Question

Sanjeev ate two-thirds of a cake. He gave two-thirds of the remainder to his friend. He kept the rest of the cake. What fraction of the cake did he keep?

Answer 1

Sanjeev kept one-third of the cake.

Step-by-step explanation:

To find the fraction of the cake that Sanjeev kept, we need to calculate the fractions that he ate and gave to his friend and subtract them from the whole cake.

1. If Sanjeev ate two-thirds of the cake, the fraction he ate is 2/3 of the whole.
2. Sanjeev gave two-thirds of the remainder to his friend. The fraction he gave to his friend is 2/3 of the remaining cake after he ate his share.
3. To find the fraction he kept, we subtract the fraction he ate and gave to his friend from the whole cake. The whole cake is represented by the fraction 1.

Therefore, the fraction of the cake that Sanjeev kept is:

1 - (2/3 + 2/3) = 1 - (4/3) = 1 - 1 1/3 = 1/3 (or one-third)