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104. What decimal of a bushel is 3 pecks?
105. What decimal of an ounce is 16 pennyweights ?

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109. Reduce 2 yd. 2 ft. 8.94 in. to a decimal of a rod.

193. Rule for Reduction of Integers to a Denominate Fraction.

Change the given number of the smallest denomination to a fraction of the next larger. Write this fraction as a part of the number of that larger denomination. Change, in like manner, the number thus formed, and so proceed as far as required.

110. Reduce 68 sq. rd. 155 sq. ft. to a fraction of an acre. 111. Reduce 10 oz. 13 pwt. 8 gr. to a fraction of a pound. 112. Reduce 232 d. 10 h. 21 min. to a fraction of a year. 113. Reduce 248 rd. 4 yd. 2 ft. 8 in. to a fraction of a mile. 114. Reduce 67 lb. 4 oz. to a decimal of a cental. 115. Reduce 5 cwt. 64 lb. to a decimal of a ton. 116. Reduce 4 yd. 2 ft. 5.25 in. to a decimal of a rod. 117. Reduce 18 h. 15 min. 50.4 sec. to a decimal of a day.

194. When it is required to find the part that one denominate number is of another,

Reduce the numbers to the same denomination, and divide the result denoting the part by that denoting the whole.

118. What part of 2 A. 112 sq. rd. is 144 sq. rd ? 119. What part of 3 mi. 120 rd. 4 yd. is 2 mi. 120 rd. 3 yd. ? 120. What part of 1 lb. 4 oz. 12 pwt. 12 gr. is 5 oz. 10 pwt. ? 121. What decimal of 74 mi. 80 rd. is 9 mi. 90 rd. ? 122. What decimal of 7 bu. 1 pk. 5 qt. is 82 bu. 3 pk. 1 qt. ?

ADDITION.

195. The operations with compound numbers differ from those with simple numbers only in the fact that compound numbers have an irregular instead of a decimal scale.

The principles, however, being the same, no special rules are required for adding, subtracting, multiplying, or dividing compound numbers.

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In Ex. 124, the 4 ft. in the sum, reduced to units of a lower denomination, gives 6 in., which added with the 8 in. of the sum, and reduced, gives the second form of answer. In Ex. 125, the 4 sq. ft., in like manner, gives 36 sq. in., which added to the 66 sq. in. of the sum, and reduced, gives the second form of answer.

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131. Find the sum of 7t of a ton, it of a cental, and 1 T. 2 cwt. 3 lb.

132. A man traveled one day 60% miles, the second day 50 mi. 120 rd., and the third day 563 miles. How far did he travel in the three days ?

133. I have three lots, – the first contains of an acre, the second of an acre, and the third ti of an acre. How many acres have I ?

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137. From 116 A. 53 sq. rd. 100 ft. 113 in. take 87 A. 137 sq. rd. 100 sq. ft. 113 sq. in.

138. The longitude of Boston is 71° 4' 9" W. and that of Chicago 87° 35' W. What is the difference in the longitude of the two places ?

139. From 1} of a pound troy take 2 oz. 19.2 gr.

140. From a hogshead of molasses had leaked out. How much remained ?

141. From .367 of a year take .761 of a day.

142. The distance between two places is .7895 of a mile. How much is that more than of a mile ?

To find the Time between two Dates.

143. What is the time from May 16, 1819, to April 20, 1881 ?

Solution.
May 16, 1819, to May 16, 1880, = 61 y.
May 16, 1880, to April 16, 1881, = 11 mo.
April 16, 1881, to April 20, 1881, =

4d.
May 16, 1819, to April 20, 1881, = 61 y. 11 mo. 4 d.

196. Rule. Find first the number of entire years, then the number of entire calendar months remaining, and then the remaining days.

144. What is the time between Oct. 16, 1876, and Aug. 9, 1882 ?

145. A note was given Nov. 15, 1879, and paid July 5, 1881. How long did it run ?

146. How long from the surrender of Cornwallis, Oct. 19, 1781, to the battle of New Orleans, Jan. 8, 1815 ?

147. What time elapsed from the declaration of American independence, July 4, 1776, to the emancipation proclamation, Jan. 1, 1863 ?

148. How many days are there from Dec. 19, 1879, to Mar. 16, 1880 ? 12 + 31 + 29 + 16 = 88 Solution. — There are 12 days

remaining in December, 31 in January, 29 in February, and 16 in March, or, in all, 88 days.

149. A note dated April 9 is to be paid June 8, 1881. How long has it to run ?

150. Find the exact time, in days, between May 25, 1880, 10 P. M., and March 4, 1881, 9 A. M.

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