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ADDITION.

439. Denominate numbers are added, subtracted, multiplied, and divided by the same general methods as are employed for like operations in Simple Numbers.

The corresponding processes are based upon the same principles. The only modification of the rules needed is that which is required by a varying scale instead of a uniform scale of 10.

The principles will be made sufficiently plain in the operations and analyses to render special rules unnecessary.

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440. 1. Find the sum of 4 cwt. 46 lb. 12 oz., 12 cwt. 91 lb., 21 cwt., and 21§ lb.

OPERATION.

cwt. lb.

oz.

4

46

12

12

9

8

2

25

0

21

10

19

2

14

ANALYSIS.-Write the numbers so that units

of the same denomination stand in the same column, and begin at the right to add.

The sum of the ounces is 30, equal to 1 lb. 14 oz. Write the 14 oz. under the column of ounces, and add the 1 lb. to the pounds of the next column.

The sum of the pounds is 102 lb., equal to 1 cwt. and 2 lb. Write the 2 lb. under the

column of pounds, and add the 1 cwt. to the cwt. of the next column. The sum of the cwt. is 19 cwt., which write under the column of cwt. Hence the entire sum is 19 cwt. 2 lb. 14 oz.

2. What is the sum of wk., da., and hr.?

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1 wk.

=

Reduce the given fractions to fractions of the same denomination (434), then add the results and find the value

5 da. 12 hr. 22 min. 30 sec. of their sum in integers of lower denominations.

If denominate fractions occur in the given numbers, they should be reduced to integers of lower denominations (433) before adding.

3. Add 7 yd. 2 ft., 5 yd. 14 ft., 2 ft. 9 in., 3 yd. 1 ft. 61 in., 24 ft., 44 yd.

4. Add 5 Cd. 7 cd. ft., 2 Cd. 2 cd. ft. 12 cu. ft., 6 cd. ft. 15 cu. ft., 73 Cd., and 3 Cd. 2 cu. ft.

5. What is the sum of 1 gal., 2 qt. pt., and 1.75 pt.?

hhd., 36 gal. 3 qt. 11 pt.,

6. What is the sum of § of a day added to of an hour? 7. To of a hhd. add § of 10 gal.

8. What is the sum of 224 cwt., 267 lb., and 14 oz.? 9. Add 5 Pch., 18 cu. ft., 86.6 cu. ft., and Pch. 10. Find the sum of tb 4 36 35, and b 6 341 39. 11. A Missouri farmer received $.75 a bushel for 4 loads of corn; the first contained 48.4 bu., the second 2626 lb., the third 36 bu., and the fourth 41 bu. 52 lb. What did he receive for the whole ?

12. Bought three loads of hay at $15 a ton. The first weighed 1.125 T., the second 13 T., and the third 2750 lb. What did the whole cost?

13. When B was born, A's age was 3 yr. 9 mo. 24 da.; when C was born, B's age was 12 yr. 19 da.; when D was born, C's age was 5 yr. 11 mo., and when E was born, D's age was 10 yr. 1 mo. 20 da. What was A's age when E was born?

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441. 1. From 25 rd. 2 yd. 2 ft. 6.3 in., subtract 12 rd.

4 yd. 11.6 in.

OPERATION.

rd.

yd.

ft.

in.

25

2

2

6.3

12

4 0

11.6

12

3 (1) 1

6.7

= 1

6

12

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ANALYSIS.-Write the numbers so that units of the same denomination stand in the same column, and begin at the right to subtract.

Since 11.6 in. cannot be subtracted from 6.3, take 1 ft., equal to 12 in., from the 2 ft., leaving 1 ft. and add it to the 6.3 in., making 18.3 in. Subtract 11.6 in., and write the remainder, 6.7 in., under the inches.

Since 1 ft. has been taken from 2 ft., subtract 0 ft. from 1 ft., and write the remainder 1 ft. under the feet.

Since 4 yd. cannot be taken from 2 yd., take 1 rd., equal to 5 yd., from 25 rd., leaving 24 rd., and add it to the 2 yd., making 74 yd. Subtract 4 yd. from 7 yd., and write the remainder, 31 yd., under the yards.

Since 1 rod has been taken from 25 rd., subtract 12 rd. from 24 rd., and write the remainder, 12 rd., under the rods.

Theyd., reduced to feet and inches, and added to 1 ft. 6.7 in. of the remainder, gives 12 rd. 4 yd. .7 in.

2. From 1 bu. subtract bu.

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nation (434), then subtract the less from the greater, and find the value of their difference in integers of lower denominations.

3. From a pile of wood containing 42 Cd. 5 cd. ft., take 16 Cd. 6 cd. ft. 12 cu. ft., and how much remains? 4. From the sum of of 3 mi. and 174 rd., take 1204 rd.

Find the difference between

5. 8 cwt. and 483 lb.

6. £ and of is.

7.3 lb. and 5 lb. 4 oz. 8 pwt.
8. .659 wk. and 2 wk. 35 da.
9. 11 hhd. and 3.625 gal.

mi.

10.lea. and
11. § gross and † doz.
12. 32 1 and 3 4.
13. .9 da. and † wk.
14. 1 A. and 84.56 P.

15. If from a hhd. of molasses 14 gal. 1 qt. 1 pt. be drawn at one time, 10 gal. 3 qt. at another, and 29 gal. 1 pt. at another, how much will remain?

16. Of a farm containing 250 A., two lots were reserved, one containing 75 A. 136.4 P., and the other 56 A. 123.3 P.; the remainder was sold at $621 an acre. What did it sell for?

17. From 1 T. 11 cwt. 30 lb., take of a long ton.

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18. From a pile of wood containing 125 Cd., was sold at one time 26 Cd. 7 cd. ft.; at another, 30 Cd. 4 cd. ft.; at another, 37 Cd. How much remained?

442. To find the interval of time between two dates.

1. How many yr., mo., da., and hr., from 3 o'clock P. M. of May 16, 1864, to 9 o'clock a. M. of Sept. 25, 1875?

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1. When hours are to be obtained, reckon from 12 at night, and if minutes and seconds, write them still at the right of hours.

2. In finding the difference of time between two dates, 12 mo. are usually considered a year, and 30 days a month.

3. When the time is less than a year, the true number of days in each month and parts of a month is added.

4. The day on which a note, draft, or contract is dated, and that on which they mature, are not both included. The former is generally omitted.

2. The war between England and America was commenced April 19, 1775, and peace was restored Jan. 20, 1783. What length of time did the war continue?

3. The American Civil War began April 11, 1861, and closed April 9, 1865. What time did it continue?

4. How long has a note to run that is dated Jan. 16, 1873, and made payable July 10, 1875 ?

5. A note dated May 28, 1875, was paid Feb. 10, 1876. What length of time did it run?

6. A person started on a tour of the world at 9 o'clock A.M., Sept. 3, 1874, and returned to the same depot at 3 P.M., July 15, 1876. What time was he absent?

7. How many years, months, and days from your birthday to this date; or, what is your age?

8. How many days from June 20th to the 10th of Jan. following?

9. What length of time elapsed from 12 o'clock M., Jan. 10. 1876, to June 16, 9 o'clock A. M.?

10. What length of time elapsed from 16 min. past 10 o'clock A. M., July 4, 1873, to 22 min. before 8 o'clock P. M., Dec. 12, 1875 ?

11. What length of time will elapse from 40 min. 25 sec. past 12 o'clock M., April 21, 1875, to 4 min. 36 sec. before 5 o'clock P. M., Jan. 1, 1878 ?

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