106. An apple dealer in Chicago finds that out of 1849 +956+987 barrels of apples sent to him from Michigan, 280 barrels of them are damaged. How many orders of 800 bbls. can be filled from the remainder? How many barrels will be left?

107. Bought a house, lot, horse, and chaise, for $17800. If I paid $7890 for the lot, and $480 for the horse and chaise, how much was paid for the house?

108. If 11500500 and 12567658 be added to 7984307, the sum will be the number of inhabitants in France in 1830. The population of the British Empire at the same time was 22297621. Which country had the larger population? and how many more?

109. A speculator bought 3 houses, paying for the first $7010, for the second $13000, and for the third as much as for the first and second, less the number of dollars which the second cost more than the first. How much did he pay for the third house?

110. The source of the Missouri River is 6800 feet above the level of the sea; that of the Mississippi is 1680 feet above the sea level. A certain spring is located 1009 feet below the source of the Missouri. How far above or below the source of the Mississippi is it?

111. 3 houses are found to be standing in a straight line; the second 5420 feet from the first, and the third 7337 feet from the second. A certain tree standing between the second and third is 538 feet from the third. How far is the tree from the first house?

112. $6385 was paid for each of four houses, which were soon after sold so as to lose $987 on each of two of them. How much was received for the houses?

113. A commission merchant received 7598 barrels of flour for each of six months, and sold 7438 for each of five months. How many barrels has he left?

114. If I can save $568 a year from my income, how much less than $3600 can I save in 6 years?

115. Bought a house, farm, and 4 horses for $15310. If I paid $4375 for the house, and $560 for the horses, how much does my farm cost?

116. A herds 19020 sheep, B 12780, and C 5460 less than A. How many sheep more or less does C herd than B?

117. A, B and C, form a partnership with a capital of $25800; if their gains the first 3 years are respectively $1800, $2500 and $4875, and their losses $980, $650 and $298, what are they all worth at the end of that time?

118. An army of 100000 men engaged in battle, and was re-enforced by 29000 more; 237 deserted, 12888 were killed, 1500 were missing. How many were left in the army?

119. The population of New York is about 4362834, of New Jersey 905794, of Pennsylvania 3519601, and of Delaware 125015. How much is the population of New York greater or less than the three other Middle States?

120. In the year 1860 the number of teachers employed in the public schools of Illinois was 11099, and the number of pupils in attendance 433018; in Massachusetts the number of teachers 5308, and of pupils 206974; in New York the number of teachers 15872, and of pupils 697273. How many more pupils than teachers in these States?

121. Three brothers bought a factory, the first paying $5682.40, the second $8624.80, and the third as many dollars more than the second as the second paid more than the first. How much did the third brother pay?

122. The brothers mentioned in the above example sold the factory for $30450, the first receiving $932.50 more than he paid, the second $1720.60 more than he paid, and the third the remainder. How much did the third brother receive?

123. A man purchased a house and farm for $7630.50; he expended $1230 in repairing the house, $987.50 in improving the farm, and $556.75 in planting an orchard, when he sold both for $12579. How much did he gain?

124. Bought a quantity of grain of one man for $1210.60, another quantity of another man for $929.85, a third quantity of a third man for as many dollars less than the second as the second is less than the first. How much was paid to the third man?

125. If a man's income is $200 a month, and his expenses are $35 a month for rent, $48.60 for grocery bills, and $45.75 for other expenses, how much can he save in 6 months?

126. The difference of $17846 and $27984, is what was paid for a certain property, it was soon after sold for $14025. How much was the gain?

127. George Washington died in 1799 at the age of 67 years. How long before his birth was the discovery of America in 1492?

128. C has $15890; A has $1546 less than C. How many dollars has A? B has $6430 less than A; how many dollars has B? D has $62 more than A and B together; how many dollars has D?

129. A farmer filled 4 bins with grain. Into the third he put 2240 bushels; into the first, 420 bushels less than into the third; into the second, 840 bushels less than into the first; and into the fourth he put 650 less than into the first and second together. How many bushels did he put into each bin?

130. A farmer being asked how many sheep he had, replied that if he had 420+560 more, he should have 3628 sheep. How many had he?

131. After A, B, C, and D had traded for a year, it was found that C owned $21360, that A owned $930 less than C, that B owned $930 less than A, and that D owned $930 more than B. How many dollars did each own?

132. A gentleman dying bequeathed his property, consisting of real estate to the value of $380500, and bank stocks amounting to $360500, as follows: to his brother $95640; to his sister as much as to his brother, less $15000;

to his son $59880 more than to his sister; to his wife as much as to the other three plus $18000; and the remainder to a charity. How much was given to charity?

133. A grain merchant in Chicago received two orders from New York, one for 15000, the other for 10000 bushels of corn, and a smaller order. In fulfillment of these orders How much was the smaller

he shipped 31780 bushels. order?

134. From three times the sum of eighty-seven thou、 sand six hundred four, forty-nine thousand three hundred fifty-eight, and twenty-nine thousand one hundred ninety, take four times the difference of the first two numbers, and tell how much the remainder exceeds the last of the given numbers?

135. Bought 5 houses, each for $6788, and gave in payment 6 lots, each for $3790, and the rest in money. How much money did I give?

136. A revenue cutter cruising in the Pacific Ocean started from a certain point and sailed north 1525 miles, then south 825 miles, then north 728 miles, then south 960 miles, then north 588 miles, then south 1438 miles, then north 980 miles, then south 840 miles. How far was the vessel from the starting point? In what direction?

137. An aeronaut ascended from a certain point 3987 feet during the first hour, descended 1876 feet the second hour, ascended 2019 feet the third hour, dropped down 2569 feet the fourth hour, rose 3289 feet the fifth hour, sailed due east 12 miles the sixth hour, and then descended 3429 feet the seventh hour. How far from the earth is the aeronaut at the end of the seventh hour?

SECTION V.

MULTIPLICATION.

Art. 41. A farmer gave to each of his 4 sons 5 acres of ground. How much did he give them all?

PROCESS OF ADDITION.

5 acres+5 acres +5 acres+5 acres 20 acres.

ANALYSIS. Since the farmer gave to each son 5 acres, he gave to the 4 sons the sum of 5 acres+5 acres+5 acres+5 acres 20 acres. The above is an illustration of examples in which it is required to obtain the sum of several numbers each equal to the other, and the method of obtaining this sum may be either by the above process called " process by addition," or by a much shorter process, as follows:

PROCESS BY MULTIPLICATION.

4 times 5 acres 20 acres.

66

=

ANALYSIS.-Since the farmer gave

to each son 5 acres, he gave to the four sons 4 times 5 acres 20 acres.

This latter method is called the

'process by multiplication." Hence,

42. Multiplication is a short method of obtaining the sum of several equal numbers.

Thus, instead of saying 3+3+3+3+3=15, we say 5 times 3=15, or 5 3's 15. When the numbers to be added are both large and numerous, the process by addition would be very laborious.

43. The terms employed in multiplication are multiplicand, multiplier, and product.

44. The Multiplicand is any one of the equal

numbers to be added.

Thus, in the problem above, 5 acres is the multiplicand.