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How to Add & Subtract Fraction Monomials

Monomials are variables that consist of one term in its denominator or numerator or plain number values, such as "x," "4," "2/3y" and "5x." On the other hand, polynomials such as "x + y - 1" makes up three monomials -- "X," "Y," and "-1" -- and cannot be combined into one monomial. However, if you have three monomials of the same terms in one polynomial equation, you can add and subtract fraction monomials in order to condense them into a single monomial expression.

Instructions

- 1
  Write out the equation. An example equation would look like:
  
  4/5 + 1/2x + 3/4x - x - 5/6x^2 + 1/3x^2 - 1/10
  
  The symbol "^" represents the "power," with the number following the "^" known as the exponent.
- 2
  Combine the like terms. If you have the numbers without "x" or "x^2," combine them. Next, combine all the numbers with the like terms "x" and "x^2." For example, combining the like terms of the equation, 4/5 + 1/2x + 3/4x - x - 5/6x^2 + 1/3x^2 - 1/10 would be:
  
  (1/2x + 3/4x - x) + (-5/6x^2 + 1/3x^2) + (4/5 - 1/10)
- 3
  Find the common denominators of each "like term" group of fractions. You can only add or subtract fractions if the bottom number is the same. For this example, if the equation is:
  
  (1/2x + 3/4x - x) + (-5/6x^2 + 1/3x^2) + (4/5 - 1/10)
  
  The denominators for our first "like term" group is 2, 4 and 1. Since the 1 and 2 can fit into the 4, you can use 4 as your common denominator for the first group. Remember, if you change the denominator of the 1/2 to 4, you must multiply the top and bottom by 2 to keep the proportions of the fraction. Repeat for the next two groups and you should end up with this:
  
  (2/4x + 3/4x - 4/4x) + (-5/6x^2 + 3/6x^2) + (8/10 - 1/10)
- 4
  Add or subtract the numbers within each group. For this example, use the equation in the previous step: (2/4x + 3/4x - 4/4x) + (-5/6x^2 + 3/6x^2) + (8/10 - 1/10).
  
  After you add and subtract the numbers, your equation should look like this:
  
  1/4x - 2/6x^2 + 7/10

Numerology