5. If 1 acre of land cost 36 dollars, what will 10 acres cost?

Ans. 360 dollars.

6. If 1 bushel of corn cost 65 cents, what will 1000 bushels cost? Ans. 65000 cents.

CASE III.

70. When there are ciphers at the right hand of one or both of the factors.

1. Multiply 1200 by 60.

OPERATION.

Multiplicand, 1200

Multiplier,

Product,

60 72000

ANALYSIS. Both multiplicand and multiplier may be resolved into their component factors; 1200 into 12 and 100, and 60 into 6 and 10. If these several factors be multiplied together they will produce the same product as the given numbers (67). Thus, 12×6=72, and 72 × 100=7200, and 7200 × 10 72000, which is the same result as in the operation.

RULE. Multiply the significant figures of the multiplicand by those of the multiplier, and to the product annex as many ciphers as there are ciphers on the right of both factors.

4. Multiply 70340 by 800400.
5. Multiply 3400900 by 207000.
6. Multiply 634003000 by 40020.
7. Multiply 10203070 by 50302000.

Ans. 56300136000.
Ans. 703986300000.
Ans. 25372800060000.

Ans. 513234827140000.
Ans. 18056887264000.

8. Multiply 30090800 by 600080. 9. Multiply eighty million seven thousand six hundred, by eight million seven hundred sixty. Ans. 640121605776000. 10. Multiply fifty million ten thousand seventy, by sixtyfour thousand. Ans. 3200644480000. 11. Multiply ten million three hundred fifty thousand one hundred, by eighty thousand nine hundred.

Ans. 837323090000. 12. There are 296 members of Congress, and each one receives a salary of 3000 dollars a year; how much do they all receive?

EXAMPLES COMBINING ADDITION, SUBTRACTION, AND

MULTIPLICATION.

1. Bought 45 cords of wood at 4 dollars a cord, and 9 loads of hay at 13 dollars a load; what was the cost of the wood and hay? Ans. 297 dollars.

2. A merchant bought 6 hogsheads of sugar at 31 dollars a hogshead, and sold it for 39 dollars a hogshead; what did he gain?

3. Bought 288 barrels of flour for 1875 dollars, and sold the same for 9 dollars a barrel; what was the gain?

Ans. 717 dollars.

4. If a young man receive 500 dollars a year salary and pay 240 dollars for board, 125 dollars for clothing, 75 dollars for books, and 50 dollars for other expenses, how much will he have left at the end of the year? Ans. 10 dollars.

5. A farmer sold 184 bushels of wheat at 2 dollars a bushel, for which he received 67 yards of cloth at 4 dollars a yard, and the balance in groceries; what did his groceries cost him?

6. A sold 2 farm of 320 acres at 36 dollars an acre; B sold one of 244 acres at 48 dollars an acre; which received the greater sum, and how much? Ans. B, 192 dollars.

7. Two persons start from the same point and travel in opposite directions, one at the rate of 35 miles a day, and the other 29 miles a day: how far apart will they be in 16 days? Ans. 1024 miles. 8. A merchant tailor bought 14 bales of cloth, each bale containing 26 pieces, and each piece 43 yards; how many yards of cloth did he buy? Ans. 15652 yards.

9. If a man have an income of 3700 dollars a year, and his daily expenses be 4 dollars; what will he save in a year, or 365 days? Ans. 2240 dollars.

10. A man sold three houses; for the first he received 2475 dollars, for the second 840 dollars less than he received for the first, and for the third as much as for the other two; what did he receive for the three? Ans. 8220 dollars.

11. A man sets out to travel from Albany to Buffalo, a distance of 336 miles, and walks 28 miles a day for 10 days; how far is he from Buffalo ?

12. Mr. C bought 14 cows at 23 dollars each, 7 horses at 96 dollars each, 34 oxen at 57 dollars each, and 300 sheep at 2 dollars each; he sold the whole for 3842 dollars; what did he gain? Ans. 310 dollars.

13. A drover bought 164 head of cattle at 36 dollars a head, and 850 sheep at 3 dollars a head; what did he pay for all?

14. A banker has an income of 14760 dollars a year; he pays 1575 dollars for house rent, and four times as much for family expenses; what does he save annually?

Ans. 6885 dollars.

15. A flour merchant bought 936 barrels of flour at 9 dollars a barrel; he sold 480 barrels at 10 dollars a barrel, and the remainder at 8 dollars a barrel; what did he gain or lose? Ans. Gained 24 dollars.

DIVISION.

MENTAL EXERCISES.

71. 1. How many hats, at 4 dollars apiece, can be bought for 20 dollars?

ANALYSIS. Since 4 dollars will buy one hat, 20 dollars will buy as many hats as 4 is contained times in 20, which is 5 times. Therefore, 5 hats, at 4 dollars apiece, can be bought for 20 dollars.

2. A man gave 16 dollars for 8 barrels of apples; what was the cost of each barrel?

3. If 1 cord of wood cost 3 dollars, how many cords can be bought for 15 dollars?

4. At 6 shillings a bushel, how many bushels of corn can be bought for 24 shillings?

5. When flour is 6 dollars a barrel, how many barrels can be bought for 30 dollars?

6. If a man can dig 7 rods of ditch in a day, how many days will it take him to dig 28 rods?

7. If an orchard contain 56 trees, and 7 trees in a row, how many rows are there?

8. Bought 6 barrels of flour for 42 dollars; what was the cost of 1 barrel?

9. If a farmer divide 21 bushels of potatoes equally among 7 laborers, how many bushels will each receive? 10. How many oranges can be bought for 27 cents, at 3 cents each?

11. A farmer paid 35 dollars for sheep, at 5 dollars apiece; how many did he buy?

72. Division is the process of finding how many times one number is contained in another.

73. The Dividend is the number to be divided.

74. The Divisor is the number to divide by.

75. The Quotient is the result obtained by the process of division, and shows how many times the divisor is contained in the dividend.

1. When the dividend does not contain the divisor an exact number of times, the part of the dividend left is called the remainder, and it must be less than the divisor.

2. As the remainer is always a part of the dividend, it is always of the same name or kind.

3. When there is no remainder the division is said to be exact.

76. The sign, ÷, placed between two numbers, denotes division, and shows that the number on the left is to be divided by the number on the right. Thus, 20÷4=5, is read, 20 divided by 4 is equal to 5.

12

Division is also indicated by writing the dividend above, and the divisor below a short horizontal line; thus, shows that 12 divided by 3 equals 4.

CASE I.

7. When the divisor consists of one figure. 1. How many times is 4 contained in 848?

OPERATION.

Dividend,

Divisor, 4)848

Quotient,

212

3 −4,

ANALYSIS. After writing the divisor on the left of the dividend, with a line between them, begin at the left hand and say: 4 is contained in 8 hundreds, 2 hundreds times, and write 2 in hundreds' place in the quotient; then 4 is contained in 4 tens 1 ten times, and write the 1 in tens' place in the quotient; then 4 is contained in 8 units 2 units times; and writing the 2 in units' place in the quotient, and the entire quotient is 212.

Define division. Dividend. Divisor. Quotient. Remainder. What is complete division? What is the sign of division? Case I is what? Give first explanation.