Question 120202
Start with the number: x.  Two-thirds of the number is {{{2x/3}}}.  Two-thirds of a number decreased by one-half is {{{(2x/3)-1/2}}}.  This expression is equal to {{{5/6}}}, so we can write:


{{{(2x/3)-(1/2)=5/6}}}


The LCD of 2, 3, and 6 is 6, so:


{{{(4x/6)-(3/6)=5/6}}}


Add {{{3/6}}} to both sides:


{{{4x/6=8/6}}}


Multiply both sides by 6:


{{{4x=8}}}


Divide by 4:


{{{x=2}}}


Check:

{{{(2/3)*2=4/3}}}.  {{{(4/3)-(1/2)=(8/6)-(3/6)=5/6}}}, answer checks.