Skill: Simplify fractions using common factors

Explanation and Free Practice Resources

Equivalent fractions name the same quantity, so dividing the numerator and denominator by the same nonzero common factor produces an equivalent fraction; for example, $6/8=3/4$ . 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.

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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 $\frac{8}{12}$ .

Find a number that divides evenly into both $8$ and $12$ .
A common factor is $4$ .
Divide the numerator and denominator by $4$ :

\frac{8}{12}=\frac{8\div4}{12\div4}=\frac{2}{3}.

Check the answer. The numbers $2$ and $3$ have no common factor greater than $1$ , so $\frac{2}{3}$ is in simplest form.

Thus,

\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.

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