15. Reduce

16. Change

mi. to lower denominations.

of a year to months and days.

17. In 1 gal. how many qt. and pt. ?

19.4 acres are equal to how many sq. rods, etc.?

20. Reduce bu. to integers of lower denominations. 21. What is the value of of of a hhd. in integers of lower denominations?

22. What is the value of of an acre in integers of lower denominations?

23. Reduce £ to integers of lower denominations.

24. What is the value of of 13 of a mile?

155. To reduce denominate numbers to Fractions of Higher Denominations.

1. Reduce 2 qt. 1 pt. 2 gi. to the fraction of a gallon.

1 pt. pt.2 &qt.

=

=

2 qt. 14 qt. ÷ 4 gal. Ans.

2. Reduce 2 qt. 1 pt. 2 gi. to the decimal of a gallon.

Rule. Change the number of the lowest
denomination to a fraction (or deci-

mal) of the next higher, write this
fraction (or decimal) as a part of

4/2 gi.

2/1.5 pt.

4/2.75 qt.

.6875 gal.

the number of that higher denomination, and reduce

this number in like manner, and so proceed to the required denomination.

3. Reduce 213 rd. 1 yd. 2 ft. 6 in. to a fraction of a mile.

4. What fraction of an acre is 3 R. 13 sq. rd. 10 sq. yd. 108 sq. in.?

5. What part of a year is 273 da. 18 hr.?

6. Reduce to a fraction of a pound 8 oz. 11 pwt. 10 gr. 7. What part of a ton is 857 lb. 2% oz.?

8. Change 3 fur. 19 rd. 5 yd. 1 ft. 4.7328 in. to the decimal of a mile.

9. Reduce 1 da. 14 hr. 24 min. to the decimal of a month.

10. What decimal of a gallon is 1 qt. 2 gi. ?·

11. Reduce 68 sq. rd. 8 sq. yd. 2 sq. ft. 7.488 sq. in. to the decimal of an acre.

12. What decimal of a pound Troy is 6 oz. 3 pwt. 21.6

gr.?

13. Reduce 131 da. 18 hr. 21 min. 36 sec. to the decimal of a year.

14. Reduce 2 qt. 13 gi. to the fraction of a gallon.

5. What fraction of a mile is 71 rd. 1 ft. 10 in. ?

16. Reduce 12 da. 34 min. 144 sec. to the fraction of a month.

17. What decimal of a ton is 4 cwt. 72 lb. 128 oz.?

18. Reduce 48 cu. ft. 1636.7616 cu. in. to the decimal of a cord.

19. What decimal of a circle is 10° 53′ 24′′ ?

20. Reduce 4 fur. 5 rd. 1 yd. 3.6 in. to the decimal of a mile.

21. Reduce 6 pwt. to a fraction of a pound.

22. 3 qt. 1 pt. 2 gills are what part of a peck?
23. Change 6 rd. 4 yd. 1 ft. to the fraction of a mile.
24. What part of a cord of wood are 8 cu. ft.?
25. Reduce 5 gross 7 doz. to the fraction of a score.

To find what part one denominate number is of another.
1. What part of 2 gal. 1 qt. 1 pt. is 3 qt. 1 pt. 1 gi. ?
3 qt. 1 pt. 1 gi.

2 gal. 1 qt. 1 pt.

29 gi. 76 gi.

NOTE.

nator.

The question now is, 29 gi. is what part of 76 gi. ?

--

29 gi. is of 76 gi. Ans.

- To find the decimal part, divide numerator by denomi

2. What part of 5 lb. 9 oz. 3 pwt. is 2 lb. 8 oz. 6 pwt. 10 gr.?

3. What part of 3 mi. 24 rd. 5 yd. is 2 mi. 34 rd. 4 yd. ? 4. What part of 3 da. 5 hr. 22 min. is 1 da. 10 hr. 3 min. 12 sec.?

5. What decimal of 3 gal. 2 qt. 1 pt. is 2 gal. 2 qt. 2 pt.?

lb. ?

6. What decimal of 4 T. 5 cwt. 10 lb. is 2 T. 6 cwt. 13

7. What part of a rod is 4 yd. 2 ft. 7 in. ?

8. What part of 6 rods is g of 7 feet?

9. What part of 33 mi. is 160 rd. 5 yd.?

10. pint is what part of a bushel?

11. What decimal of 8 bu. 3 pk. 4 qt. is 4 bu. 1 pk. 5 qt.

ADDITION OF COMPOUND NUMBERS.

156. 1. Add 14 lb. 5 oz. 17 pwt. 12 gr., 18 lb. 10 oz. 14 gr., 6 lb. 4 oz. 8 pwt. 16 gr.

gr. 1 pwt. 18 gr.

SOLUTION. The sum of the grains

42

We place the 18 gr. under

the column of grains, and add the 1 pwt. to

the column of pennyweights.

Add the other

columns in like manner.

10. Find the sum of 3 T. 15 cwt. 25 lb. 9 oz., 4 T. 17 cwt. 30 lb. 10 oz., 6 T. 18 cwt. 15 lb. 12 oz., 2 T. 12 cwt. 20 lb. 16 oz.

11. Find the sum of 7 hr. 30 min. 45 sec., 12 hr. 25 min. 20 hr. 15 min. 33 sec., 10 hr. 27 min. 46 sec.

30 sec.,

12. Add 10 mi. 101 rd. 3 yd. 2 ft. 11 in., 16 mi. 4 yd. 6 in., 3 mi. 560 rd. 3 ft., 175 rd. 4 ft. 7 in.

13. Add 3 A. 50 sq. rd. 25 sq. yd. 10 sq. ft. 102 sq. in., 5 A. 110 sq. rd. 30 sq. yd. 8 sq. ft. 34 sq. in., 6 A. 75 sq. rd. 14 sq. yd., 7 sq. ft., 82 sq. in., 7 A. 215 sq. rd., 17 sq. yd. 16 sq. ft. 53 sq. in.

14. Find the sum of 18 cd. 6 cd. ft. 12 cu. ft., 19 cd. 4 cd. ft. 6 cu. ft., 24 cd. 2 cd. ft. 1 cu. ft.

15. Find the sum of 18 T. 18 lb. 12 oz., 16 cwt. 21 lb., 14 cwt. 75 lb. 10 oz.

16. What is the entire length of a railway consisting of 5 different lines measuring respectively 160 mi. 185 rd. 2 yd., 97 mi. 63 rd. 4 yd., 126 mi. 272 rd. 3 yd., 67 mi. 199 rd. 5 yd., and 48 mi. 266 rd. 5 yd. ?

17. A merchant sold 48 had 15 gal. 1 qt. 1 pt. left.

gal. 3 qt. 1 pt. of coal oil and What quantity had he at first?

18. A starts from a point in Lat. 21° 25′ 35′′ N. and travels north 24° 36′ 45". At what latitude does he arrive? 19. Find the difference in longitude between a point 46° 15′ 30′′ E. and a point 21° 18′ 16′′ W.

NOTE. When one place is in east and the other in west longitude, their difference in longitude is the sum of their longitudes.

20. Charles walks 5 mi. 15 rd. 2 ft. north of the schoolhouse, and James 6 mi. 28 rd. 5 yd. south. How far are they apart?

21. Find the sum of 3 mi. 35 rd. 43 rd.