13. If a printer one day use 4 bundles 1 ream 15 quires 20 sheets of paper, the next day 3 bundles 1 ream 10 quires 10 sheets, and the next 2 bundles 13 sheets, how much does he use in the three days?

Ans. 10 bundles 1 ream 6 quires 19 sheets. 14. A tailor used, in one year, 2 gross 5 doz. 10 buttons, another year 3 gross 7 doz. 9, and another year 4 gross 6 doz. 11; how many did he use in the three years?

Ans. 10 gross 8 doz. 6.

15. A ship, leaving New York, sailed east the first day 3° 45' 50"; the second day, 4° 50' 10"; the third, 2° 10′ 55′′; the fourth, 2° 39"; how far was she then east from the place of starting? Ans. 12° 47' 34".

16. A man, in digging a cellar, removed 127 cu. yd. 20 cu. ft. of earth; in digging a drain, 6 cu. yd. 25 cu. ft. ; and in digging a cistern, 17 cu. yd. 18 cu. ft.; what was the amount of earth removed, and what the cost at 16 cent a cu. yd.? Ans. 152 cu. yd.; $24.37.

17. A farmer received 80 cents a bushel for 4 loads of corn, weighing as follows: 2564, 2713, 3000, and 3109 lbs.; how much did he receive for the whole? Ans. $162.657.

18. A druggist sold for medicine, in three years, at an average price of 9 cents a gill, the following amounts of brandy, viz. : 1 bbl. 4 gal. 1 pt.; 30 gal. 2 qt. 1 gi.; 2 bbl. 15 gal.; how much did he receive for the whole ?

Ans. $415.17.

ANALYSIS. Find the value of each fraction in integers of less denominations (213), and then add their values as in compound numbers (217).

Or, Reduce the given frac tions to fractions of the same denomination (212), then

add them, and find the value of their sum in lower denominations (213)

2. Add of a rod to of a foot.

Ans. 13 ft. 1 in.

3. What is the sum of 3 of a mile, 284 rods?

Ans. 308 rd. 2 ft. 9 in.

4. What is the sum of of a pound and of a shilling?

Ans. 13s. 10d. 2 qr.

5. What is the sum of 3 of a ton and of 1 cwt.?

Ans. 12 cwt. 42 lb 13 oz.

Give explanation of the process of adding denominate fractions.

6. What is the sum of 3 of a day added to an hour? Ans. 9 h. 30 min.

7. What is the sum of of a week, of a day, and of an hour? Ans. 1 da. 22 h. 15 min.

8. Add of a hhd. to of a gal. 6 9. What is the sum of 4 of a cwt., 88 lb., and 3 oz. by long ton table? Ans. 73 lb. 1 oz.

10. What is the sum of of a mile, of a yard, and o a foot?

120:12ft 9an.

11. Sold 4 village lots, the first contained of of an acre; the second, 60 rods; the third, of an acre; and the fourth, of of an acre; how much land in the four lots? Ans. 146 P. 126,45 sq. ft. 12. A farmer sold three loads of hay; the first weighed 1 T., the second, 1 T., and the third, 184 cwt.; what was the aggregate weight of the three loads?

Ans. 3 T. 5 cwt. 91 lb. 10 oz.

SUBTRACTION.

219. 1. If a druggist buy 25 gal. 2 qt. 1 pt. 1 gi. of wine, and sell 18 gal. 3 qt. 0 pt. 2 gi., how much has he left ?

OPERATION.

2

ANALYSIS. Writing the subtrahend gal. qt. pt. gi. under the minuend, placing units of the 25 2 1 1 same denomination under each other, 18 3 0 we begin at the right hand, or lowest denomination; since we cannot take Ans. 6 3 0 3 2 gi. from 1 gi., we add 1 pt. or 4 gi. to 1 gi., making 5 gi.; and taking 2 gi. from 5 gi., we write the remainder, 3 gi., underneath the column of gills. Having added 1 pt. or 4 gi. to the minuend, we now add 1 pt. to the 0 pt. in the subtrahend, making 1 pt.; and 1 pt. from 1 pt. leaves 0 pt., which we write in the remainder. Next, as we cannot take 3 qt. from 2 qt., we add 1 gal. or 4 qt. to 2 qt., making 6 qt., and taking 3 qt. from 6 qt., we write the remainder, 3 qt., under the denomination of quarts. Adding 1 gal. to 18 gal., we subtract 19 gal. from 25 gal., as in simple

What is subtraction of compound numbers? Give explanation.

numbers, and write the remainder, 6 gal., under the column of gal. lons.

RULE. I. Write the subtrahend under the minuend, so that units of the same denomination shall stand under each other. II. Beginning at the right hand, subtract each denomination separately, as in simple numbers.

III. If the number of any denomination in the subtrahend exceed that of the same denomination in the minuend, add to the number in the minuend as many units as make one of the next higher denomination, and then subtract; in this case add 1 to the next higher denomination of the subtrahend before subtracting. Proceed in the same manner with each denomination.

6. A Boston merchant bought English goods to the

amount of £4327 13s. 74d., and he paid £1374 10s. 11d;

how much did he then owe?

2

7. From 300 miles take 198 mi. 305 rd. 2 yd. 1 ft. 10 in. Ans. 101 mi. 14 rd. 2 yd. 2 ft. 8 in. 8. What is the difference in the longitude of two places one 75° 20′ 30′′ west, and the other 71° 19′ 35′′ west?

Ans. 4° 55".

9. From 1073 43 19 15 gr. take 3lb 8 3 2 3 2 18 gr.

Ans. 6b 113

13 10 17 gr.

Give the Rule.

10. The apparent periodic revolution of the sun is made in 365 da. 6 h. 9 min. 9 sec., and that of the moon in 29 da. 12 h. 44 min. 3 sec.; what is the difference?

Ans. 335 da. 17 h. 25 min. 6 sec.

11. A man, having a hogshead of wine, drank, on an average, for five years, including two leap years, one gill of wine a day; how much remained? Ans. 5 gal. 3 qt. 1 pt. 1 gi.

12. A section of land containing 640 acres is owned by four men; the first owns 196 A. 961 P.; the second, 200 A. 60 P.; the third, 177 A. 36 P.; how much does the fourth own? Ans. 65 A. 127.75 P.

13. From a pile of wood containing 75 Cd. was sold at one time 16 Cd. 5 cd. ft.; at another, 24 Cd. 6 cd. ft. 12 cu. ft.; at another, 27 Cd. 112 cu. ft.; how much remained in the pile? Ans. 6 Cd. 3 cd. ft. 4 cu. ft.

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

409

220. To find the difference in dates.

1. What length of time elapsed from the discovery of America by Columbus, Oct. 14, 1492, to the Declaration of Independence, July 4, 1776?

ANALYSIS. Place the earlier date under the later, writing first on the left the number of the year from the Christian era, next the number of the month, counting January as the first month, and

next the number of the day from the Instead of the number of the year, month, number of years, months, and days that have

elapsed since the Christian era, thus: instead of saying July is the 7th month, we say 6 months and 3 days have elapsed, and instead of saying October is the 10th month, we say 9 months and 13 days have elapsed.

How is the difference of dates found?