To Integers of Lower Denominations.

SLATE EXERCISES.

Example.-1. Find the value of the fractional part of 21/36 lb. Troy in integers of lower denominations.

Answer to both.-2 lb. 5 oz. 13 pwt. 8 gr.

89

2. How many pounds and ounces in 2/3, 5%, 3/8, 59, 7/10, 11/12 */159 17/339 90/91 cwt.?

Analysis.-2/3 cwt. = 2/3 of 100 lb. = 662/3 lb.

=

2/3 lb. 2/3 of 16 oz. =

102/3 oz. Hence 2/3 cwt. = 66 lb. 102/3 oz.

3. How many yards and feet in %, 2/3, 5%, 4% acre?

4. How many hours, minutes, and seconds in 1/21, 47, 5/9, 3/10, 5/1697/199 20/27 day?

5. How many feet and inches in %, 4/7, 5/11, 7/18 yard ?

6. How many pence and farthings in 5/6, 7/8, 9/10, 11/129 12/139 14/17, 65% shillings?

7. How many weeks, days, and hours in 234, 57, 11/19, 21/317 3/17 common years?

8. How many cubic yards and feet in 11, 957, 71/12, 32, 1113/120 cords?

9. How many pennyweights and ounces in 11, 7/8, 5/13, 67/139 335/32, 251/16 pounds Troy?

10. How many grains and scruples in 37, 39, 33167 37/480? In 3 15/1993 152, 333? In fb 752, b 111, b 521?

Reduce 5 d. 14 h. 24 min. to a fraction of a week.
Explanation.-Reducing the two periods of time to be compared,

denomination, we have

the same

8064 10080

or 4/5 of a week.

247. Second Method. The lowest denomination may be reduced to a fraction of a unit of the next higher; then this fraction, together with the integer to which it now belongs, may reduced to a fraction of the next higher, and so on till the entire compound number is reduced to the required fraction, as follows:

Suggestion. The work is conveniently arranged by writing the several denominations in a column, beginning with the lowest, and writing the resulting fractional quotients on the right of a light vertical line, as below. In the progress of the work this line is disregarded. It is useful only to prevent mistakes.

Process.

60)24 min. 24)14.4 h. 7) 5.6 d. 0.8 wk.

Explanation. Here the process of reasoning is precisely the same as for similar reductions in integers, thus: Since there is 1 h. in 60 min., there are as many h. in 24 min. as there are times 60 min. in 24 min. .4 times, etc. etc. But this process differs from the process of reduction in integers in the addition of the higher denominations as we come to them, while in integers there are no such additions to make.

What part of

SLATE EXERCISES.

1. 1 ton is cwt. 79 lb. 11 oz.?

2. £5 is 1100 d.?

3. 1 cwt. is 79 lb. 91/4 oz.? 4. 3 acres is 1700 ft.? 5. 1 yr. is 89 d. 1 h. 12 min.? 6. £1.7835 is £1 15 s. 8.04 d.? 7. 6.75 bu. is 3 pk. 3 qt.? 8.5 ft. is 289 □ in.?

9.4

miles is 347 acres? 10. 59° is 13° 13′ 13′′ ? 11. 13 cu. ft. is 578 cu. in.? 12. 3 oz. is 51/10 pwt.? 13. 7 days is 37 min. 37 sec.? 14. 1 yr. is 89 d. 17 h. 8 min. ? 15. 52 d. 16 h. is 49 d. 9 h.? 16. 1 cwt. is 13 lb. 16 oz.?

What part of

17. 25 cu. ft. is 864 cu. in.?
18. 6 d. 1 hr. is 4 d. 20 h.?
19. 13 cords is 13 cu. ft.?
20. 1.25 ton is 173 oz.?
21. 13 yd. is 13 in.?

22. 13 gal. is 3 qt. 1 pt. 11⁄4 gi.?
23. 36 gal. is 27 gal. 2 qt. 1 pt.?
24. 1728 cu. in. is 445 cu. in.?
25. 1 lb. Troy is 7 oz. 6 pwt.?
26. 1 lb. Troy is 11 oz. 7 pwt.?
27. 1 ton is 47.73 lb.?
28.3 mi. is 527.3994 yd.?
29. 2 acre is 420.1883 □ yd.?
30. 1 oz. Troy is 1 oz. avoir.?
31. 1770 oz. is 11⁄2 cwt.?

32. 1 ton is 6 cwt. 7 lb.?
33. 34 lb. Troy is 12 gr.?
34. 17 h. is 19 min. 13 sec.?
35. 17 h. is .1175 d.?

5

36. 777 oz. Troy is 3 lb. 11 oz.?
37. 1⁄2 lb. avoir. is 21 gr.?
38. 3⁄41⁄2 lb. avoir. is 3⁄41⁄2 lb. Troy?
39. 3 cwt. 99 lb. is 1⁄2 ton 33 lb.?
40. 69 cwt. is 69 lb.

41. 2 □ mi. is 345 a. 17 □ rd.?
42. 5 cords is 7.125 cord feet?
43. I 3 is 33 31 −2 gr. 16?
44. 180° is 5° 18′ 22′′ ?
45. 1 ch. is 3 rd. 3 li. 5 in.?
46. 1 yr. is 5 h. 46.4 sec.?

Addition.

(Compound Denominate Numbers.)

Example.—1. What is the sum of 13 gal. 2 qt. 1 pt. 3 gi.; 14 gal. 2 qt. 2 gi.; 7 gal. 3 qt. 3 gi.; 9 gal. 1 qt. 1 pt. 2 gi.;

6 qt. 1 pt. 1 gi.?

Written Work.

Gal. qt. pt. gi.

13

2

1

3

14 2

0

2

7

3

0

9

1

1

2

6 1

1

3

47 0 1 3

Explanation.—Numbers of the same denomination are written in the same column for convenience of addition. The sum of the column of gills is 11=2 pt. 3 gi. The 3 gi. is written under the column added, and the 2 pt. are added with the column of pints. The sum of the pints is 5 = 2 qt. 1 pt. The 1 pt. is written under the column of pints, and the 2 qt. are added to the quarts, and so on.

Note.—The pupil will perceive that the process at the left is like that of simple addition, except that instead of the divisor being always 10, as in simple numbers, it varies with the denomination. It is always as many units of the denomination of the column added

as are required to make a unit of the next higher.

Notes.-1. In Ex. 4, the sum of the yards is 10, or 1 rod 411⁄2 yd.; we write

6.

Oz. pwt.

24

gr.

5

16

153

16

1

14

235/8

15

0

17

07/12 14

2

4

the 4, and for the 1/2 yd. we add 1 ft. 6 in.

2. In Ex. 5, the sum of the □ yards is 112, or 3 rods 211/4 yd.; write the 21 □ yd., and for the 1⁄ □ yd. add 2 □ ft. 36 in.

3. The fractions of the lowest denomination being added together, and reduced, the resulting integer, if any, is added to the given integers of that denomination.

Examples.-7. Find the sum of 13 cwt. 21 lb. 13% oz.; 3 cwt. 18 lb. 9/10 oz.; 25 cwt. 31 lb. 15% oz.

2

8. Add 58 gal. 3 qt. 1 pt. 31⁄2 gi.; 45 gal. 3 qt. 1 pt. 1% gi.; 38 gal. 1 qt. 1 pt. 314 gi.; 26 gal. 3 qt. 31⁄2 gi.

9. Add £7305 14 s. 81% d.; £8737 13 s. 4 d.; £513 6 s. 5 d.; £67 5 s. 10% d.

10. Add 37 cu. yd. 15 cu. ft. 1084 cu. in.; 9 cu. yd. 13 cu. ft. 1556 cu. in.; 86 cu. yd. 22 cu. ft. 695 cu. in.; 24 cu. yd. 8

11. Add 17 tons 11 cwt. 99 lb. 15 oz.; 7 cwt. 97 lb. 13 oz.; tons 7 cwt. 7 lb. 77/10 oz.; 11 tons 11 cwt. 11 lb. 11 oz.; 179 cwt. 1780 lb. 11797 oz.; 137 tons 19 cwt. 89 lb. 15 oz.