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Although the Rule before delivered be universal, as appears by the foregoing examples, yet the following method will be generally more convenient in practice.
I. To Multipya whole Number by a Fraction.
Multiply the whole number by the numerator of the fraction, and divide that product by the denominator.
Application. A B E Let 4 be multiplied by #; 4 multiplied 3c by the numerator 3 makes 12, which pro
3 duct divided by the Denominator 4, the 4d. quotient is 3, which is the product of 4 mnltiplied by 3. Cor. Since 1 doth not multiply a number, it follows, that when the numerator of a fraction is 1, the product is found by dividing by the denominator. . Let the examples II, be done of this. Again, To multiply a whole number by the integral part of the mixt number, and then by the fractional part, and add the products together,
- Application. 8 8 As suppose it was required to 5#. 5; multiply 8 by 5 and 3; first, 8 —- - multiplied by 5 is 40 and 8 in222 ) 40 40 to 3 makes 5}, or else by #, #; 5; # 23 and again, by #, and lastly the — # 23 sum of 40 and 5%, is 45; the
45; -- product required. - -
Multiply the Numerator of the Dividend by the Denominator of the Divisor for a Numerator, and the Denominator of the Dividend by the Numerator of the Divisor for the Denominator of the Quotient. Appli- . quotient, in like manner 4 multiplying I produces 4 for the denominator of the quotient, which is 4 or 14
Application. Let 3 be to be divided by , 3 (the A numerator of the dividend) inultiply- a 1 ing 2 (the denominaior of the devisvr) —— produces 6 for the numerator of the b 2
Note. When the denominator of the divisor and of the dividend are equal, the quotient may be found by common Division, viz. by dividing the numerator of the dividend by the Numerator of the divisor, rejecting the common denominator entirely.
As suppose 4 to be dividend by 3, 3 dividing 6 the quotient is 2, which is likewise the quotient of #, 3 dividing #
(See the Example, Case I.) N OWr
Now this rule may be made very extensive or universal, thus: reduce the divisor and a dividend to one common denominator, and divide the numerator of the dividend by the numerator of the divisor.
As if were to be divided by ; ; ; is equal to #, and I dividing 4, the quotient is 4, the true quotient of ; divided by #; or if # be divided by 3, i. e. 3, 4 by dividing 1 the quotient is #,
Note. 2. If a whole number be to be divided by a fraction, multiply the whole number by the denominator of the fraction, and divide the product by the numerator thereof, thus 48 being to be divided by #, the quotient is 48 x 7 E84.
4. To divide a fraction by a whole number, multiply the denominator of the given fraction by the given whole number for the denominator of the quotient, and make the numerator of the given fraction the numerator. Thus iet the examples of the second class be resolved. To divide a mixed number by a whole number. 1. If the integral part of the mixt number be less than the divisor, change the mixed number into an improper fraction, and divide the said fraction according to last. So 1; being to be divided by 4 ; the mixed number reduced to an improper fraction makes +4, which being divided by 4, makes the quotient #. 2. But if the integral part of the mixed number be greater than the divisor, divide the said integral part by the said divisor, and if any thing remain, reckon it together with the fractional part, a mixed number to be divided. So 13 3, divided by 4 quotes 3 #; for 4 in 13 is 3 times, and 1 remains, viz. 1 #, which divided by 4, as above, makes #. - If nothing remains after the divisor divides the integral part, then divide the fractional part as before.