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189. In counting certain articles, the following is used:

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Two things of a kind are often called a pair, and six things a set; as

a pair of horses, a set of chairs, etc.

190. Used by stationers and by the paper trade:

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In 34 da. ? In 5 da.?

P. M. ?

In 5 wk. 4 da.?

192. 1. How many hours in 2 da. ? 2. How many hours from 6 A. M. to 3. In 4 wk. 3 da., how many days? 4. How many minutes from 10 min. past 9 o'clock to 25 min. past 10 A. M.?

5. How many days from May 10 to July 16, inclusive? 6. How many things in 3 doz.? In 6 doz.? In 1 gro.?

7. How many dozens in 3 gro.? In 5 gro. ?

8. How many dozens in of a great gross?

9. Find the cost of a gross of pens, at 10 cts. a dozen? 10. How many sheets of paper will be required to make a 12mo book of 320 pages? Of 480 pages?

DENOMINATE NUMBERS.

193. Denomination is the name of a unit of measure. Thus, feet is the denomination of 6 ft.; pounds, of 25 lb., etc.

194. A denominate number is a number composed of one or more units of any denomination, and may be either simple or compound.

1. A simple denominate number is a number composed of but one denomination.

Thus, 7 miles, 10 acres, 5 tons are simple denominate numbers.

2. A compound denominate number is a number composed of two or more denominations of the same nature.

Thus, 10 lb. 6 oz., 5 yr. 4 mo, 4 ft. 2 in., are compound denominate numbers.

195. A denominate fraction is a fraction of a denominate number.

Thus, of a pound, .9 of a ton, are denominate fractions.

REDUCTION.

196. Reduction of denominate numbers is the process of changing their denomination without changing their value.

Denominate numbers may be changed from higher to lower, or from lower to higher denominations.

In integral numbers and in decimals, the law of increase and decrease is by the uniform scale of 10; but in compound numbers the scale varies.

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197. To change a denominate number from higher to lower denominations.

1. How many inches in 26 rd. 3 yd. 2 ft. 9 in. ?

EXPLANATION.-Since 1 rod equals

5 yards, 26 rd. 3 yd. equal 26 times 5 yd., plus 3 yd.; 51 yd. × 26 + 3 yd. = 146 yards.

Since 1 yard equals 3 feet, 146 yd. 2 ft. equal 146 times 3 ft., plus 2 ft.; 3 ft. x 146+2 ft. = 440 feet

Since 1 foot equals 12 inches, 440 ft. 9 in. equal 440 times 12 in., plus 9 in.; 12 in. x 440+9 in. = 5289 in. the number of inches in 26 rd. 3 yd. 2 ft. 9 in.

26 rd. 3 yd. 2 ft. 9 in. 51 146 yd.

3

440 ft.

12

5289 inches.

PRINCIPLE. A denominate number is changed to lower denominations by MULTIPLICATION.

2. Reduce 7 lb. 10 oz. 16 pwt. 11 gr. to grains.
3. In 3 T. 6 cwt. 21 lb. 12 oz., how many ounces?
4. Change 6 wk. 5 da. 9 hr. 25 min. to minutes.

RULE.-1. Multiply the highest denomination of the given number by that number of the scale that will reduce it to the next lower denomination, and to the product add the given number, if any, of that denomination.

2. Proceed in like manner with this and each successive denomination obtained, until the reduction is brought to the required denomination.

Reduce

5. 12 mi. 36 rd. 10 ft. to ft.
6. 10 rd. 5 ft. to inches.
7. 1 A. 15 sq. yd. to sq. ft.

Change

8. 7 T. 9 cwt. 18 lb. to lb. 9. 22 lb. 10 oz. to pwt. 10. 1 common year to min.

Change

11. 75 Cd. 6 cd. ft. to cu. ft. 12. 12 hhd. 21 gal. to pt.

13. 24 bu. 3 pk. to quarts.

Reduce

14. 5 bundles to quires. 15. 6 G. gro to dozens. 16. 31 gal. to gills.

17. How much is 5 lb. 9 oz. 14 pwt. of gold dust worth, at $.75 a pwt.?

18. How many rods of fence will enclose a farm of a mile square?

19. If 1 barrel will hold 2 bu. 3 pk., how many barrels will be required to hold 1548 bu. 1 pk.?

20. How many boxes, each containing 12 lb., can be filled from a hogshead containing 9 cwt. 60 lb. of sugar?

21. If I buy 9 bu. of chestnuts at $4 a bushel, and retail them at 12 cents a pint, what is my whole gain?

22. If it require 4 reams 10 quires of paper to print a book, how many sheets are required?

23. At 12 cents each, what will be the cost of 2 great gross of writing books?

24. If a clock tick seconds, how many times will it tick during February, 1877 ?

25. How many pint, quart, and 2-quart bottles, of each an equal number, can be filled from a barrel of 31 gallons?

26. What will be the cost of 1 hhd. molasses at $.28 per gal.? 27. How many rods of fence will inclose a farm 11⁄2 mi. square? 28. If 14 A. of land are sold from a field containing 50 A., how many square rods does the remainder contain?

29. A man returning from Pike's Peak has 36 lb. 8 oz. of pure gold. What is its value, at $1.04 per pwt.?

30. In the eighteenth century, how many hours?

31. How large an edition of a 12mo book can be printed from 2 bales 2 bundles 15 quires of paper, allowing 8 sheets to the volume?

32. How many pages, 2 pages to each leaf, will there be in an 8vo book, containing 16 fully printed sheets?

How many pounds 33. In 361 centals of grain? 34. In 424 bbl. of flour? 35. In 29.5 quintals of fish? 36. In 116 bbl. of salt? 37. In 63.25 kegs of nails?

38. In .75 of 75 bu. of salt? 39. In 125 bu. of wheat? 40. In of 21648 bu. oats? 41. In .7 of 40 bu. corn? 42. In 7.5 casks of lime?

198. 1. Reduce bu. and .645 da. each to integers of

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