You can determine equivalent fractions by either multiplying or dividing both the numerator and denominator by the same numbers.
For instance, I could divide both 9 and 12 by 3, giving me 3/4, which is an equivalent fraction to 9/12. 3/4 is also the simplified form of 9/12.
I could also multiply both numbers by 2, giving me 18/24, which is also an equivalent fraction to 9/12.
Multiplying and dividing is the only way to come up with equivalent fractions. Adding and subtracting will not work, as well as exponents.
If I add 5 to both sides, I'll get 14/17, which is larger than 9/12, and therefore not an equivalent fraction. Same goes with subtracting - if I subtract 5 from both sides, I'll get 4/7, which is smaller than 9/12, and therefore not an equivalent fraction as well.
And for exponents, if I square both sides, I'll get:
(9^2)/(12^2) = 81/144, which is smaller than 9/12, and therefore not an equivalent fraction.
