Jane made of her free throws in the first half
and in the second half.
So, she made two out of five in the game.
so: ? . . . . . You're kidding, right?
No, it is not kidding!
Too bad . . . It's gruesomely incorrect.
By your reasoning, she will always average
First of all: . . . . we can't add fraction like you did.
Secondly, it depends on how many attempts were made in each half.
Suppose in the first half, she made 5 out of 10 . . . That's
And in the second half, she made 10 out of 30 . . . That's
Then she made 15 out of 40 during the whole game . . . That's
Suppose in the first half, she made 1 out of 2 . . . That's
And in the second half, she made 16 out of 48 . . . That's
Then she made 17 out of 50 during the whole game . . . That's
Is -1/3+4/6=3/9 correct?
Yest, it is.
However, it is correct due to the common rules of the addition - and for no other reason.
As Soroban noted, -1/3+4/6 = -1/3 + 6/9 which, acording to your rule would be 5/12 quite different from 3/9.
Sometimes things come out correct for wrong reasons. This does not make wrong reasons right.
0.5 + 0.2*0.3 = (0.5 + 0.2)(0.5 + 0.3), or
3^(2/3) * 9^(7/6) = (3*9)^(9/9) = 27.
(The examples are from E. J. Barbeau, Mathematical Fallacies, Flaws, and Flimflam.)