6. Multiplication and Division of Fractions
Recall the following fraction facts:
When multiplying by a fraction, multiply numerators and multiply denominators:
If you can, simplify first :
(I canceled the 13 & 39 to give 1/3 and the 12 with the 24 to give 1/2.)
When dividing by a fraction, invert and multiply:
(I multiplied by the inverse of 2/7, which is 7/2)
When we do the same things with algebraic expressions, remember to SIMPLIFY FIRST, so that the problem is easy to perform:
Example 1:
Simplifying first, we cancel the 11 in the first fraction with the 33 on the bottom of the second fraction to give 1/3:
Example 2:
Simplifying:
The first step in this problem involved expanding out the (ax)2 on the top of the second fractionto give a2x2.
Also, because it is multiplication, we can write it as one fraction (multiply tops, multiply bottoms).
Next, we cancel the 18 on top with the 3 on bottom (giving 6 on top).
Also we can cancel the s on top and bottom.
The a2 on top cancels with the a on bottom to give a on top.
The x2 on top cancels with the x2 on bottom to give 1.
We then multiply out what is left to give the final answer.
Let's see how LiveMath performs this example:
Example 3:
We invert the st/4 first to give 4/st and then multiply by that inverse:
To get from the first to the second row, I cancelled out the two s's on the top and bottom; and also cancelled the 4 on top with the 2 on bottom to give 2 on top.
Exercises.
Simplify:
(1) 
(2) 
(3) 
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