Reduce Fractions
Algebra Help: Section 3.7
Learn to reduce fractions to a common denominator.
1. Reduce fractions a/x, b/y and c/z to a common denominator.
OPERATION:
a ayz - = --- x xyz b xbz - = --- y xyz c xyc - = --- z xyz
ANALYSIS -
We multiply both terms of each fraction
by the product of the denominators of the others.
In other words, multiply the terms of the first by yz.
Multiply the terms of the second by xz.
Multiply the terms of the third by zy.
This process doesn't alter the value of the fractions. This process reduces the fractions to a common denominator. Each new denominator is the product of all the given denominators.
Notice the numerator from the product with a/x includes all but x.
Notice the numerator from the product with b/y includes all but y.
Notice the numerator from the product with c/z includes all but z.
Similar common denominators would cancel out similar numerators, if we multiplied each
fraction by the entire common denominator.
a xyz axyz - * --- = ---- x xyz xxyz cancel the x in both numerator and denominator: a xyz ayz - * --- = ---- x xyz xyz
RULE - Multiply each numerator by the product of all the denominators except its own, for the new numerators. All the denominators together form the common denominator.
NOTE - Mixed quantities must first be reduced to fractions, and entire quantities to fractional forms by writing 1 for a denominator.
Page 86-87
Page 86-87
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.
Windows algebra games, designed to help with classwork, coming soon!
Windows games, in progress, work with this set of free tutorials, modified
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.
