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How to Simplify Into a Single Fraction

To fully simplify a fraction, you must perform any operations in both the numerator and denominator. You must also simplify the fraction so that the numerator and denominator are reduced to their lowest possible values while representing the same quotient. All of these operations can be performed by working through each part of the fraction separately.

Instructions

    • 1

      Perform any required mathematical operations in the numerator and denominator. For example the numerator may include an addition operation rather than a single number. Perform all operations until the numerator and the denominator are reduced to a single value.

    • 2

      Multiply or divide the multiple fractions if necessary. For multiplication, multiply the two numerators, then the two denominators. The multiplication products are the numerator and denominator of the single, multiplied fraction. To divide two fractions, multiply the first fraction's numerator by the second fraction's denominator, then the first fraction's denominator by the second fraction's numerator. The first product is the numerator of the new fraction, and the second product is the denominator. This is known as cross multiplication.

    • 3

      Add or subtract the multiple fractions by finding the lowest common denominator, the lowest number that each fraction's denominator will divide evenly into. Multiply each numerator by the same value that you multiplied the denominator by. Then add or subtract the two numerators to reach a single fraction.

    • 4

      Reduce the fraction so that the numerator and denominator are the lowest possible values by finding both numbers' greatest common factor, the highest number that will divide evenly into the numerator and the denominator. Divide the greatest common factor into the numerator and denominator. The resulting quotients are the numerator and denominator of the fully simplified fraction.

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