DIVISION OF DIVERS DENOMINATIONS,

OR,

COMPOUND

DIVISION.

PLACE the divisor on the left hand, as in simple division, Begin at the left of the dividend, and divide the highest denomination by the divisor, and write down the quotient; multiply, the remainder, if any, by as many as make one of the next lower denomination, taking the number of the same denomination in the dividend, and divide the result as before, this will give that part of the quotient which belongs to this denomination; if there is again a remainder, multiply by the parts in the next lower denomination, and proceed as before directed, until all the denominations are gone through, annexing the fractional part, if any, to the last quotient, as before explained in simple division.

If in any of those divisions, there should be no remainder, divide the next denomination of the dividend by the divisor, and proceed as if commencing a new operation, placing a cipher in the quotient when any denomination of the dividend is less than the divisor, and taking the whole of said denomination as a remainder; proceed with it as before directed. NOTE. The quotients are always of the same name as the respective dividends.

Compound Division is proved by the multiplication of the quotient or answer by the divisor, and in general, one variation of the rule may be applied to prove another.

From the illustrations given of Simple Division, and Compound Multiplication, this rule is evident, as to divide any compound quantity, or number whatever, is the same as dividing the component parts of the compound quantity or number, seperately, by the given divisor.

When the divisor is a composite number, divide by one of the component parts, and the quotient arising by the other, and this by the third if the divisor consists of more than two parts, but in general, when this is the case, it may be as concise to proceed as in long division. When there are only two component parts, the rule already given in simple division, must be strictly observed, when determining the fractional parts, that is, to multiply the second remainder by the first divisor, and to the product add the first remainder. When there are three component parts, multiply the third remainder by the second divisor, and to the product add the second remainder; then multiply the result by the first divisor, and to the product add the first remainder, and the last sum will be the whole remainder, the same as if long division had been employed.

Framples.

When the divisor is greater than 12, and not a composite number, the several quotients must be found by the method of long division, multiplying each remainder by the number of parts which make one of the next lower denomination, and taking in the numbers of the dividend which are of the same denomination, which results are to be successively divided, until all the donominations are gone through, as explained in the general rule.

£ S d

Examples.

£

Divide 943 15 6 by 415, and 1000 by 365,

50

To divide any sum of money by 100.

Cut off two figures from the right hand of the pounds of the dividend; the figures to the left, are the pounds of the quotient; one-fifth of the figures cut off, are the shillings; to the remainder, if any, annex half the shillings of the dividend, from which, subtract one for every 24 therein, remainder consider as farthings, and those when divided by 4 will give the remainder of the quotient with as much accuracy as is generally required; but for greater, cut off by a perpendicular line the two right-hand figures of the pounds, those to the left will be the pounds of the quotient; multiply the figures cut off by 20, adding in the shillings of the dividend, and set down the two first figures of the product on the right side of the line, and the rest of the product on the left, which will be the shillings; multiply the figures now on the right by 12, adding in the pence of the dividend, and place the product as before, which will give the pence, then multiply the figures now at the right by 4, adding in the farthings of the dividend, and place the product as before; and the several numbers to the left of the line will be the quotient required, and if any number be on the right hand after the last multiplication, it will be the remainder and the numerator of a fraction of a farthing, of which 100 will be the denominator.