How do you solve equations with fractions?


Quick Answer

Equations containing fractions are solved by first eliminating the denominator of any fractions. In practice, they are solved by converting the fractions into whole numbers.

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Full Answer

To eliminate the denominators it is necessary to convert them all into the number 1 by finding what is called a common denominator.

  1. Eliminate the denominator. For the equation 2/5 + 4x = 2 - with only one denominator - multiply both sides by 5 to get 10/5+ 20x = 10.
  2. Where there are more than one fraction, it is necessary to find the common denominator - one that works with all the fractions in the equation in order to perform addition or subtraction. For the equation 2/5 + 4x = 2/4, the lowest common denominator is 20 and the equation becomes: 4/4(2/5) + 4x = 5/5(2/4) or 8/20 + 4x = 10/20.
  3. Add or subtract any fractions as in a linear equation. In the above example, 8/20 + 4x = 10/20 becomes 4x = 2/20
  4. Eliminate the denominator by multiplying all of the numbers in the equation by the denominator. In the above example, multiply all numbers in the equation by 20 - 20(4x) = 20(2/20) or 80x = 2.
  5. Once the denominators have been eliminated the equation may be solved using algebraic functions. Using the same example, 80x = 2 becomes x = 2/80 or x = 1/40.
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