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COMPARATIVE TABLE OF WEIGHTS

437.5 Troy grains 1 oz. Avoirdupois. 480 Troy grains 1 oz. Troy= 1 oz. Apothecaries'.

1 oz. Avoirdupois =}}} oz. Troy=131 oz. Apothecaries'. 7000 Troy grains 1 lb. Avoirdupois. 5760 Troy grains

1 lb. Troy

1 lb. Apothecaries'. 1 lb. Apothecaries'=144 lb. Avoirdupois.

IV. CIRCULAR MEASURE

60 seconds ("') = 1 minute (').
60 minutes 1 degree (°).
30 degrees 1 sign (S.).

360 degrees = 1 circumference of a circle. NOTE.—This table is used in measuring angles, and in estimat ing latitude and longitude.

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VI. MEASURES OF VALUES

U. S. MONEY

ENGLISH MONEY 10 mills (m.) 1 cent (ct.). 4 farthings = 1 penny (1d.). 10 cents 1 dime (d.).

1 shilling (1s.). 10 dimes

1 dollar ($). 20 shillings 1 pound (£1). 10 dollars 1 eagle (E.). | £1

$4.8665 U.S.

12 pence

VII. MISCELLANEOUS MEASURES

PAPER MEASURE

24 sheets = 1 quire.
20 quires 1 ream.
2 reams = 1 bundle.
5 bundles= 1 bale.

COUNTING 12 things = 1 dozen (doz.). 12 dozen

1 gross.

= 1 great gross. 20 things 1 score.

12 gross

REDUCTION 217. The principles involved in reduction are the same in all the measures; therefore, one example in reduction ascending and one in reduction descending will be sufficient for models. 1. Reduce 684 pints to higher denominations.

SOLUTION:
1. Since 2 pints = 1 quart.
I.

1 pint = quart.
3. And 684 pints = 684 * $ quart = 342 quarts.

1. Since 8 quarts = 1 peck. II. 2. .. 1 quart = $ peck.

3. And 342 quarts = 342 * $ peck = 42 pecks and 6 qt.

2. ..

III.

2. ..

( 1. Since 4 pecks

= 1 bushel.
1 peck

:t bushel.
3. And 42 pecks = 42 x bushel

10 bu. and 2 pk. .. 684 pints = 10 bu. 2 pk. 6 qt.

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2. Reduce 10 bu. 2 pk. 6 qt. to pt.

SOLUTION: 1. Since 1 bu. = 4 pk. I. 2. ..

10 bu.

= 10 x 4 pk. = 40 pk. 3. 40 pk. + 2 pk. = 42 pk.

1. Since 1 pk. = 8 qt. II. 2. .. 42 pk.

42 8 qt. = 336 qt. 3. 336 qt. + 6 qt.

342 qt. 1. Since 1 qt. = 2 pt. III. 2. .. 342 qt.

= 342 x 2 pt. = 684 pt. .:. 10 bu. 2 pk. 6 qt.

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684 pt.

Exercise XXV

1. Reduce 8 bu. 3 pk. 1 qt. 1 pt. to pints. 2. Reduce 5 mi. 17 rd. 2 yd. to feet. 3. Reduce 2 mi. 25 ch. 12 li. to links. 4. Reduce 2 lb. 6 oz. 12 pwt. 6 gr. to grains. 5. What part of 3 wk. is 4 da. 16 hr. 30 min.? 6. How many acres in four townships? 7. How many cubic inches in 5 gallons? 8. Reduce 40 sq. rd. 25 sq. yd. 7 sq. ft. to sq. ft. 9. How many cords of wood in 846 cu. ft. of wood? 10. Reduce 52875 cu. in. to higher denominations. 11. How many gills of water in 462 cu. in. of water? 12. How many bu. of wheat in 430084 cu. in. of wheat?

13. Reduce 1728 pt. to higher denominations.
14. Reduce 4 T. 15 cwt. 6 lb. 3 oz. to ounces.
15. Reduce 6 lb. 73 53 20 18 gr. to grains.
16. Reduce 5286 Troy gr. to higher denominations.
17. Reduce 66 feet to rods.

18. Troy weight is used in weighing gold, and Avoirdupois in weighing feathers. Which is heavier, a pound of gold or a pound of feathers? An ounce of gold or an ounce of feathers ?

19. Reduce 5287"' to higher denominations. 20. Reduce 7 wk. 3 da. 6 hr. 8 min. 5 sec. to seconds. 21. How many seconds in Feb. of 1904? 22. Express £8 15s. 8d. in U. S. money. 23. How many sheets of paper in 4 bales? 24. How many dozen in 16 gross? 25. Reduce 146 lb. Troy weight to Avoirdupois weight. 26. Reduce .216 gr. to oz. Troy.

27. How many sq. ft. in the four sides of a room 21.5 ft. long, 16.5 ft. wide, and 13 ft. high?

28. Reduce 96 oz. Avoirdupois to oz. Troy. 29. Reduce 10240 sq. rd. to sq. ch.

30. Allowing 800 shingles to a square, how many shingles will be required to cover the roof of a house which is 60 feet long, and 15 feet from the comb to the eaves?

THE FOUR FUNDAMENTAL OPERATIONS

218. The processes of addition, subtraction, multiplication, and division of compound denominate numbers are based upon the same principles as those governing similar opera

tions in simple numbers. In simple numbers, however, the scale is uniform, while in compound numbers the scales vary.

EXAMPLES
1. Add 2 bu. 1 pk. 1 pt. and 4 bu. 3 pk. 5 qt. 1 pt.

OPERATION.
4 8 2

SUGGESTION.—The reduction may be bu. pk. qt. pt.

made as the additions are made, if de2 1

sired; but one is less likely to make a 4 3 5 1

mistake, if the additions are all made 5 2

first and the reductions afterwards. 7

6

0, result.

1

0

6

4

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2. Subtract 4 yd. 2 ft. 6 in. from 8 yd. 1 ft. 10 in. OPERATION.

EXPLANATION.–From 8 yd., 1 yd, is 3 12

taken and reduced to ft., and added to yd. ft. in.

the 1 ft., making 4 ft. Now, 4 ft. – 2 8 1 10

ft. 2 ft. Only 7 yd. remained 4 2 6

above. 7 yd. – 4 yd. = 3 yd. 3 2 4, result.

3. Multiply 4 bu. 3 pk. 2 qt. by 12.

OPERATION.

4 8 bu. pk. qt.

EXPLANATION.- The multiplications 4 3 2

are made first, and the reductions

afterward. 48 36 24 57

3 0, result.

12

4. Divide 27 bu. 3 pk. 3 qt. by 6.

EXPLANATION.—(1) 27 + 6 = 4, rem. OPERATION.

3. Write the 4 in the result, and re4 8 2

duce the 3 bu. to pk. bu. pk. qt. pt.

(2) 3 bu. + 3 pk. 15 pk. 15 = 6 6)27 3 3 0

= 2, rem. 3. Write the 2 in the result, 4 2 4 1, result.

and reduce 3 pk. to qt.

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