Which one of us is doing the math wrong?

Hello, OP!

Fractions are a little different, you can't simply add up numerators and denominators because fractions represent portions of something. Like a decimal.

To add up fractions you need to have a common denominator. This means converting the top and bottom numbers of ALL fractions to have the same bottom number. Then you can add them all up. From there you can average them.

25/50 + 17/20 + 13/20 -> 50/100 + 85/100 + 65/100 -> 50% ,85%, 65%.

(50 + 85 + 65) /3 = = 66%
Do these grades have different weights?
The way you added the scores is not correct. a/b + c/d does not equal (a+c)/(b+d). The usual way to average 3 test scores is to add them and divide by 3 like this.

* 25/50=50/100
* 17/20=85/100
* 13/20=65/100
* Average = 200/300
TBH, I suspect she probably made a mistake. 25+17+13 = 55, but that's out of 90.

It's possible to obtain 55%, but only if the first test (25/50) had a particularly high weight. It would have to be between 2/3 (which means the 17/20 has zero weight) and 6/7 (which means the 13/20 has zero weight). If the second and third tests (20 marks) had the same weight, the weight would have to be 80% for the first test and 10% for each of the other two.
Why do you average the percentages? .85 + . 65 + .5 = 2/3 (66%) but the .5 has a greater weight, being out of 50 instead of 20. And for the 55%, she probably just messed up.

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