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375

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365 days

21

2 1
20

2. Reduce .375 wk. to the fraction of a year. Process.

Explanation. .375 wk.= wk.

.375

ģ. wk. g of 7 da. Š x 7= 21 da.

1 yr., therefore 41 41 X 365 = zito yr. 21 X

da. 21 X 355 zšio yr.

EXERCISES. Reduce: 1. } gi. to gal.

11. sq. yd. to A. 2. 18 min. to da.

12. } pt. to bbl. 3. 13 ft. to mi.

13. $gi. to gal. 4. 54 oz. to T.

14. 414 sq. in. to sq. rd.

. 5. 4 in. to rd.

15. 94 in. to mi. 6. 2 pt. to bu.

16. sof m to cong. 7. 41 sec. to deg.

17. 5} x 74 cu. in. to cd. 8. 3} min. to da.

18. 1 li. to mi.
9. .45 lb. to T.

19. 76 lb. to T.
10. 4 cu. in. to cu. ft. 20. .89725 oz. to cwt.

THE FRACTIONAL RELATION OF ONE DE

NOMINATE NUMBER TO ANOTHER.

EXERCISES.

8

1. What part of 4 ft. 7 in. is 3 ft. 4 in. ? Process.

Explanation. 4 ft. 7 in. 55 in.

1 in. 55 of 55 in.; therefore, 40 in. = 3 ft. 4 in. 40 in. 45 of 55 in.

4. =

*reduced = it 2. What decimal part of £1 is 16s. 8d. 1st Process.

Explanation.

Both quantities must be reduced £1 240d.

to the same denomination. 16s. 8d. 200d.

£1 = 240d. 16s. 8d. = 2000. 200d. £24= £ £.8333 +.

246 or å of 240d.
reduced to a decimal = £.8333 +:

200

3. What fraction of:

1. 1 yd. is 2 ft. 9 in. ?
2. 1 mi. is 4 rd. 21 yd. ?
3. 1 A. is 24 sq. rd. 33 sq. yd. ?
4. 48 lb. is 51 oz. ?
5. 3 mi. is 5 rd. 2 yd. 2 ft. 2 in. ?
6. 3 bbl. are 13 gal. 3 qt. 3 pt. 3 gi. ?
7. 3 bu. is 1 bu. 3 pk. 4 qt.

4
8. 5 lb. troy is 6 oz. 6 pwt. 6 gr.?
9. 4 lb. avoirdupois is 4 lb. troy?
10. A 6-in. cube is 6 cu. in. ?
11. 65 ch. is 1430 ft.?
12. 365 da. is 4 wk. 4 da. 4 hr.?
13. 360° is 40° 40' ?
14. £1 is 18s. 5 d.?

15. 1 cwt. is 16 lb. 11 oz. ? 4. What decimal fraction of 1 bu. is 3 pk. 6 qt. 1 pt. ?

2 pt.

2d Process.

Explanation. 21.

1 qt. ; therefore į the number of pt. the 8 6.5

number of qt. 1 of 1 .5 qt., which added to 6 qt.

6.5 qt. 8 qt. = 1 pk. ; therefore { of the number 43.8125

the number of pk. } of 6.5 .8125 .953125

pk., which added to 3 pk. 3.8125 pk. 4 pk.

1 bu.; therefore the number of pk. = the number of bu. 4 of 3.8125 .953125 bu.

of qt.

5. What decimal fraction of:

1. 1 S. is 6° 25' 36/?
2. 1 mi, is 5 rd. 3 ft. 10 in. ?
3. 1 yd. is 31 in.?
4. 1 T. is 3 cwt. 48 lb. 9 oz. ?
5. 1 A. is 1 R. 39 P.?
6. 1 T. is 6 cwt. 75 lb. ?
7. 1 da. is 11 hr. 55 min. 41.7 sec. ?

8. 1 A. is 4276 sq. ft.?
9. 1 lb. is 14 oz. ?
10. 82 mi. 70 rd. is 10 mi. 10 rd. ?
11. 228 bu. 3 pk. is 8 bu. 2 pk. 6 qt. ?
12. 1 lb. is 4 oz. 8 pwt. 12 gr. ?
13. 1 mi. is 765 yd. 9 in. ?
14. 1 cd. is 4 cd. ft. 8 cu. ft. ?

REVIEW.

1. What will be the cost of:

1. 1 T. 15 cwt. 36 lb. of sugar @ 3 cts. a pound ?
2. 3 lb. 9 oz. 13 pwt. of gold dust @ $.75 a pwt. ?
3. 8 tons of coal @ $.264 a cwt. ?
4. 9 barrels of flour at $.03 a pound ?
5. 16 lb. 9 oz. butter at $.30 a pound ?
6. 4 pk. 5 qt. cherries at 10 cts. a quart?
7. 40 rd. 8 ft. 9 in. fence at $.80 per ft. ?
8. 25 bu. of seed at 8 cts. a pint ?
9. 7 bu. 3 pk. 2 qt. blackberries at 7 cts. a qt. ?

10. 14 hhd. of molasses at 12 cts. a qt.?
2. How many bu. of wheat in 1260 lb. ?
3. How many min. in the yr. 1898 ?

4. How many cords of wood in a pile 4 ft. wide, 7 ft. high, 70 ft. long ?

5. How many days of 12 hrs. each will it require to make a million figures if one figure is made each second ?

6. How many bu. of carrots will a 10-acre field produce if each sq. rd. produces 5 bu. ? 7. How many sec.

are there in 365 da. 5 hr. 48 min. 49 sec. ?

8. How many bu. of oats in 2000 lb. ?

9. How many sec. from 7 A.M., Aug. 15th, to Dec. 7th, 7 P.M.?

a

10. How many kegs, each holding 7 gal. 3 qt. 1 pt., can be filled from 11 bhd. of wine ?

11. How many degrees in a quadrant measured on meridian of the earth's surface? How many miles ?

12. If 1 ton of phosphorus is used in making 10,000,000 matches, how many gr. of phosphorus on each match ?

13. If a cistern holds 4890 gal. of water, how many bbl. does it hold ?

14. If hay at $15 per T. is exchanged for flour at $5.85 per bbl., how many bbl. will a ton of hay buy ?

15. If a druggist put 83 43 59 of a medicinal substance in 2-gr. pills, how many pills did he make ?

16. If a man constructed a cistern 12 ft. long and 8 ft. wide to hold 150 bbl., how high did he make it?

17. If 10 bales of goods weigh 22 cwt. 86 lb., what will 155 bales of like size weigh ?

18. If a silver dollar weighs 4127 gr., what will 1,000,000 dollars weigh? 19. If a bbl. of flour costs £1 4s. 9d., how

many be bought for £275 10s. 3d. ? (Reduce before dividing.)

20. If a man travels 24 mi. 7 fur. 30 rd. in a day, how long will it take him to travel 300 mi. 6 fur. 20 rd. ?

bbl. can

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21. If a cu. ft. of ice weighs 58.1 lb., how many tons will an ice-house hold that is 45 ft. long, 32 ft. wide, and 20 ft. high?

22. Find the cost of 1 qt. of olive oil when 1 doz. pt. cost $3.50.

23. Find the number of gal. in a cistern 51 ft. square and 7 ft. deep.

24. Find the cost of covering the floor of a hall 461 ft. long and 14 ft. 9 in. wide with matting 11 yd. wide at $.25 a yard.

25. If a glacier moves uniformly 100 ft. a year, how far will it go in 181 days?

26. If a man earns $3 per day and pays $6 a week for board, etc., how much can he save in 7 mo. ?

27. A square lot, having 32 chains on a side, contains how many acres ?

28. How many times will the wheel of a carriage 17.5 ft. in circumference revolve in going 1 mi. 5 ft. ?

29. How many board ft. in 3 planks 12 ft. long, 9 in. wide, and 34 in. thick?

30. What will it cost to carpet a room 18 ft. by 24 ft. with carpet i yd. wide at $1.25 per yd., the breadths to run lengthwise?

31. What decimal part of a yr. has passed with August 15th ?

ADDITION OF DENOMINATE NUMBERS. In the addition of simple numbers we have a uniform decimal scale ; in the addition of compound numbers we have a varying scale ; apart from this there is no difference in the process of adding:

EXERCISES. 1. What is the sum of 12 lb. 5 oz. 13 pwt., 21 lb. 8 oz. 15 pwt., 13 lb. 7 oz. 10 pwt., 51 lb. 3 oz. 17 pwt. ?

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lb. 12 21 13 51 99

8 7 3 1

20 pwt. 13 15 10 17 15

Explanation. Units of the same denomination must stand in the same column.

The scale is 24, 20, 12. We use 20 and 12.

The sum of the pwt. is 55. 55 pwt. = 2 oz 15 pwt. We write the 15 under the column of pwt. and add the 2 oz. with the column of ounces. The sum of the oz. is 25, which equals 2 lb. and 1 oz. We write the 1 oz. under the column of oz. and add the 2 lb. with the column of lb., making 99 lb.

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