Fraction Rules
Algebra rules for combining fractions. These rules apply for both proper fractions and improper fractions. They apply for all rational expressions as well.
A. Special Fractions 1. simplifies to b. 2. does not simplify any further. 3. simplifies to 0. 4. is undefined. | Examples does not simplify. is undefined. So is . |
Special note: Why is it OK to have 0 on top (in the numerator) and not on the bottom (in the denominator)? Consider for a moment what division means. The reason that is because The fraction because What about ? It's undefined, too, but for a slightly different reason. If you multiply the 0 in the denominator by any number at all you get the 0 in the numerator. It seems that can equal any number. As a result we say is indeterminate, which is a special kind of undefined expression. | |
B. Negative Fractions 2. simplifies to 3. is NOT the same as | Examples |
1. cancels to 1 2. cancels to 3. cancels to 4. cancels to 5. cancels to b 6. cancels to b | Examples |
D. Addition 1. 2. 3. | Examples |
E. Subtraction 1. 2. 3. 4. | Examples |
F. Multiplication 1. 2. 3. | Examples |
Careful!! 1. 2. Mixed numbers are shorthand for addition and not multiplication. For example, means and NOT . | |
G. Division 1. 2. 3. | Examples |
See also
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