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Simplify fractions using common factors

Equivalent fractions name the same quantity, so dividing the numerator and denominator by the same nonzero common factor produces an equivalent fraction; for example, 6/8=3/46/8=3/4. The fraction is in simplest form when its numerator and denominator have no common factor greater than 1, and a bar model or number line can show that the amount remains unchanged. The focus is on familiar whole-number fractions, not algebraic fractions, prime-factorization methods, or advanced rational-number simplification.

Detailed Explanation: Simplify fractions using common factors

Equivalent fractions name the same amount. To simplify a fraction, divide the numerator and denominator by the same common factor.

Example: Simplify 812\frac{8}{12}.

  1. Find a number that divides evenly into both 88 and 1212.
    A common factor is 44.

  2. Divide the numerator and denominator by 44:

812=8÷412÷4=23.\frac{8}{12}=\frac{8\div4}{12\div4}=\frac{2}{3}.
  1. Check the answer. The numbers 22 and 33 have no common factor greater than 11, so 23\frac{2}{3} is in simplest form.

Thus,

812=23.\boxed{\frac{8}{12}=\frac{2}{3}}.

The amount has not changed: eight parts out of twelve is the same quantity as two parts out of three.

Learn by doing: Simplify fractions using common factors

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Fraction Division As Fraction - Simple


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