202. Sometimes, as in the following examples, it is necessary to borrow two of the higher denomination of the minuend instead of one; but in all such cases we must carry two to the next term of the subtrahend; i. e. we must PAY as much as we

203. To find the time between two dates.

17. What is the difference of time between July 15, 1857, and Apr. 25, 1862 ?

Ans. 4yr. 9m. 10d.

SECOND OPERATION.

yr. m. d. 1861 3 24 1856 6 14

203. How many

modes of finding the time between two dates? What are they?

NOTE. In subtracting an earlier from a later date, it is customary to consider 30 days a month. In the first operation, the number of the year, month, and day of the month, is used; in the second, the number of years, months, and days that have elapsed since the commencement of the Christian era, is used. The two operations give the same result, but the first is most convenient.

18. How long from the battle of Waterloo, June 18, 1815, to the death of Napoleon, May 5, 1821? Ans. 5yr. 10m. 17d. 19. How long from the battle of Lexington, Apr. 19, 1775, to the surrender of Cornwallis, Oct. 19, 1781?

20. How long from the inauguration of Washington, Apr. 30, 1789, to the battle of New Orleans, Jan. 8, 1815?

21. How long from the Declaration of Independence, July 4, 1776, to the present time?

22. Daniel Webster was born Jan. 18, 1782, and died Oct. 24, 1852; at what age did he die?

23. A note given July 6, 1857, was paid Sept. 9, 1861; how long was it on interest?

24. Find the time from Apr. 4, 1857, to Dec. 12, 1862. 25. Find the time from Dec. 16, 1839, to Mar. 26, 1848. 26. Find the time from Nov. 13, 1816, to May 12, 1841. 27. Find the time from June 21, 1842, to Feb. 20, 1860.

EXAMPLES IN ADDITION AND SUBTRACTION.

1. A farmer raised 150bush. 3pk. 4qt. of oats. Having sold 50bush. 2pk. and used 27bush. 1pk. 4qt., how many has he remaining? Ans. 73bush.

2. Having a journey of 127m. 4fur. 10rd. to perform in 3 days, I travel 48m. 2fur. 6rd. the first day, and 54m. 4rd. the second; how far must I travel on the third day?

3. I have one piece of land containing 47a. 3r. 25rd. and another containing 25a. 2r. 15rd.; how much land shall I have after selling 37a. 3r.?

4. From the sum of 8bush. 3pk. 2qt. 1pt. and 10bush. 2pk. 7qt. 1pt., take the difference between 54bush. 1pk. 3qt. 1pt. and 49bush. 3pk. 2qt. 1pt.? Ans. 15bush. 1qt.

203. Which is preferable? How many days are considered a month?

5. From the sum of 5rd. 1yd. 2ft. 4in. 1b.c. and 4rd. 2yd. 1ft. 9in. 2b.c., take the difference between 10rd. 5yd. 2ft. 7in. 2b.c. and 1rd. lyd. 1ft. 6in. Ans. 1b.c.

6. From a piece of silk measuring 49yd. 1qr. 3na. 2in., there were cut 3 dresses, the first measuring 15yd. 3qr. 1na. lin., the second 14yd. 3qr. 3na. lin., and the third 14yd. 2qr. 3na. 2in.; what remnant remained?

also 2 swine

7. B sold an ox which weighed 16cwt. 1qr. 15 lb., and 2 cows that weighed 6cwt. 1qr. 10lb. and 5cwt. 3qr. 20lb.; that weighed 4cwt. 3qr. 18 lb. and 3cwt. 3qr. 24 lb. more beef than pork did he sell?

How much

8. If from 2 casks of wine, containing 63gal. 3qt. 1pt. 3gi. and 56gal. 2qt. 2gi., there be taken 75gal. 2qt. 1pt. 3gi., how many gallons, quarts, etc., will remain ?

9. From a mass of silver weighing 47 lb. 8oz. 16dwt. 22gr., a silversmith made 48 spoons weighing 71b. 8dwt. 14gr. and a cake-basket weighing 3 lb. 6oz. 8dwt. 15gr.; how much silver remained in the mass?

MULTIPLICATION.

204. In the multiplication of both simple and compound numbers, the multiplier is always and necessarily a simple abstract number; for, to attempt to multiply by a concrete number, e. g. 4 miles times 10, is, in the highest degree, absurd, though it is perfectly proper to say 10 times 4 miles. The product is of the same kind as the multiplicand; for repeating a number does not change its nature.

205. The principle is the same as in multiplication of simple numbers. Hence,

To multiply a compound by a simple number,

RULE. Multiply the lowest denomination in the multiplicand, divide the product by the number it takes of that denomination

204. What is the multiplier in all cases? What the product? 205. Rule? Proof? Explain Ex. 1.

to make one of the next higher, set down the remainder, add the quotient to the product of the next denomination, and so proceed.

NOTE. Multiplication and division prove each other. It is profitable to teach reverse operations simultaneously.

and the whole product, .., is 43a. 3r. 18rd. 8yd. 1ft. 72in., Ans.

17. Bought 5 loads of wood, each measuring 1c. 5c. ft. 8cu. ft., at $6 per cord; what was the quantity bought and the cost of the whole? Ans. 8c. 3c. ft. 8cu. ft.; $50.621.

18. If a ship sail 2° 30′ 20′′ per day, how far will she sail in 8 days?

19. Multiply 8m. 6fur. 12rd. 3yd. 2ft. 6in. 1b. c., by 6.

20. If a man travel 25m. 6fur. 25rd. per day, how far will he travel in 9 days?

21. If the crop of hay on 1 acre is 2t. 15cwt. 2qr. 12 lb., what will be the crop on 10 acres?

22. What cost 7 yards of cloth, at 15s. 6d. 3qr. per yard? 23. How much wine in 3 casks containing 28gal. 3qt. 1pt. 2gi. each?

24. Multiply 9m. 7fur. 8ch. 3rd. 15l. 6in. by 8. 25. Multiply 3circ. 5s. 25° 18′ 25′′ by 9.

206. To multiply by a composite number:

RULE. Multiply by the factors of the multiplier (see Art. 61).

205. Explain Ex. 14. 206. Rule when the multiplier is composite?