DIVISION 55
NOTE 1.- The proper remainder is in all cases less than the divisor. If, in the course of the operation, it is at any time found to be as large as, or larger than the divisor, it will show that there is an error in the work, and that the quotient figure should be increased.
NOTE 2.- If, at any time, the divisor multiplied by the quotient figure, produces a product larger than the part of the dividend used, it shows that the quotient figure is too large, and must be diminished.
§ 49. SECOND METHOD OF PROOF.- Add together the remainder, if any, and all the products that have been produced by multiplying the divisor by the seve- ral quotient figures, and the result will be equal to the dividend, if the work is right.
S 50. THIRD METHOD.-Subtract the remainder, if any, from the dividend, and divide this remainder by the quotient. The result will be equal to the original divisor, if the work is right.
NOTE.— The first method of proof (8 46) is usually most convenient.
EXAMPLES FOR PRACTICE.
2. How many times is 48 contained in 28618?
Ans. 596.
COOPERATION.
Dividend. PROOF BY MULTIPLICATION. Divisor 48) 28618 (596 Quotient. 596 Quotient. 240 48 Divisor. 461 432 4768 23840 298 288 28608 10 Remainder. 10 Remainder. 28618 Dividend.
