Simplifying Complex
Fractions
by multiplying by
a common denominator
Method 1: This is one of two methods
for simplifying complex fractions.
Also see Method 2.
Remember ... a complex fraction is just a fraction
within a fraction.
To Simplify a
Complex Fraction by Multiplying by a Common Denominator
1. Find the least common denominator (LCD) of
all fractions appearing within
the complex fraction.
2. Multiply both the numerator and the denominator of the
complex fraction by the LCD of the
complex fraction from step 1.
3. Simplify whenever possible.
Let's see Method 1
at work on the following problems:
1.
2.
3.
4.
5.
Remember ...
Complex Fractions are EASY to simplify
if you show your work!
1.
Solution: The least common denominator
for the ENTIRE problem is 8. Multiply the top and the bottom
by 8.
2.
Solution:
The mixed number should be changed
to an improper fraction before starting Method 1. Remember
that the unseen denominator for 9 is 1. The least common
denominator for the ENTIRE problem is 3. Multiply the top and
the bottom by 3.
3.
Solution:
The least common denominator for the ENTIRE problem
is 32. Multiply the top and the bottom by 32.
Be careful
to distribute the 32 through
the parentheses.
Now simplify: factor the
top and the bottom. Simplify the final answer.
4.
Solution:
The least common
denominator for the ENTIRE problem is 12x. Multiply the top and
the bottom by 12x.
Be
careful
to distribute the 12x through
the parentheses.
Now simplify: factor
the top and the bottom.
5.
Solution:
The least common denominator for the ENTIRE problem
is 6x2. Multiply the top and the bottom by 6x2.
Be
careful
to distribute the 6x2
through the parentheses.
Write the
final answer.
Don't let
these fractions trip you up!
Just work carefully through
each problem, showing your work as you progress.
