DIVISION.

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

86. The Dividend is the number to be divided.

87. The Divisor is the number by which we divide.

88. The Quotient is the result obtained by the division. It shows how many times the dividend contains the divisor.

89. The Remainder is the part of the dividend which is sometimes left after dividing.

90. The Terms in Division are the Dividend, the Divisor, and the Quotient.

91. The Sign of Division is a short horizontal line (in the line of writing), with a dot above and another below the middle of it÷. It denotes that the number before it is to be divided by the number after it.

Thus, 82 is read 8 divided by 2. The forms 2J 8, and also indicate that 8 is to be divided by 2.

92. PRINCIPLES.-1. The dividend and divisor are like numbers. 2. The quotient is an abstract number.

3. The divisor is abstract in dividing a number into equal parts.

4. The product of the divisor and quotient, plus the remainder, if any, is equal to the dividend.

EXPLANATION.—This table is made the same as the multiplication table. The numbers in the left hand column may be regarded as the divisors, the numbers to the right as the dividends, and those across the top as the quotients.

Thus, 2 in 2, 1 time; 2 in 4, 2 times; 2 in 6, 3 times, etc.

There is little need of committing a table of quotients, if the pupil readily recalls the products in multiplication. Should we wish to know how many fives there are in 35, if we recall that five sevens are 35, we have the answer at once. Five is contained in 35 seven times; because five 7's are 35. Nine is contained in 54 six times; because nine 6's are 54.

Hence, division is the reverse of multiplication, or reverse multiplication, the product being regarded as the dividend, and the two factors as divisor and quotient.

DRILL EXERCISES.

93. Tell at once the quotients of the following:

94. When anything is divided into two equal parts, each part is called one half; when into three equal parts, one third; when into four equal parts, one fourth, etc.

95. A Fraction is one or more of the equal parts of anything.

96. Fractions are expressed as follows:

EXPLANATION —7 equals6 +1; 1 of 6 is 3, 1 of 1 is 1. Hence, 1⁄2 of 7 is 3}.

98. 1. Divide 1373 by 3.

Divisor. Dividend.

3)1374

Quotient. 458

EXPLANATION.-For convenience, we write the divisor at the left of the dividend with a curve line between them, draw a line under the dividend, and begin at the left to divide.

3 is not contained in 1 thousand any thousand times; 1 thousand equals 10 hundreds, which with 3 hundreds are 13 hundreds. 3 is contained in 13 hundreds 4 hundreds times and 1 hundred remaining. We write the 4 hun

dreds under the line in hundreds' place.

We write

1 hundred, the remainder, equals 10 tens, which added to 7 tens are 17 tens. 3 is contained in 17 tens 5 tens times and 2 tens remaining. the 5 tens under the line in tens' place.

tens, the remainder, equal 20 units, which added to 4 units are 24 units.

3 units is contained in 24 units 8 units times. We write the 8 under the line in units' place.

Hence, the quotient is 458.

In practice, we say: 3 in 13, 4 times; in 17, 5 times; in 24, 8 times. Answer, 458

Proof. The quotient, 458, multiplied by 3, the divisor, is 1374. Hence, the work is correct (Prin. 4).

When the work is performed by writing only the dividend, divisor, and quotient, as above, the process is called Short Division.

99. Short Division is the method in which only the dividend, divisor, and quotient are written, the operation being performed mentally.

Short division should be employed when the divisor does not exceed 12.

RULE. Write the divisor at the left of the dividend with a curve

line between them, and draw a line under the dividend.

Beginning at the left, divide each figure of the dividend by the

divisor, and place the quotient under the figure divided.

If there is a remainder after any division, regard it as prefixed to the next figure of the dividend, and divide as before.

If any partial dividend is less than the divisor, write a cipher in the quotient, and prefix such dividend to the next figure.

When there is a final remainder, write it after the quotient, or with the divisor beneath it as part of the quotient.

PROOF.-Multiply the quotient by the divisor, and add the remainder, if any, to the product. If the work is correct the result will equal the dividend.

We begin at the left to divide, so that the remainder can be united to the number of units of the next lower order, giving a new partial dividend.

100. 1. There are 3 feet in one yard. How many yards in 873 feet?

2. In one peck there are 8 quarts. How many pecks in 1952 quarts?