The question is: "What is half of 1/4?" Kartik solves it as 1/2 + 1/4 = 3/4

Why

Kartik has spotted two fractions in the same sentence and reached for the operation he's most used to combining fractions with — addition. The word 'of' between two fractions is actually a signal for MULTIPLICATION, not addition: 'half of 1/4' means take half of that quantity, exactly the way 'half of the class' means splitting the class into two, not adding a class to a half. So the calculation is 1/2 × 1/4 = 1/8, not 1/2 + 1/4. Picture a quarter of a roti sitting on a plate, and now take half of just that piece — you end up with a much smaller sliver, one-eighth of the whole roti, nowhere near three-quarters of it. Test: 'half of 10' clearly means 5, found by multiplying (1/2 × 10), never by adding 1/2 and 10 — the same 'of means multiply' rule carries straight over when both quantities happen to be fractions. His sister is right, the answer is 1/8: 'of' between two amounts signals multiplication, and mistaking it for addition here changes 1/8 into a very different 3/4.