Here we multiply by 48, i. e. by 6 and 8; then subtract the multiplicand.

This plan may be indefinitely modified; hence this general direction : Multiply by two or more numbers whose product is nearly the multiplier, and add to or subtract from the product such numbers as the case may require.

10. Multiply 27yd. 3qr. 2na. by 59.

11. Multiply 17gal. 3qt. 1pt. 3gi. by 97.

12. What is the cost of 857 yards of cloth, at 3£ 15s. 6d. 1qr. per yard?

Multiply by 100, i. e. by 10 and 10; then multiply the cost of 100 yards by 8, the cost of 10 yards by 5 and the cost of 1 yard by 7, which will give the cost of 800, 50 and 7 yards, severally; finally, add the cost of 800, 50 and 7 yards together, and thus find the cost of 857 yards, the answer.

13. Bought 131 loads of wood, each measuring 1c. 3c.ft. 7cu.ft., at $5.67 per cord; what was the quantity bought, and the cost of the whole ?

14. If a ship sail 2° 14′ 27′′ per day, how far will she sail in 29 days?

15. If 3 men build 7rd. 5ft. of wall in 1 day, how much will they build in 17 days?

§. 15. COMPOUND DIVISION.

178. Here, as in the three preceding sections, the principle is the same as in the corresponding operation in simple numbers. Hence,

To divide a Compound by a Simple Number,

RULE.-Divide the highest denomination of the dividend, and set down the quotient; if there is a remainder, reduce it to the next lower denomination; to the result add the given quantity of that denomination and divide as before, setting down the quotient and reducing the remainder, etc.

Ex. 1. Divide 30£ 7s. 1d. 1qr.

£ S. d. qr.

7)30 7 1

qr.

4 6

8

3, Ans.

7

30 7 1

1, Proof.

by 7.

30£ 7 gives a quotient of 4£ and a remainder of 2£. 2£ reduced to shillings and added to 7s., give 47s., which, divided by 7, gives a quotient of 6s., and a remainder of 5s., etc., etc.

2. Divide 1fur. 29rd. Oyd. 2ft. 10in. 2b. c. by 7.

3. Divide 14gal. 2qt. 1pt. 2gi. by 5.

4. Divide 46t. 9lb. 10oz. 12dr. by 11.

5. Divide 71a. 3r. 14rd. 8yd. 1ft. 72in. by 12.

179. When the divisor is composite, we may divide by its factors, as in simple division (56).

7. Divide 530 lb. 23 33 29 8gr. by 63.

8. Divide 958m. 5fur. 5ch. 12li. 51gin. by 96.

180. When the divisor is large and not composite, set down the work of dividing and reducing. There is no device for rendering the operation easier.

9. Divide 135bush, 3pk. 3qt. 1pt. by 47.

bush. pk. qt. pt.

47) 135 3 3 1 (2bush. 3pk. 4qt. 1 pt., Ans.

10. Divide 1644yd. 2qr, 2na. by 59.

11. Divide 1742gal. 3qt. 1pt. 3gi. by 97.

12. If 857 yards of cloth cost 3236£ 1s. 4d. 1qr., what is the price per yard?

13. Sold 131 equal loads of wood, measuring 187c. 2c. ft. 5cu. ft. for $1061.9211; what was the quantity per load and the price per cord?

14. If, in 29 days, a ship sail 2s. 4° 59′ 3′′, how far is that per day?

15. If 5 men build 124rd. 2ft. 6in. of wall in 17 days, how much would they build in one day?

181. Duodecimals * are compound numbers which decrease uniformly from the highest to the lowest denomination by the constant divisor, 12.

182. This measure is usually applied to feet and parts of a foot, and is used by artificers in determining distances, areas and solidities.

Its denominations are feet (ft.), inches ('), seconds ("), thirds ("), fourths (""), etc., etc.

The accents used to designate the denominations are called indices.

183. The foot being the unit, the denominations have the relations indicated by the following

Thus 12 of any lower denomination make 1 of the next higher; e. g.

12"""

=

= 1′′

184. Addition, subtraction and division of duodecimals are performed as the like operations of other compound numbers; the same is true of multiplication, except that, when both factors are in the form of compound numbers, we are required to determine the denomination of the product.

185. In this investigation, for the sake of convenience, we familiarly speak of multiplying feet by feet, feet by inches, inches by inches, etc., though here, as everywhere (173), the multiplier is strictly an abstract number; e. g., suppose a board is 10 feet long and 1 foot wide, it evidently contains 10 square feet, and if it is 10 feet long and 2 feet wide, it as evidently contains 2 times 10 square feet = 20 square feet, though it would be nonsense to affirm that it contains 2 feet times 10 feet; still, we are accustomed to say that the area of a board is equal to its length multiplied by its breadth. Again, if a board is 10 feet long and 1 inch wide, it contains as many square feet as it is feet in length; i. e. it contains of 10 square feet and if the board is 10ft. long and 2in. wide, it contains 10sq.ft. 29 of a sq. ft. 18sq. ft. tration can be carried to any extent.

186. Since 1'=ft., 1′′=144ft., 1′′

12sq. ft.

10';

of

1ft. and 8'. This illus

17ft., etc., whether the measure is linear, square or cubic, it follows that 1', in linear measure, is a line, of a foot in length; in square measure, l' is an area, 1 foot long and 1 inch wide, and 1′′ is an area, 1 inch square; in cubic measure, l' is a solid, 1 foot long, 1 foot wide and 1 inch deep, 1′′ is a solid, 1 foot long, 1 inch wide and 1 inch deep and 1′′ is a cubic inch; etc.

187. Let us now proceed to determine the denomination of the product obtained by multiplying any two denominations together.

PHILOSOPHICALLY.

FAMILIARLY.

2 units X 3 units= 6 units, i. e. 2ft. X 3ft. = 6ft.