Question 292612
Changing signs in exactly____BOTH__________positions of a fraction will not alter the value of the fraction.


What this means is as follows:


Suppose the fraction is {{{5/12}}}


If I just change the sign in the numerator, then the fraction is {{{(-5)/12}}} which is the same as {{{-(5/12)}}} which is not the same as the original fraction.


If I just change the sign in the denominator, then the fraction is {{{5/(-12)}}} which is the same as {{{-(5/12)}}} which is not the same as the original fraction.


If I change the sign in both the numerator and the denominator, then the fraction is {{{(-5)/(-12)}}} which is the same as the original fraction because a minus divided by a minus gives you a plus.


Here's how that works:


-5 is the same as (-1)*5 and -12 is the same as (-1)*12.


Your fraction of {{{(-5)/(-12)}}} becomes {{{((-1)*5)/((-1)*12)}}}


The (-1) in the numerator and the (-1) in the denominator cancel out and you are left with {{{5/12}}}.