DIVISION.
In division two numbers are given, and it is required to find how often the for mer contains the latter. Thus it may be asked how often 21 contains 7, and the answer is exactly 3 times. The former given number (21) is called the dividend ; the latter (7) the divisor ; and the num ber required (3) the quotient. It fre quently happens that the division cannot be completed exactly without fractions. Thus it may be asked, how often 8 is con. tained in 19? the answer is, twice, and the remainder of 3. This operation con sists in subtracting the divisor from the dividend, and again from the remainder, as often as it can be done, and reckoning the number of subtractions. As this ope ration, performed at large, would be very tedious, when the quotient is a high num ber, it is proper to shorten it by every convenient method; and, for this purpose, we may multiply the divisor by any num ber, whose product is not greater than the dividend, and so subtract it twice or thrice, or oftener, at the same time. The best way is, to multiply it by the greatest number that does not raise the product too high, and that number is also the quotient. For example, to divide 45 by 7, we inquire what is the greatest multi plier for 7, that does not give a product above 45; and we shall find that it is 6; and 6 times 7 is 42, which, subtracted from 45, leaves a remainder of 3. There fore 7 may be subtracted 6 times from 45; or, which is the same thing, 45 divided by 7, gives a quotient of 6, and a remain der of 3. If the divisor do not exceed 12, we readily find the highest multiplier that can be used from the multiplication table. If it exceed 12, we may try any multiplier that we think will answer. If the product he greater than the dividend, the multiplier is too great; and if the re mainder, after the product is subtracted from the dividend, be greater than the divisor, the multiplier is too small. In either of these cases we must try another. But the attentive learner, after some prac tice, will generally hit on the right multi plier at first. if the divisor be contained
oftener than ten times in the dividend, the operation requires as many steps as there are figures in the quotient. For instance, if the quotient be greater than 100, but less than 1000, it requires three steps.
Example. Divide 48764312 by 9.
9)48764312 Ans. 5418::;56-8 remainder.
9 Proof 48764312 In this example, we say the 9's in 48, 5 times and 3 over ; put down 5 and carry 3, and say 9's in 37, 4 times and 1 over ; put down 4 and carry 1; 9's in 16, 1 and 7 over ; and so on to the end ; there is 8 over as a remainder. The proof is ob tained by multiplying the quotient by the divisor, and taking in the remainder : this is called " Short Division," of which we give for practice the following exam 1. Divide 4732157 by 2 2. . . 342351742 by 3 3. . . 435234174 by 4 4. . . 49491244 by 5 5. . . 94942484 by 6 6. . . 4434983 by 7 7. . . 994357971 by 8 8. . . 449246812 by 9 9. . . 557779991 by 11 10. . . 665594765 by 12 The second part of this rule is called "Long Division," for the practice of which we give these directions.
Count the same number of figures on the left of the dividend as the divisor has in it; try whether the divisor be contain ed in this number ; if not contained there in, take another dividend figure, and then try how many times the divisor is contain ed in it.
To find more easily how many times the divisor is contained in any number ; cast away in your mind all the figures in the divisor, except the left hand one, and cast away the same number from the di vidend figures as you did from the divi sor : the two numbers, being thus made small, will be easily estimated.
If the product of the divisor with the quotient figure be greater than the num ber from which it should be taken, the number thought of was too great, the multiplying must be rubbed out, and a less quotient figure used.
When, after the multiplying and sub tracting, the remainder is more than the divisor, the quotient figure was too small, the work must he rubbed out, and a larg er number supplied.