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It was shown in Arithmetic, Art. XXII, that a common denominator may frequently be found much smaller than that produced by the above rule. This is much more easily done in algebra than in arithmetic.
9. Add together-or, d, and J. b co be cg Here the denominators will be alike, if each be multiplied by all the factors in the others not common to itself. If the first be multiplied by eg, the second by cog, and the third by b ce, each becomes b c e g. Then each numerator must be multiplied by the same quantity by which its denominator was multiplied, that the value of the fractions may not be altered.
15 a b c 2 m” r 15. Add together TT 2 Fo and F noz'
16. Add together #. and 13 c d.
17. Add together 2 a m, and 2 a c – 5 b. 4 a n
which is the answer.
2 a b d – 3 cm.
sign — was changed to +. See Art. WI, example 6th
When the fraction was subtracted, the
XIX. Division of whole numbers by Fractions, and Fractions by
How many times is ; contained in 7 ?
1 + as - - - 3 many times; that is, * or 114 times. 2. How many times is ; contained in a 2 .Ans. } is contained in a, 8 a times, and # is contained ; as
many times; that is, *.
3. How many times is # contained in c :
..Ans. # is contained b c times in c, and # is contained".
g as many times; that is, bc. 0. * Arith. Art. XXIII. 4. Of what number is c the # part .Ans. If c is the # part of some number, f will be + &
part of the same number, and is ; part of bc. 0. 0. Arith. Art. XXIV.
Hence, to divide a whole number by a fraction, multiply it by the denominator of the fraction, and divide the product by the numera
6. How many times is # contained in # ?
Solution. If # is the } part of some number, 1. part of 0.
Hence, to divide a fraction by a fraction, multiply the numerator of the dividend by the denominator of the divisor, and the denominator of the dividend by the numerator of the divisor.
Or more generally, when the divisor is a fraction, multiply the dividend (whether whole number or fraction) by the divisor inverted.
Arith. Arts. XXIII. and XXIV.