SOLUTION: If {{{p/q}}} is a fraction in lowest terms, must {{{p^2/q^2}}} be in lowest terms also? How about {{{(p + a)/(q + a)}}} for some integer {{{a}}}?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If {{{p/q}}} is a fraction in lowest terms, must {{{p^2/q^2}}} be in lowest terms also? How about {{{(p + a)/(q + a)}}} for some integer {{{a}}}?      Log On


   

Question 1132162: If p%2Fq is a fraction in lowest terms, must p%5E2%2Fq%5E2 be in lowest terms also? How about
%28p+%2B+a%29%2F%28q+%2B+a%29 for some integer a?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(a) Yes. If p/q is in lowest terms, then p and q have no common divisors.

In that case, p^2/q^2 = (p*p)/(q*q) will also have no common divisors.

(b) No, of course not. It is easy to find counterexamples.

5/7 is in lowest terms; (5+1)/(7+1) = 6/8 is not.