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How to Get Rid of the Bottom of a Fraction When There Are Multiple Fractions

Equations containing multiple fractions are much easier to solve when you get rid of the bottoms, or denominators. The least common multiple, which is the number that you use when adding or subtracting fractions with different denominators, is also the means for getting rid of the denominators in equations. Before you calculate that number, make sure that each fraction is fully reduced and that any mixed numbers, or numbers containing both a whole number and a fraction, are converted to improper fractions.

Instructions

    • 1

      Perform any operations possible on the given equation; for example, in the equation 3x/8 + 5x/15 = 3/4 + (1 1/2), the term 5x/15 reduces to x/3, and (1 1/2) converts to the improper fraction: 3/2, yielding: 3x/8 + x/3 = 3/4 + 3/2. Find the common denominator by factoring each denominator and multiplying them out: 2 * 2 * 2 * 3 = 24.

    • 2

      Multiply each numerator (top number) and denominator in the equation by the number needed to get a product in the denominator equal to the common denominator: ((3/3) 3x/8) + ((8/8) x/3) = ((6/6) 3/4) + ((12/12) 3/2) which results in: 9x/24 + 8x/24 = 18/24 + 36/24. Combine like terms: 17x/24 = 54/24.

    • 3

      Multiply both sides of the equation by the denominator to get rid of it: ((24/1)17x/24) = ((24/1)54/24). The common denominator cancels out in the multiplication process, resulting in the whole number equation: 17x = 54.

Tips & Warnings

  • Finding the smallest, or least, common denominator will result in smaller numbers when converting.

  • Any action applied to one side of an equation must be applied to the other side to get a correct solution.

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