The terms folio, quarto, octavo, applied to books, indicate the number of leaves into which a sheet of paper is folded. Thus, when a sheet of paper is folded into 2, 4, 8, 12, 16, 18, or 24 leaves, the forms are called respectively, folio, 4to, or quarto, 8vo, or octavo, 12mo, 16mo, 18mo, and 24mo.

EXERCISES.

3 gr.

1. How many eggs are there in 5 dozen? 7 doz.? 10 doz.? 2. How many crayons are there in 2 gross? 5 doz.? 3. How many things are there in a great gross?

4. What will be the cost of 3 dozen brushes at $.45 each? 5. A man lived 3 score and 10 years. What was his age? 6. What will 3 reams of paper sell for at $.15 per quire?

REDUCTION OF DENOMINATE FRACTIONS.

283. The principles, processes and analyses are essentially the same as those of denominate integers.

CASE I.

284. To reduce denominate fractions to equivalent numbers of lower denominations.

EXERCISES.

1. How many hours are there in 1 day? In day? In of a day? In of a day? In § of a day?

2. How many ounces are there in

In lb.? In 1 lb.?

pound avoirdupois?

3. How many pints are there in of a peck? In pk.? 4. How many pecks and quarts are there in g of a bushel? 5. How many pounds and ounces are there in § cwt.? 6. How many inches are there in of a foot? & ft.? ft.?

REDUCTION OF DENOMINATE FRACTIONS. 187

7. Change of a rd. to units of lower denominations.

Therefore of a rod is equal to 3 yd. 2 ft. 9 in.

16. Express

12. of a peck.

13.3 of a day.

5 흉

14. of a sq. rd.

15. of a cu. yd.

of a gallon as a fraction of a gill.

ANALYSIS. Since in 1 gallon there are 32 gills, in 15 of a gallon there are of 32 gi., orgi. Hence gal. = 1 of a gill.

17. Express of a bushel as a fraction of a pint. 18. Express 7112ʊ of a mile as a fraction of a foot. 19. Express 1944 of a pound as a fraction of a scruple. 20. Express .006 of a bushel as a decimal of a pint. 21. Express in lower denominations .685 of a pound Troy.

PROCESS.

.685
12

8.220 oz.
20

4.400 pwt. 24

9.600 gr.

ANALYSIS. Since in 1 pound there are 12 ounces, in .685 of a pound there are .685 of 12 ounces, or 8.220 ounces.

Since there are 20 pennyweights in 1 ounce, in .220 of an ounce there are .220 of 20 pennyweights, or 4.400 pennyweights.

Since in 1 pennyweight there are 24 grains, in .400 of a pennyweight there are .400 of 24 grains, or 9.600 grains.

Therefore .685 lb. is equal to 8 oz. 4 pwt. 9.6 gr.

Express in units of lower denominations:

22. £.575.

23. .1935 of a pound Troy. 24. .436 of a ream.

25. .1845 of a gallon.

26. .135 of a rod.

27. .455 of a mile.
28. .4832 of a bushel.
29. .684 of a league.

CASE II.

285. To change denominate fractions to equivalent fractions of higher denominations.

EXERCISES.

1. What part of a pound Troy is 1 ounce? Is oz.? Is oz.?

2. What part of a ton is 1 pound? Islb.? Is lb.? 3. What part of a mile is 1 rod? Is rd.? Is rd.? & 4. What part of a league is 1 mile? Is 1 rd.? Is frd.? 5. What part of an hour is of a minute? Is of a min. ? 6. What part of a week is of a day? of a day? 7. What part of a bushel is

of a pint?

8. Reduce of an inch to the fraction of a yard. 9. Change of a second to the fraction of an hour. 10. Express .375 of a week as a fraction of a year. 11. Express .35 of a pound as a fraction of a ton. 12. Express of a cubic inch as a fraction of a cubic foot.

REDUCTION OF DENOMINATE FRACTIONS.

189

13. Change of a square yard to a fraction of an acre. 14. Reduce § of a pint to a fraction of a barrel.

CASE III.

286. To express one denominate number as a frac

tion of another.

1. What part of a foot are 3 in.? 6 in.? 9 in.? 2. What part of an hour are 30 min.? 15 min.? min.?

45

3. What part of a gallon is 1 pint? 2 pints? 1 quart? 4. What part of a gallon are 2 quarts? 2 qt. 1 pt.? 3 qt. 1 pt.?

5. What part of 3 ft. 6 in. are 2 ft. 3 in.?

ANALYSIS-Since 3 ft. 6 in. = 42 in., and 2 ft. 3 in. = 27 in., 27 in. =2 of 42 in.

6. What part of 3 yd. 2 ft. are 2 yd. 2 ft.?

7. What part of 5 gal. 3 qt. 1 pt. are 2 gal. 1 qt. 1 pt.? 8. What part of 2 pounds Troy are 3 oz. 10 pwt.? 9. What part of 3 pecks are 2 qt. 1 pt.?

10. What part of 3 barrels are 13 gal. 3 qt. 2 pt. 2 gi.? 11. Express 15s. 7d. in the decimal of a pound sterling:

ANALYSIS.-In order to find what part one number is of another, both must be reduced to the same denomination. 15s. 7d. 187d. and £1240d. Therefore 187d.= £117, which, reduced to a decimal, is equal to £.7791+. Or,

ANALYSIS.-Since 7d. is of a shilling, it may be reduced to a decimal by annexing ciphers to the numerator and dividing by 12, which gives .5833+s. Therefore 15s. 7d.: 15.5833+s.

Since 1 shilling is of a pound, 15.5833+s. £15.5833, or £.7791+.

20

12. Reduce 4 hr. 15 min. to the decimal of a day.
13. Reduce 3 pk. 2 qt. to the decimal of a bushel.
14. Reduce 3 ft. 6 in. to the decimal of a rod.
15. Reduce 18s. 5 d. to the fraction of a pound.
16. Reduce 18s. 5 d. to the decimal of a pound.

17. Reduce 16 lb. 11 oz. to the fraction of a hundred-weight.
18. Reduce 37 rd. 14 ft. 3 in. to the decimal of a mile.
19. Reduce 3 da. 5 hr. 14 min. to the decimal of a week.
20. Reduce 8 quires, 15 sheets, to the decimal of a ream.
21. Change 3 cd. ft. 7 cu. ft. to the decimal of a cord.
22. Change 654 yd. 9 in. to the decimal of a mile.

23. Change 4 oz. 7 pwt. 13 gr. to the fraction of a pound Troy.

24. Write rules for each of the cases in denominate numbers.

REVIEW EXERCISES.

287. 1. What will be the cost of 15 lb. 8 oz. of butter at $.31 per pound?

2. What must be paid for 3 pk. 2 qt. of berries at 9 cents a quart?

3. Mr. A. sold 18 bu. 3 pk. of barley at $1.05 per bushel. How much did he get for it?

4. How much must be paid for making 42 rd. 7 ft. 8 in. of fence at $.75 per foot?

5. How much butter at $.30 a pound must be given for 12 gal. 3 qt. of molasses, at $.50 per gallon?

6. Bought 15 bu. of oats at $.374 a bushel, and sold them at 15 cents a half-peck. How much did I gain?

7. How many cords of wood are there in a pile 4 ft. wide, 6 ft. high, 60 ft. long? What would it cost at $4.25 a cord? 8. A man built a cistern 10 ft. long and 6 ft. wide, that would hold 100 barrels. How high did he make it?