SIMPLE DIVISION. ^^ 



the dividend j which number divide as before 5 and sq 

 on, till the whole is finished. 



Method 



on. In order, therefore, to complete the quotient, put the last 

 remainder at the end of it, nbove a small line, and the divisor be<» 

 low it. 



It is sometimes difficult to find how often the divisor may be 

 had in the numbers of the several steps of the operation ; the best 

 way will be to find how often the first figure of the divisor may 

 be had in the first, gr two first, figures of the dividend, and the 

 answer made less by one or two is generally the figure \yanted : 

 beside, if after subtracting the product of the divisor and quo-, 

 tient from the dividend, the remainder be equal to, or excee4 

 the divisor, the quotient figure must be increased accordingly. 



If, when you have brought down a figure to the remainder, it 

 is still less than the divisor, a cypher must be put in the quotient, 

 ^nd another figure brought down, and then proceed as before. 



The reason of tbe method of proof is plain : for since the quo- 

 tient is the number of times the dividend contains the divisor, the 

 product of the quotient and divisor must evidently be equal to th^ 

 dividend. 



There are several other methods made use of to prove division ; 

 the best and most useful arc these following. 



Rule I. Subtract the remainder from the dividend, and divide 

 this number by the quotient, and the quotient found by this divis- 

 ion will be equal to the former divisor, when the work is right. 



The reason of this r^lc is plain from what has been observed 

 above. 



Mr. Malcolm, in his Arithmetic, has been drawn into a mistake 

 concerning this method of proof, by making use of particular num- 

 bers, instead of a general demonstration. He. says, the dividend 

 being divided by the integral quotient, the quotient of this du ision 

 will be equal to the former divisor, with the same remainder.— 

 This is true in some particular cases ; but it will not hold, v/hen 



the 



