Algebra2go®
Complex Fractions
Objective 1
Learn how to simplify Complex Fractions
using the Clearing Fractions Technique
3+1
4 3
Consider the complex fraction 5 3 .
6−2
While simplifying this complex fraction
looks a bit complicated, it can be simplified
rather easily using the clearing fractions
technique.
Using the LCD for all four fractions, we can
clear away all four fractions! This can be done
by multiplying the LCD to the top and bottom
of the complex fraction.
This technique is demonstrated below.
3 1
4+ 3
5−3
6 2
LCD=12
12 ( 43 + 31 )
12 ( 56 − 23 )
Page 1 of 3
12 ( 43 ) + 12 ( 31 ) 9 + 4 13
=
=
=
3
5
−
−
8
12 ( 6 ) − 12 ( 2 ) 10 18
−
13
8
Algebra2go®
Again, the more you practice the clearing
fractions technique, the faster you will get at
simplifying the complex fraction expressions.
Example 1: Use the clearing fractions
technique to simplify the complex fraction.
2
a) 31
5
LCD=15
15 ( 23 )
15 ( 51 )
b)
2 + 83 − 61
5 −
12
1
LCD=24
24( 2 + 83 − 61 )
5 −1
24( 12
)
24( 2 ) + 24( 83 ) − 24( 61 )
5 − 24 1
24( 12
)
( )
Page 2 of 3
Algebra2go®
Part b) in Example 1 can be done very quickly
once you master this technique. Here’s what
the work of a “math Kung Fu” black belt would
look like. See if you can follow the work.
2 + 83 − 61
5 −
12
LCD=24
1
48 + 9 − 4
10 − 24
53
−
14
Answer the following homework questions.
In Exercises 1 – 6, simplify each complex fraction.
1)
2)
Page 3 of 3
8
7
6
5
3
8
2
9
3
3) 11
6
4)
5) 1
−1
2
2
1
3− 3 + 2
7 4
+
10 5
2
3
−3+
5
6
2− 3 + 4
1+ 4
6)
1
1
+ −
3
6
2 5
+ −
9 6
2
1