Remember the reciprocal of a number x is 1/x, for example the
reciprocal of 8 is 1/8. To divide by a fraction you simply multiply
by the reciprocal of the fraction.
Example
Let’s do an example:
(4/5) / (6/y) = (4/5) x (y/7) = (4y/35)
Example
Lets try another example, I will show you two different ways you
can solve this problem and you can decide for yourself which one is
easier.
Simplify the following: (4 + 1/x) / (4/x + 4)
Solution 1: multiplying by the reciprocal:
First lets take the top expression (numerator) and turn it
into a single fraction with a denominator x:
4 + (1/x) = (4x +1) / x
Do the same thing with the bottom expression (denominator)
(4/x) + 4 = (4 + 4x) / x
So now we have the following:
So if we think of the right side as a division of the top by the
bottom we get the following:
So now we can carry out the multiplication procedures to get the
following answer:
Solution 2: multiplying the top and bottom
In our original problem you will notice that there is a “/x”
in both the numerator and denominator. So if we multiply the top
and bottom by x, it will simplify the equation by removing the
fractions on the top and bottom. Remember that by multiplying by
1 we are not changing the original value of the fraction, just
its form.
| (4 + 1/x) / (4/x + 4)
x |
 |
= |
|
= |
 |
Notice that the two answers are the same.
|
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