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What Happens to a Fraction After the Denominator Has Been Distributed?

The distributive property is one of the most powerful simplification tools available in mathematics. You can use it to simplify many mathematical expressions, including many kinds of fractions, by distributing the division across addition or subtraction signs.
  1. Nothing

    • When a denominator has been distributed in a fraction, the value of the expression afterwards is exactly the same, so in a sense nothing has happened to the fraction. The numbers and appearances might change, but the mathematical quantities they represent are still the same.

    Simplified Into Integers

    • If the denominator of the fraction divides evenly into all or part of the numerator, the fraction can disappear as it is simplified into integers. For example in the expression (4x + 8)/2 the 2 can be distributed to be 4x/2 + 8/2 and then simplified to 2x + 4.

    The Single Fraction Becomes Many

    • If the denominator does not divide evenly into parts of the numerator, the single fraction can be replaced by the sum or difference of multiple fractions. For example the fraction (3x + 5)/4 can have the denominator distributed to become 3x/4 + 5/4.

    Terms Cancel

    • If parts of the numerator are the same as parts of the denominator, they can possibly cancel out and disappear. For example, (3x + 2) / x becomes 3 + 2/x when the x in the denominator is distributed and the x's in the first term of 3x / x cancel out.

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