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Given a rational fraction in the from p/q where p and q and co-prime integers and q > 0, an equivalent fraction is a fraction of the form (p*k)/(q*k) where k is any non-zero integer. Conversely, given a fraction in the form x/y which are not co-prime, you can divide both x and y by any common factor to give an equivalent fraction in simpler form. When the two numbers become co-prime, you have the simplest equivalent fraction.

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