## Algebra Rule 9

#### Factors in the numerator of a fraction that are the same as the denominator can be cancelled

**Description:**

Division can be thought of as the inverse of multiplication: if ``{a \over b} = c`` then ``b*c = a``. This means that the fraction ``{ac \over c}`` is equal to ``a``, since we are multiplying ``a`` by ``c`` and then immediately dividing it by ``c`` again, which puts us right back to where we started. This rule is an extension of that fact. Since we know that ``{ac+bc \over c} = {ac \over c} + {bc \over c}`` (see rule 8), and based on the above we can see that ``{ac \over c} = a`` and ``{bc \over c} = b``, from that we have our result: ``a+b``.