My teacher said my grade will be broken down as 40% for mid-term exam,
40% for final, and 20% for the project. If I got a 90 on the final, 80
on the mid-term and 75 on the final, how do I calculate my final grade
for the course?

Hi, captain577-ga:

If all the parts, mid-term exam, final exam, and project, counted
equally toward the final grade for your course, then we would take an
"unweighted" average:  add the three parts and divide by 3.

Here the calculation is called a weighted average, because the
contribution of parts to the final grade can be different.  Notice
that the three percentages add up to 100% (or to a whole, in other
words):

  40% + 40% + 20% = 100%

To calculate your final grade, multiply each part by the percentage
that it counts towards the final grade and sum up these products:

  40% * 80  (mid-term exam grade)
  40% * 90  (final exam grade?)
  20% * 75  (project grade ??)

I put question marks in because you give two different grades for the
final and leave out mentioning a project grade.  So, if I guessed
correctly, you meant 90 on the final and 75 for the project, but
perhaps I have these backwards.

If the above is correct, your final grade for the course is:

  (0.4*80) + (0.4*90) + (0.2*75) = 32 + 36 + 15 = 83

If the final and project grades should be switched, then:

  (0.4*80) + (0.4*75) + (0.2*90) = 32 + 30 + 18 = 80

It's not a huge difference, but since the final exam is "more heavily
weighted" than the project, a better final grade for the course would
be earned when the higher grade you got was for the final exam rather
than for the project (other things being equal).  Note that since the
mid-term and final exams have the same weight (40%), switching those
two grades would not affect your final average.

regards and good luck with your classes, mathtalk-ga

What a great answer, and so easily understood. Thanks.