There's a lot of stuff in this topic! Read through each of the subtopics below carefully!
We use the same rules we have for arithmetic fractions when we are working with algebraic ones:
|1.|| add numerators when denominators are equal, or
|2.|| find a common denominator
|3.|| multiply numerators and denominators for a product
|4.|| to divide a fraction, multiply by its reciprocal
| this is the same as rule 4: we're multiplying by 1/c
| also the same as rule 4.
In no case can we divide by zero: (a/0) is undefined, and
(0/0) is also undefined. (a/a) = 1. And the sign
of a fraction is changed by changing the sign of either the numerator
or the denominator, but not both:
As in the last of the examples above, we can multiply (or divide) both
the numerator and denominator of a fraction by the same non-zero
factor without changing the fraction's value. This is equivalent to
multiplying by 1. We are using this rule when we add or subtract
fractions with different denominators. For example, to add
The reverse of multiplying the numerator and denominator of a fraction
by something is canceling common factors that appear
in both numerator and denominator:
A complex fraction is one whose numerator or denominator (or both) contains one or more fractions. To simplify a complex fraction, we change the numerator and enominator to single fractions and then divide.
We can reverse the rule for adding fractions to split up an expression
into two fractions:
Sometimes we can alter the form of the fraction even further by creating a duplicate of the denominator in the numerator, as shown in the second example below.
Be sure you've gone through each step in the examples above before doing these. Then work the practice problems. Once you've worked them until you're sure that you understand them, go on to the next section. There are more problems of this type in the section test at the end of the section.
Note that you can get new practice problems by clicking the "Refresh" button at the bottom of the practice set.