Q:

# How do you solve equations with fractions?

A:

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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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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