Reduce Fractions
Algebra Help: Section 3.8
Learn to reduce fractions to the least common denominator.
Since a fraction can be reduced to higher terms only by multiplication, each of the higher denominators it may have must be some multiple of the given denominator. Hence, a common denominator for two or more fractions must be a common multiple of their denominators, and the least common denominator must be the least common multiple.
1. Reduce the following to fractions to their least common denominator.
c --- ab2
and
m --- a2b
OPERATION:
a2b2 ÷ ab2 = a a2b2 ÷ a2b = b c ac --- = --- ab2 a2b2 a * c = ac b * m = bm m bm --- = --- a2b a2b2
ANALYSIS -
We find by inspection that a2b2 is the least
common multiple of the given denominators; it is therefore, the least denominator
to which the fractions can be reduced. To ascertain what factor will
reduce each denominator to a2b2, we divide this term by each denominator,
and obtain a and b. Since the given denominators must be multiplied
by a and b respectively to reduce them to the required denominator,
the corresponding numerators must also be multiplied by these factors
for the new numerators. We have a * c or ac, for the first numerator.
We have b * m or bm for the second numerator. Therefore the
answer follows:
ac bm ---- and --- a2b2 a2b2
RULES -
- Find the least common multiple of all the denominators, to determine the least common denominator
- Divide this common denominator by each of the given denominators. Multiply each numerator by the corresponding quotient. The products we be the new numerators.
Before commencing the operation, each fraction must be in its lowest terms.
Page 87-88
Page 87-88
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.
