Question 588187
One way of looking at it is pretending the first 2 quizzes were really one exam and the last 2 quizzes were really another exam. That would be 3 exams worth the same fraction of the grade, so each would be worth 1/3 of the grade.
 
We can make it look a little more complicated, or a lot more complicated, but I will only go for a little.
If each quiz is worth {{{x}}} as a fraction of the grade, the final is worth {{{2x}}} as a fraction of the grade.
Adding all the fractions of the grade we get {{{1/1}}} of the grade (as a fraction).
{{{4*x+2x=6x=1}}} --> {{{x=1/6}}} --> {{{2x=2/6}}} --> {{{2x=1/3}}}
The exam is worth 1/3 of the grade.
 
You could also have calculate what fraction of {{{6x}}} is {{{2x}}} as
{{{2x/6x=(2/6)(x/x)=2/6=1/3}}}
The exam is worth 1/3 of the grade.