algebraic fractions

Computational Tricks
Rewrite problem with parentheses before you begin.
When creating equivalent fractions, use pairs of parentheses: to make room for needed factors: ()() - ()()

Create Equivalent Fractions
When creating equivalent fractions, think:: I have ...; I need ...; What's missing?

Reducing Fractions: Recall arithmetic; Do the same with algebraic expressions

Negative Fractions
Placement of a Negative Sign in a Fraction
- 5 5 5 ----- = ----- = - ---- 3 - 3 3 The first and the last are prefered.


Use Parenthises To Simiplify The Expression: Rewrite problem with parentheses before you begin.

Add or Subtract Fractions
To Add Fractions:
1st: Put parenthises around the numerators.
2nd: Factor each denominator writing the factors below the denominator.
3rd: Use Common Factors First Method or One Fraction At-A-Time Method for finding a common denominator.
Alt. 3rd: Use these factors to create the common denominator by listing the factor of each denominator that are not duplicated in another fraction.: "I have ...", "I need ... "
4th: Recopy numerators leaving "holes" with parenthesis
5th: Rewrite the numerator with missing factors to create equivalent fractions.: "I have ...", "I need ... "
6th: Simplify numerator (top of fraction).
7th: Factor the numerator if possible.
8th: Reduce the fraction if possilbe.
Add these fractions.
1st: Put parenthises around the numerators.
2nd: Factor each denominator writing the factors below the denominator.
3rd: Use these factors to create the common denominator by listing the factor of each denominator that are not duplicated in another fraction.: "I have ...", "I need ... "
4th: Recopy numerators leaving "holes" with parenthesis: (x - 2) becomes (x - 2)( )
5th: Rewrite the numerator with missing factors to create equivalent fractions.: "I have ...", "I need ... "
6th: Simplify numerator (top of fraction).
7th: Factor the numerator if possible.
8th: Reduce the fraction if possilbe.