Activity (Process)

Procedure for Simplifying a Fraction

To reduce a fraction to its simplest form, follow a three-step process:

  1. Rewrite the numerator and denominator to reveal common factors. If the shared factors are not immediately obvious, break the numerator and denominator into their prime factorizations.
  2. Divide out the common factors using the Equivalent Fractions Property. Cancel every factor that appears in both the numerator and the denominator, since cc=1\frac{c}{c} = 1 for any nonzero cc.
  3. Multiply any factors that remain in the numerator and in the denominator to obtain the simplified fraction.

For example, to simplify 1015\frac{10}{15}: factor as 2535\frac{2 \cdot 5}{3 \cdot 5}, cancel the common factor 55 to get 23\frac{2}{3}, and no further multiplication is needed. This procedure systematically ensures that the final fraction has no common factors other than 11 in its numerator and denominator.

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Updated 2026-05-02

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