Question

now, you find that the fourth shelf of the return cart is divided into seven equal sections. the first five sections of this shelf are filled with books.
as you observe, aisha takes some of the books from the cart for shelving. she puts away half the books from the fourth shelf.
what fraction of the fourth shelf is now filled after aisha has put away half the books from it?
five-fourteenths
ten-fourteenths
three-fourteenths
two-thirds

Explanation:

Step1: Define initial filled fraction

The shelf has 7 equal sections, 5 filled: $\frac{5}{7}$

Step2: Calculate remaining books

Half the books are left: $\frac{5}{7} \times \frac{1}{2}$

Step3: Compute final filled fraction

$\frac{5}{7} \times \frac{1}{2} = \frac{5}{14}$

Answer:

Five-fourteenths