5. Equivalent Fractions
Recall the following fraction properties:
This is true because we have multiplied both the top (numerator) and the bottom (denominator) by 5. We say 3/4 and 15/20 are equivalent fractions.
This is true because we have divided both the numerator and the denominator by 7. We say 7/21 and 1/3 are equivalent fractions.
We now apply these ideas to fractions involving algebraic expressions.
Example 1:
Divide the numerator and the denominator of
by
3ab2.
NOTE: This answer is not in simplest form. We could divide top and bottom again by a2.
KNOW WHEN TO STOP!
The following expression cannot be simplified further because there is an addition sign in the numerator and a subtraction in the denominator:
We cannot cancel the x and the x2.
However, if the terms in the numerator and denominator are multiplied, then we can do further simplifying:
Example 1:
Reduce to simplest form:
First, let's see this LiveMath document where you can play with this idea.
We start by factoring the numerator:
Example 2:
Reduce to simplest form:
We need to factor both numerator and denominator:
At this point we can only cancel the [leading] 2 and 4:
Now, we recognise that the numerator is the difference of 2 squares:
Now, since the terms in brackets are connected by multiplication, we can cancel the (x + 2) from top and bottom:
Exercises.
Simplify:
(1) 
(2) 
(3) 
(4) 
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