To add 1/2 and 1/3, Vivaan adds the top numbers and the bottom numbers separately: 1+1=2 on top…

Why

Vivaan's method feels natural — adding whole numbers means adding matching parts, so adding tops and bottoms separately seems like the same idea carried over. But fractions only add cleanly when the PIECES are the same size, and 1/2 and 1/3 are cut differently — halves and thirds aren't the same size piece, so their numerators can't just be combined. First make the pieces match: 1/2 = 3/6 and 1/3 = 2/6, both now cut into sixths. Now add: 3/6 + 2/6 = 5/6, because when pieces ARE the same size you just add how many of them you have. Compare that to Vivaan's 2/5 — as a decimal 5/6 is about 0.83, while 2/5 is exactly 0.4, nowhere close. Picture combining half a roti with a third of a different roti — you can't just say "2 out of 5 rotis," because the pieces were never the same size to begin with. Meher is right: find a common denominator first, and only then add the numerators.