finding the difference between two dates, 30 days are considered a month, and 12 months a year. 2. Some prefer reckoning the number of the given month, instead of the number of months that have elapsed since the beginning of the year; the result is the same in both cases. See 2d operation. EXAMPLES FOR PRACTICE. 2. What is the time from March 21st, 1843, to Jan. 6th, 1847? 3. A note was given Nov. 15th, 1832, and paid April 25th, 1837; how long was it on interest? 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? 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? 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? |