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1.10 Simplifying Complex Fractions
Complex fractions are just fractions within fractions, so there may be a
fraction in either the numerator or the denominator or both. When this
happens, one way to approach the problem is to get the numerator as a
single fraction and get the denominator as a single fraction so that you can
flip the denominator and multiply. It is not the only way, but we find it to
be the simplest in most cases. (Another method would be to find the LCD
for all terms in the numerator and denominator and then multiply both of
them by this to clear the fractions, but we find that students often forget at
least one term, so we refrain from using that method and instead focus on
this method, which also reinforces the operations we covered in recent
lessons). Once again, we will begin with arithmetic and apply the same
procedure in algebra.
Arithmetic Example:
1
3 + 1
2
1
5 – 1
4
=
2
2∙1
3 + 1
2∙3
3
4
4∙1
5 – 1
4∙5
5
=
2
6 + 3
6
4
20 – 5
20
=
5
6
−1
20
= 5
6÷−1
20
=5
6∙−20
1=5
6∙−5 ∙ 2 ∙ 2 ∙ 5
2 ∙ 3 = − 50
3
Rewrite the numerator as one fraction and the denominator as one fraction.
To do this, get a common denominator for the numerator and the
denominator separately and simplify. Then rewrite the fraction as division
(numerator divided by denominator.)
We will now apply the same process on our algebraic examples.
