# Calculating divisions

#### TonyMcc

Hi guys!
I've an issue and I need a good explanation how I can solve it!

The problem is: I've an exam with five questions; I got at every question 6/20,
so my final grades from 100 should be:
6/20 + 6/20 + 6/20 +6/20 +6/20 = 30/20 = my final grade, but it's wrong because the answer in the book is 30 / 100 .. any help how is that really right?
I mean I'm not understanding how I calculate ratios to find total amount?
what's confusing me if I have got 6/20 for every questions then my total grade should be (6/20)*5=30/20 and not 30/100 .. any help please?! and why specifically 30/100 not, for instance, 30/80 or 30/300 or 30/10000? Why exactly the answer is 30 divided by 100?

Thanks a lot!

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#### idontknow

The numerator must multiply 5 , same for denominator.
$$\displaystyle \frac{6\cdot 5}{20\cdot 5}=30/100$$.

#### TonyMcc

But you didn't understand me . . . let's assume I did what you say, then I get
30/100 + 30/100 + 30/100 + 30/100 + 30/100 = 300/100 !!!
I've five questions and at every question I get grade 6/20 ... you're telling me to do 30/100 for every questions then I get in my final grade: 30/100 + 30/100 + 30/100 + 30/100 + 30/100 = 300/100 !!! Is that right?!

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#### greg1313

Forum Staff
There are 100 possible marks for the five questions. You scored 6 * 5 = 30 marks so your final score is 30/100.

#### TonyMcc

What? How come it's really 6*5 gives me the number divided by 100?! That's what I didn't understand. I got 6/20 for every question, I have five questions, then
(6/20)*5 = 30/20 and not 30/100 !!! Any help?

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#### weirddave

30/100 + 30/100 + 30/100 + 30/100 + 30/100 = 300/100 !!!
That's actually 150/100.

Now back to your original question, at the risk of repeating Greg....

You score 6 out of 20, 5 times. Let's call them points.
You score 6 points out of 20 possible points, 5 times.
There are 5 x 20 possible points that you could have collected, of which you collected 5 x 6
So that's 30 points out of a possible 100.

A clue that 30/20 is wrong is that this would be 150%, you can't score more than 100% on a test.

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1 person

#### skipjack

Forum Staff
I'm not understanding how I calculate ratios to find total amount
You need to combine the individual scores to obtain your overall score. However, summing them as though they are just fractions is not the correct method of combining them.

Instead, obtain your overall result as "total marks"/"total possible marks" by summing the numerators of your individual scores to get "total marks" and summing the denominators of your individual scores to get "total possible marks".

For your data, 6 + 6 + 6 + 6 + 6 = 30 and 20 + 20 + 20 + 20 + 20 = 100, so the correct overall score is 30/100.