Question 831481
The difference in votes, as a fraction of the total number of votes was
{{{2/3-1/6=4/6-1/6=3/6=highlight(1/2)}}}
Scott got {{{2/3}}} of the vote, and {{{2/3=4/6}}}, so the difference is
{{{4/6-1/6=3/6}}} .
Then we simplify to {{{1/2}}} because {{{3/6=1/2}}} .
Those fractions represent the same number, just written in a different way.
They have the same value, so we say they are equivalent.
 
You can see that {{{2/3=4/6}}} because any cake that is cut into 3 equal pieces (thirds) can be made into 6 equal pieces by cutting each piece in half.
That doubles the total number of pieces to 6, so each (smaller)piece is {{{1/6}}} .
At the same time, each of the {{{1/3}}} pieces turns into two {{{1/6}}} pieces, so getting {{{2/3}}} of the cake is the same as getting {{{4/6}}} of the cake.

{{{drawing(600,300,-12,72,-10,32,
rectangle(0,0,60,30),
green(line(20,0,20,30)),green(line(40,0,40,30)),
line(40,-0.5,40,-7),arrow(40,-7,0,-7),
locate(12,-1,2/3),locate(15,-2,for),locate(20,-2,me)
)}}} ---> {{{drawing(600,300,-12,72,-10,32,
rectangle(0,0,60,30),
green(line(20,0,20,30)),green(line(40,0,40,30)),
line(40,-0.5,40,-7),arrow(40,-7,0,-7),
red(line(0,15,60,15)),
locate(12,-1,4/6),locate(15,-2,for),locate(20,-2,me)
)}}}
To state that conclusion in a more general way, any fraction can be turned into an equivalent fraction by multiplying the numerator (the top number), and the denominator (the bottom number) by a number of your choice. (The same number is multiplied by both parts of the fraction, of course).
And if multiplying works, dividing must work too,
because dividing by 2 is the same as multiplying times {{{1/2}}} ,
dividing by 3 is the same as multiplying times {{{1/3}}} , and so on.
That makes {{{3/6}}} equivalent (equal) to {{{"3 ÷ 3"/"6 ÷ 3"=1/2}}}