Reduction
Algebra Help: Section 3.3
Reduction
The Reduction of a quantity is the operation of changing its form without altering its value.
Case 1
Reduce a fraction to its lowest terms.
A fraction is in its lowest terms when its numerator and denominator are prime to each other.
1. Reduce to its lowest terms:
14ab3c ------- 21a2bc2
OPERATION:
14ab3c ------- = 21a2bc2 2b2 --- 3ac
ANALYSIS -
If we divide both numerator
and denominator of this fraction by
the same number, its value will not be changed.
If we divide by the greatest common divisor,
the quotients will be prime to each other.
Consequently the fraction will be in its lowest terms. By inspection we find
7abc equals the greatest common divisor. Dividing both
terms by this quantity, we have the answer:
2b2 --- 3ac
2. Reduce to its lowest terms:
a2x + ax2 --------- a2 - x2 = ax(a + x) -------------- (a - x)(a + x) = ax ------- (a - x)
ANALYSIS -
We first resolve the numerator and denominator into their
prime factors, and then cancel the common factor (a + x).
Then we have the answer:
ax ------- (a - x)
From these examples we deduce the following rule.
RULE - Divide both numerator and denominator by their greatest common divisor.
Or, resolve the numerator and denominator into their prime factors, and cancel all those that are common.
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Page 78-79
Help with Algebra Homework
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New Elementary Algebra
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By Horation N Robinison, LL. D. Ivison, Blakeman & Company, Publishers, New York and Chicago.
