Art. 23. When any of the right hand figures of the multiplicand, or multiplier, are ciphers.

According to the principle of notation, annexing one cipher to any number, multiplies it by 10; annexing two ciphers, multiplies it by 100; annexing three ciphers, multiplies it by 1000; and so on.

ILLUSTRATION. Multiply 475 by 10, by 100, and by

From the above principle and illustration we derive the following

RULE. Place the significant figures of the multiplier under the significant figures of the multiplicand, then, omitting the ciphers, multiply the significant figures of the multiplicand by the significant figures of the multiplier, and annex as many ciphers to the product as were omitted in both factors.

89. A farmer purchased 20 cows at 25 dollars each, what did the 20 cows cost?

90. What is the value of a farm containing 200 acres, at 30 dollars an acre?

91. What will 750 shares of railroad stock amount to, at 500 dollars a share?

92. If a passenger train of railroad cars travel 20 miles an hour, how many miles will it travel in 50 hours?

93. There are 320 rods in one mile; what number of rods are there in 200 miles?

94. What would be the cost of a railroad 250 miles in length, at 30,000 dollars a mile ?

95. What is the capital stock of Boston and Lowell Railroad, there being 3600 shares, at 500 dollars a share?

96. What is the capital stock of Merchants' Bank, in Boston, consisting of 30000 shares of 100 dollars each?

Art. 24. When the multiplier is equal to the product of any two numbers, each of which does not exceed 12, it is often more convenient to multiply by the factors of the multiplier.

ILLUSTRATION. If a yard of cloth be worth 17 cents, what are 15 yards worth?

In this question, the multiplier 15, is equal to the product of the factors 3 and 5. Multiplying 17 cents, the value of one yard, by 3, the product is 51 cents, the value of 3 yards. Then multiplying 51 cents by 5, the product is 255 cents, or 2 dollars and 55 cents, the value of 15 yards.

From the preceding illustration we obtain the following RULE. Find any two numbers whose product is equal to the multiplier. Multiply the multiplicand by one of these numbers, then multiply the product by the other; the last product is the total product required.

107. What will 120 yards of cloth come to, at 6 dollars a yard?

108. What is the value of 132 acres of land, at 34 dollars an acre?

109. If 1 acre of land produce 36 bushels of corn, what number of bushels will 18 acres produce?

110. If an acre of land produce 225 bushels of potatoes, what number of bushels will 25 acres produce?

111. If a ship sails uniformly 175 miles each day, what number of miles will she sail in 27 days?

112. A man purchased a wood lot containing 33 acres, at 35 dollars an acre; what did it cost him?

113. If a bale of sheeting contains 32 pieces, and each piece measures 36 yards, what number of yards does the bale contain?

114. A merchant purchased 42 pieces of broadcloth, each piece containing 38 yards; what number of yards did he purchase?

DIVISION OF SIMPLE NUMBERS.

Art. 25. DIVISION is the method of finding the number of times, or part of a time, one number is contained in another. By division, we can also find any required part of any given number.

The terms used in division, are the dividend, divisor, quotient, and remainder.

The dividend is the number to be divided. The divisor is the number to divide by, and it indicates what part of the dividend is required by the question. The quotient is the number found by the operation, and it expresses the number of times, or part of a time, the divisor is contained in the dividend; it also expresses the number of units, or part of a unit, in that part of the dividend required by the question. The remainder, if any, is that part of the dividend which remains after the operation has been performed, and is always less than the divisor; consequently, it will contain the divisor only a part of a time, which may be expressed by writing the remainder over a short line, and the divisor under it, at the right of the quotient figures already obtained. This part is called a fraction.

ILLUSTRATION. How many times is 5 contained in 20? We know that 4 times 5 are 20; hence, it is plain that 5 is contained 4 times in 20. In this question, 20 is the dividend, 5 is the divisor, and it indicates the part of the dividend required, viz., 1 fifth. The quotient, 4, is the number of times the divisor is contained in the dividend; and it is also the number of units in 1 fifth of the dividend.

What is 1 fifth of 32? 1 fifth of 30 is 6. 1 fifth of the remainder 2, is 2 fifths of 1. Then 1 fifth of 32 is 63.

A short horizontal line between two points, indicates that the number before it is to be divided by the number after it; thus, 3065.

1. How many peaches, at 21 2. How many oranges, at 3 cents each, can you buy with 4 cents each, can you buy with 6 cents? cents?

3. 4 are how many times 2? 5. 1 half of 4 is how many? 7. How many yards of cloth, at 4 dollars a yard, can you buy with 12 dollars?

9. 12 are how many times 4? 11. 1 fourth of 12 is how many?

4. 6 are how many times 3? 6. 1 third of 6 is how many? 8. In 1 gallon there are 4 quarts; how many gallons are there in 20 quarts?

10. 20 are how many times 4? 12. 1 fifth of 20 is how many?