Question

In Mr.Johanessen's class, 1/4 of the students failed the exam. Of the remaining class, 1/3 scored an A. What fraction of the whole class passed the test but scored below an A? (The answer is NOT 1/2 and it is NOT 5/12)

Answer 1

so a whole is same/same, in this context is 4/4 = 1, or four fourths.

now, we know 1/4 failed, that means 4/4 - 1/4 = 3/4 didn't fail, so 3/4 passed.

from that remaining 3/4, how many got an A? well 1/3, how much is 1/3 of 3/4? well is just their product,    $\bf \cfrac{1}{3}\cdot \cfrac{3}{4}\implies \cfrac{1}{4}$.

so 1/4 of the remaining 3/4 got an A, that means 3/4 of the remaining 3/4 did NOT get an A.

how much is 3/4 of 3/4? well, is just their product.

$\bf \cfrac{3}{4}\cdot \cfrac{3}{4}\implies \cfrac{9}{16}\impliedby \textit{passed with score less than A}$