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7. What is the sum of 3 wk. 5 da. 23 hr. 46 min. + 6 wk. 17 hr. 57 min. + 2 wk. 1 hr. + 1 wk. 6 da. 23 hr. 59 min. + 3 wk. 1 da. 12 hr. 45 min.?

8. What is the sum of 3 hhd. 60 gal. 2 qt. 1 pt. 1 gi. +1 hhd. 13 gal. 1 pt. 1 gi. + 9 hhd. 23 gal. 3 qt. 2 gi. 4 hhd. 14 gal. 1 qt. 1 pt. 3 gi.?

9. Find the sum of 2 sq. yd. 8 sq. ft. 29 sq. in. + 1 sq. yd. 5 sq. ft. 104 sq. in. + 6 sq. yd. 7 sq. ft. 87 sq. in. 4 sq. ft. 120 sq. in.

10. Find the sum of 7 yd. 2 ft. 8 in. + 9 yd. 1 ft. 10 in. + 3 yd. 2 ft. 7 in. + 13 yd. 5 in. + 20 yd. 11 in. + 17 yd. 2 ft.

11. Add 4° 31′ 20′′, 9° 35′′, 27° 42′, 9′ 50′′, 16° 16′ 16′′, 20' 30", 20° 30′ 40′′, 3° 19′, 14° 7′ 19′′, and 7° 14' 29".

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12. A farmer had 5 fields: the first contained 35 A. 1 R. 27 P.; the second, 42 A. 3 R. 14 P.; the third, 12 A. 30 P.; the fourth, 10 A. 1 R.; the fifth, 1 A. 2 R. 35 P.: how much had he in the five fields?

13. A merchant bought 15 lb. 8 oz. 8 dr. of butter of one man, 20 lb. 12 oz. of another, 18 lb. 10 dr. of another, 22 lb. 6 oz. of another, and 25 lb. of another: how much did he buy?

14. A gentleman has 6 fields of wheat; from the first, he obtained 310 bu. 2 pk. 6 qt.; from the second, 220 bu. 1 pk. 4 qt.; from the third, 400 bu. 7 qt.; from the fourth, 85 bu. 3 pk.; from the fifth, 95 bu. 1 pk. 3 qt., and from the sixth, 103 bu. 2 pk. 6 qt.: how much wheat did he obtain?

15. A railroad company has 4 piles of wood; the first contains 148 C. 28 cu. ft.; the second, 204 C. 46 cu. ft.; the third, 196 C. 48 cu. ft.; and the fourth pile is 48 ft. long, 16 ft. high, and 15 ft. wide: how many cords in all ?

SUBTRACTION OF COMPOUND NUMBERS.

78. Subtraction of Compound Numbers is the process of finding the difference between two numbers of different denominations.

MODEL SOLUTION.

EXAMPLE.-What is the difference between 10 bu. 1 pk. 7 qt., and 6 bu. 3 pk. 3 qt.?

SOLUTION.-Write the less number under the greater, placing units of the same denomination in the same column.

Take 3 qt. from 7 qt. and 4 qt. remain, which write under the column of qt.

OPERATION. bu. pk. qt.

10 1 7

6 3

3

3 2

4

As 3 pk. can not be subtracted from 1 pk., take 1 bu. from 10 bu.; 1 bu. = 4 pk., which added to`1 pk. 5 pk.; then, 3 pk. from 5 pk. leave 2 pk., which write under the column of pk.

Since 1 bu. has been taken from 10 bu., only 9 bu. remain. 6 bu. from 9 bu. leave 3 bu., which write under the column of bu.

CONCLUSION.-Therefore, the difference between 10 bu. 1 pk.

7 qt. and 6 bu. 3 pk. 3 qt., is 3 bu. 2 pk. 4 qt. Hence, the

Rule for Subtraction of Compound Numbers.- Write the less number under the greater, placing units of the same denomination in the same column.

Begin with the lowest denomination, and, if possible, take each lower number from the one above it.

But if any lower number be greater than the one above it, increase the upper number by as many units of that denomination as it takes to make one of the next higher; subtract as before; then consider the next higher denomina.

tion diminished by one, and proceed in like manner with each denomination.

PROOF.-The same as subtraction of Simple Numbers.

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9. From a bar of silver weighing 6 lb. 2 oz. 10 pwt., a piece was cut off weighing 1 lb. 8 oz. 13 pwt.: how much was left?

10. A wagon loaded with hay weighs 39 cwt. 2 qr. 19 lb.; the wagon alone weighs 19 cwt. 3 qr. 23 lb. : what was the weight of the hay?

11. A man, having 160 A. of land, sold 39 A. 2 R. 15 P.: how much had he left?

12. A hogshead of beer leaked 36 gal. 1 qt. 1 pt.. how much was left?

13. A man has a journey of 60 miles to perform; he travels 23 mi. 3 fur. 18 rd. the first day, and the remainder, the second: how far did he travel the second day?

14. A rock weighing 1 T. 3 cwt. 1 qr. 18 lb. 6 oz. was broken in two pieces, one of which weighed 13 cwt. 19 lb. 10 oz.: what was the weight of the other piece?

79. TO FIND THE TIME BETWEEN ANY TWO DATES. EXAMPLE.-What is the time from March 17th, 1864, to January 12th, 1866?

SOLUTION. Write the first date under the last, numbering the months in their order; subtract as in subtraction of other compound numbers, remembering that 30 days are considered a month.

yr.

SOLUTION.
mo. da.

1866 1 12

1864 3 17

1 9 25

15. How long from June 5th, 1853, to Aug. 21st, 1859?

16. A note was given June 15th, 1861, and paid Aug. 9th, 1866: how long was it on interest?

17. How long from July 4th, 1776, to April 12th, 1861?

18. How long from May 27th, 1839, to Aug. 25th, 1865?

19. A certain man was born June 15th, 1837: what was his age Sept. 1st, 1861?

20. How long from the Battle of Lexington, Apr. 19th, 1775, until now?

MULTIPLICATION: COMPOUND NUMBERS.

80. Multiplication of Compound Numbers is the process of taking a number, consisting of different denominations, as many times as there are units in another.

MODEL SOLUTION.

EXAMPLE.-A merchant sold 7 bags of flour, each containing 1 bu. 3 pk. 5 qt.: how much did he sell in all?

SOLUTION.-Since one bag contains 1 bu. 3 pk. 5 qt., 7 bags will contain 7 times 1 bu. 3 pk. 5 qt.

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4 pk. 3 qt.

Write the 3 qt. under the qt., and add the 4 pk. to the product of pk.; 7 times 3 pk.

13

1

Write

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are 21 pk; 21 pk. + 4 pk. =25 pk. ; 25 pk. =6 bu. 1 pk.

the 1 pk. under the pk., and add the 6 bu. to the product of bu. 7 times 1 bu. are 7 bu.; 7 bu. + 6 bu. under bu.

=

13 bu., which write

CONCLUSION. Therefore, if a merchant sold 7 bags of flour, each containing 1 bu. 3 pk. 5 qt., he sold 13 bu. 1 pk. 3 qt. Hence, the

Rule for Multiplication of Compound Numbers.Write the multiplier under the lowest denomination of the multiplicand.

Multiply as in simple numbers, and reduce and carry as in addition of compound numbers.

PROOF. The same as in multiplication of Simple Numbers.

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