Reduce Mixed Quantities
Algebra Help: Section 3.6
Since a factor with a positive exponent may be transferred from the denominator to the numerator if its exponent is made negative, a factor with a negative exponent may be transferred if its exponent is made positive. Hence we have the general conclusion:
A factor may be transferred from either term of a fraction to the other, if the sign of its exponent is changed.
Reduce a mixed quantity to a fraction.
1. Reduce the following quantity to a fraction:
3 2 - 8
ANALYSIS -
16
2 = --
8
therefore
3 16 3 19 2 - = -- + - = -- 8 8 8 8
2. Reduce the following mixed quantity to a fraction.
x
a + -
b
OPERATION:
x
a + - =
b
ab + x
------
b
ANALYSIS - It's evident that
ab
a = --
b
Also
ab 1 -- = ab * - b b
Also
x 1 - = x * - b b
And
1
ab * - added to
b
1
x * -
b
equals
1
(ab + x) * -
b
which equals the answer:
ab + x ------ b
The algebraic operation is exactly like the arithmetical, and governed by the same principle, according to the following rule:
RULE - Multiply the entire part by the denominator of the fraction. Add the numerator if the sign of the fraction is a plus. Subtract the numerator if the sign of the fraction is a minus. Write the result over the denominator.
Page 84-85
Page 84-85
Help with Algebra Homework
Free tutorials provide math help for math problems. Tutorials start with algebra 1. Algebra tutorials include word problems related to algebra topics, as they're introduced. See the menu, above for algebra math equations, and explanation, by section.
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from the public domain text book titled,
New Elementary Algebra
containing the rudiments of the science for schools and academies.
By Horation N Robinison, LL. D. Ivison, Blakeman & Company, Publishers, New York and Chicago.
