168. 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 BORROW.

169. The following examples are similar to the preceding, but the rule for subtraction is inapplicable until the form of the minuend or subtrahend is changed.

What are the peculiarities of these examples?

(a) Another way to solve such examples is to reduce both minuend and subtrahend to the lowest denomination contained in either (87), and then subtract as in simple subtraction.

170. In subtracting an earlier from a later date, it is customary to consider 30 days a month.

15. What is the difference in time between April 17, 1827, and February 12, 1834?

16. Find the time from Aug. 15, 1843, to Dec. 12, 1851. 17. Find the time from May 12, 1841, to June 21, 1842. 18. Find the time from June 21, 1842, to Aug. 24, 1846. 19. Find the time from Aug. 24, 1846, to Sept. 1, 1847. 20. Find the time from July 21, 1836, to Sept. 1, 1847. 21. Find the time from Feb. 29, 1816, to Aug. 22, 1855. 22. Find the time from Jan. 8, 1743, to Dec. 16, 1854. 23. Find the time from Sept. 6, 1777, to Nov. 13, 1816.

171. EXAMPLES IN COMPOUND ADDITION AND SUBTRACTION.

1. My farm contained 108a. 3r. 17rd., and I have sold to one man 15a. 2r. 29rd., and to another 11a. 33rd.; how much have I left?

2. Having a journey of 187m. 7fur. 19rd. to perform in 3 days, I travel 53m. 3fur. 14rd. the first day and 71m. 18rd. the second; how far must I travel on the third ?

3. Bought 723 acres of land for 963£ 14s. 9d.; from this sold to A 253a. 3r. 17rd. for 319£ 12s., and to B 176a. 14rd. for 237£ 11d.; how much land remains, and what has it cost?

4. How long since the Declaration of American Independence, July 4, 1776?

5. A bought of one farmer 11t. 7cwt. 3qr. 181b. of cheese; of another, 6t. 19cwt. 7lb.; of another, 18cwt. 3qr.; and of another, 17t. 3qr. He also sold in Boston, 12t. 7cwt. 12lb.; in Lowell, 8t. 15cwt. 3qr., and the remainder in New York. How much did he sell in New York?

6. B sold an ox which weighed 17cwt. 3qr. 8lb.; and 2 cows that weighed 5cwt. 3qr. 18lb. each; and 3 swine that weighed 3cwt, 2qr. 12 lb., 4cwt. 1qr. 18lb., and 5cwt. 3qr. 6lb. respectively. How much more beef than pork did he sell?

7. From the sum of 7rd. 2yd. 2in. 1b.c. and 2rd. 3yd. 1ft. 3in. 2b. c., take the difference between 14rd. 2ft. 7in. 1b. c. and 4rd. 2ft. 7in. 2b.c. Ans. 1b.c.

8. From a piece of cloth measuring 18yd. 3qr. 3na. 2in. there were cut 3 garments, the first measuring 4yd. 3na., the second 3yd. 2qr., and the third 5yd. 1qr. 2na. lin. How much cloth remained?

9. If from 2 casks of molasses, containing 65gal. 3qt. 1pt. and 74gal. 1pt. 3gi., there be taken 83gal. 1qt., how many gallons, quarts, etc., will remain?

10. How long from the battle of Lexington, April 19, 1775, to the Declaration of Independence, July 4, 1776 ?

11. How long from the battle of Bunker Hill, June 17, 1775, to the erection of General Warren's Statue, June 17, 1857 ?

§ 14.

COMPOUND MULTIPLICATION.

172. In compound multiplication, the multiplicand only is compound.

173. In both simple and compound multiplication, the multiplier is always and necessarily an 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.

174. The product is of the same kind as the multiplicand; for repeating a number does not change its nature.

175. The principle is the same as in simple multiplication. 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 to make one of the next higher, set down the remainder, carry the quotient to the product of the next denomination, and so proceed.

56d., and 5d. added give

61d. 5s. and 1d., etc.

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

176. When the multiplier is a composite number, we may proceed as in like cases in simple multiplication (44).

6. Multiply 4lb. 8oz. 16dwt. 20gr. by 72.

7. Multiply 8lb. 43 73 29 16gr. by 63.

8. Multiply 9m. 7fur. 8ch. 3rd. 15li. 6in. by 96.

177. When the multiplier is large and not composite, some expedient may be adopted, as in the following examples.

9. Multiply 2bush. 3pk. 4qt. 1pt. by 47.

First multiply by 45, i. e. by 5 and 9; then add twice the multiplicand, and thus multiply by 47.

This example may be solved as follows: