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396. PROB. IX.-To divide a denominate or compound number by any abstract number.

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same as in finding one of the equal parts of a concrete number.

Thus, the of 29 lb. is 4 lb. and 1 lb. remaining. We write the 4 lb. in the quotient, and reduce the 1 lb. to ounces, which added to 7 oz. make 19 oz. We now find the of the 19 oz., and proceed as before until the entire quotient, 4 lb. 2 oz. 6 dr. is found.

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1. Divide 9 T. 15 cwt. 3 qr. 18 lb. by 2; by 5; by 8; by 12. 2. If 29 lb. 7 oz. 16 pwt. are made into 7 equal parts, how much will there be in each part?

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3. A druggist made 12 powders of 31 35 of a certain medicine; what was the weight of each powder?

4. Divide lb. 3 37 34 02 by 4; by 6; by 12; by 32. 5. The aggregate weight of 43 equal sacks of coffee is 2 T. 7 cwt. 2 qr. 12 lb.; what is the weight of each sack?

6. Divide 5 T. 14 cwt. 2 qr. 8 lb. by 3 cwt. 1 qr. 12 lb. Reduce both the dividend and divisor to the same denomination, and divide as in simple numbers.

7. Divide 2 lb. 5 oz. 2 pwt. 7 gr. by 1 oz. 3 pwt. 7 gr.

8. How many boxes, each containing 96 lb., will hold 1 T. 13 cwt. 2 qr. 10 lb. ?

9. Divide lb. 6 39 37 02 by 37 2 gr. 10.

Ans. 35.

10. Divide .98 lb. by .46 pwt.; of a ton by of a pound. 11. A druggist purchased 154 equal bottles of a certain medicine, containing in the aggregate lb. 34 32 35 1; how much did each bottle contain?

12. Divide lb. 75 by 3.58; .08 T. by .6 qr.

UNITS OF LENGTH.

39%. A yard is the Standard Unit in linear, surface,

and solid measure.

TABLE OF UNITS.

12 in. = 1 ft. 3 ft. = 1 yd. 5 yd. 1 rd. 320 rd. = 1 mi.

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LINEAR MEASURE.

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3. Use.-Used in measuring lines and distances.

4. In measuring cloth the yard is divided into halves, fourths, eighths, and sixteenths. In estimating duties in the Custom House, it is divided into tenths and hundredths.

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17.

7.92 in.
25 7. = 1 rd.
4 rd.1 ch.
80 ch.1 mi.

1. Denominations.-Link (1.), Rod (rd.), Chain (ch.), Mile (mi.).

2. Equivalents.—1 mi. 80 ch. 320 rd. =8000 1.

3. Use. Used in measuring roads and boundaries of land.

4. The Unit of measure is the Gunter's Chain, which contains 100 links, equal 4 rods or 66 feet.

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7. 15 degrees to statute miles.

8. 3.76 geographical miles to statute miles.
9. 12 rd. 4 yd. 2 ft. to inches.

10. 210 geographical miles to statute miles.
11. 2 mi. 5 ch. 3 rd. to links.

12. .73 of a mile to a compound number. 13. .85 of a yd. to a decimal of a mile.

14. 7 yd. 2 ft. to a decimal of 3 rd.

15. Find the sum of 3 of a mi., .85 of a ch., and 3 ch. 2 rd. 16. Find the difference between 3 mi. 5 ch. 2 rd. 13 l., and of (1 mi. 7 ch. 3 rd. 18 1.)

17. The four sides of a tract of land measure respectively 3 mi. 5 ch. 2 rd., 2 mi. 7 ch. 3 rd. 13 l., 3 mi. 17 1., and 2 mi. 2 rd.; what is the distance round it?

18. On a railroad 132 mi. 234 rd. 4 yd. 2 ft. long, there are 18 stations at equal distances from each other. How far are the stations apart, there being a station at each end of the road?

19. A ship moving due north sailed 15.7 degrees. How far did she sail in statute miles?

20. A ship sailing on the equator moved 45 leagues. How many degrees is she from the place of starting, and what is the distance in statute miles?

21.

of a rod is what part of 3 chains?

22. 32 fathoms are what decimal of a mile?

23. In 125 geog. miles how many statute miles?

24. 3 ft. are what decimal of 3 rods?

25. 1 link is what decimal of 1 foot?

UNITS OF SURFACE,

399. A square yard is the Standard Unit of surface

measure.

400. A Surface has two dimensions-length and breadth.

401. A Square is a plane surface bounded by four equal lines, and having four right angles.

402. A Rectangle is any plane surface having four sides and four right angles.

403. The Unit of Measure for surfaces is usually a square, each side of which is one unit of a known length. Thus, in 14 sq. ft., the unit of measure is a square foot.

404. The Area of a rectangle is the surface included within its boundaries, and is expressed by the number of times it contains a given unit of measure.

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3 feet long.

3 sq. ft. x 39 sq. ft.

Thus, since a square yard is a surface, each side of which is 3 feet long, it can be divided into 3 rows of square feet, as shown in the diagram, each row containing 3 square feet. Hence, if 1 sq. ft. is taken as the Unit of Measure, the area of a square yard is 3 sq. ft. x 39 sq. ft. The area of any rectangle is found in the same manner; hence the following

405. RULE. Find the product of the numbers denoting the length and breadth, expressed in the lowest denomination named in either; the result is the area, which can be reduced to any required denomination. To find either dimension of a rectangle.

406. RULE. Divide the number expressing the area, by the given dimension; the quotient is the other.

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3. Use.-Used in computing areas or surfaces.

4. Glazing and stone-cutting are estimated by the square foot; plastering, paving, painting, etc., by the square foot or square yard; roofing, flooring, etc., generally by the square of 100 square feet.

5. In laying shingles, one thousand, averaging 4 inches wide, and laid 5 inches to the weather, are estimated to cover a square.

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4. The Unit of land measure is the acre. The measurement of a tract of land is usually recorded in square miles, acres, and hundredths of

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