Lets say you got 46 out 55 on test which equals 83.64%
This test is worth 20% of your total mark(100), how do you find out the % you got from 20%?
Okay, you got 83.64% of 20%, so just multiply the percentages together (of means multiply): .8364 * .2 = .1672
So you have 16.72% of your total grade guaranteed. You can verify this because you know that .2 (20%) is one fifth of your total grade (.2*5 = 1 or 20%*5 =100%, or 100/5=20). So to verify, you assume you got the same percentage for each of the other 4 segments of 20%, or a total of 5 segments of 20% where you got 83.64%. So multiply .1672 * 5 = .836 (or 16.72% * 5 = 83.6%)
Because it is merely a percentage, if you got the same percentage on every grade, no matter what it was weighted, it would total that percentage, you can see that if you got 83.64% on every grade, it should equal 83.64% for the total consolidated grades, and when we check our problem this is true, so we know we did it correctly.
Another way to check (and now that I think about it, this is also a better way because it allows for unusual weights such as a test which is worth 13.4938% or any other number) would be to say you got 83.64% on the other 80%, and 20%+80% = 100% so (83.64%*20% + 83.64%*80% = 83.64%*100%=83.64%) and plug in the numbers ( .8364*.2 + .8364*.8 = .8364*1 = .8364)
So we can see, again, that it is done correctly. All this means that you just multiply the percentage you received by the weight (if the weight is given as a percentage of the total)
So you have about 16.72% locked in for sure, because 16.72 is 83.64% of 20, which is 20% of 100. And if you maintain the same average, once all the scores are added together, you will have an 83.64% average for the course.
Usually it means you can remove your lowest grade. Usually referring to tests, but it could apply to any grade really.
For example, say you had 5 tests worth equal weight each, and together they made up 75% of your grade (the other 25% being homework)
And lets just pick some values for your grades
Test1: 87%
Test2: 89%
Test3: 92%
Test4: 43%
Test5: 88%
Homework: 97%
We'll find the total grade the addition way b/c I think thats better. So remember, the first grade is 87% of 20% of 75%
(grade on test) * (weight of test with respect to all tests) * (weight of all tests with respect to total grade)
This formula tells you the total value of each test grade, then you determine the total value of your homework (Total homework grade)*(weight of homework with respect to total grade)
Then you will have 5 values that you can simply add together.
Note: Easiest way to check your equations is assume you got 100% on everything, then your final answer should be 100%, if it is not, then your equations are wrong.
Okay, so
Test1: 87% of 20% of 75% $\displaystyle \Rightarrow .87*.2*.75=.1305$
Test2: 89% of 20% of 75% $\displaystyle \Rightarrow .89*.2*.75=.1335$
Test3: 92% of 20% of 75% $\displaystyle \Rightarrow .92*.2*.75=.138$
Test4: 43% of 20% of 75% $\displaystyle \Rightarrow .43*.2*.75=.0645$
Test5: 88% of 20% of 75% $\displaystyle \Rightarrow .88*.2*.75=.132$
Homework: 97% of 25% $\displaystyle \Rightarrow .97*.25=.2425$
Total $\displaystyle .1305+.1335+.138+.0645+.132+.2425=.8509$
So you can see that you got an 85.09%
But you know that you can drop your grade, and you can see that you really bombed test4, you were sick that day, didn't study, a bit hungover, whatever. So your instructor lets you drop that grade from your total list of grades.
Now you need to calculate your total grade with test 4 taken out. You cannot use the same formula, because you have no value to put in for test 4 (and you don't want to put in a zero, that would make your grade go down even more ). So lets think about it, if you had gotten 100% on all 4 of our remaining tests, they would make up 100% of 75% of your grade, so each of the 4 tests makes up 1/4 of the 100% of 75%, so each test weight is 25% of 100% of 75% (You can see that 25% of 100% = 25%) so each test weight is 25% of 75%
Now we just need to recalculate with test4 removed, and the weight of all of the tests at 25% instead of 20%
Test1: 87% of 25% of 75% $\displaystyle \Rightarrow .87*.25*.75=.163125$
Test2: 89% of 25% of 75% $\displaystyle \Rightarrow .89*.25*.75=.166875$
Test3: 92% of 25% of 75% $\displaystyle \Rightarrow .92*.25*.75=.1725$
Test5: 88% of 25% of 75% $\displaystyle \Rightarrow .88*.25*.75=.165$
Homework: 97% of 25% $\displaystyle \Rightarrow .97*.25=.2425$
Total: .163125+.166875+.1725+.165+.2425=.91
So you can see that your grade is now a 91%
Congratulations! By removing Test4, you didn't have all that dead weight dragging your grade down, and instead you made a 91%, you get an A for the class, and your mother bakes you cupcakes. To celebrate, you hit the bars with your buddy. You have a grand old time, and stumble back to your apartment. Eventually the ringing of your alarm wakes you up, in a hungover stupor, and with a cough indicative of the flu, you realize that you have 1 final left to take, and it starts in 20 minutes. DOH!