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Is there a way to change a fraction without affecting its value?

Yes, there is only one way.  Let's say for example that we have a fraction of 2/3.  Now, the bottom number is the denominator which means the number of equal parts into which a whole circle most specifically is divided.  So the circle is divided into 3 equal parts.  On the other hand, the top number is the numerator which means how many equal parts out of all of them are lightly shaded inside the circle. So 2 out of all 3 equal parts of the circle are lightly shaded.  

Now, the only way to change the number of equal parts without affecting the fraction value is to multiply it by any number you want which will also change the numerator.  So let's say for example that in the fraction of 2/3, if you wanted to divide each of those 3 equal parts into 2 further equal parts, you will have a new number of equal parts which is 6 (3*2=6).  This will affect the numerator 2 as well since this is included in the total number of equal parts, so each of the 2 equal parts that are lightly shaded will be divided into 2 further equal parts and end up with 4 (2*2=4).  So now comes our new fraction 4/6.  However, this is still equivalent to the other fraction of 2/3 since this was done by (2/3)*(2/2).  For further explanation, we multiplied 2/3 by a fraction equivalent to 1 which was any number over the same number.  Since any number times one is that number, that is how you can convert one fraction into another but still retain its value.