Equivalent fractions name the same quantity, so dividing the numerator and denominator by the same nonzero common factor produces an equivalent fraction; for example, . 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.
Equivalent fractions name the same amount. To simplify a fraction, divide the numerator and denominator by the same common factor.
Example: Simplify .
Find a number that divides evenly into both and .
A common factor is .
Divide the numerator and denominator by :
Thus,
The amount has not changed: eight parts out of twelve is the same quantity as two parts out of three.
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