Question

mr. jones graded \\(\frac{1}{3}\\) of his students the remaining tests that evening. \\(\dots\\) in his classroom after school, and \\(\frac{1}{3}\\) of \\(\dots\\) of the math tests does mr. jones still need to grade? select one answer a \\(\frac{1}{9}\\) b \\(\frac{3}{9}\\) c \\(\frac{1}{3}\\) d \\(\frac{4}{9}\\)

Explanation:

Step1: Define total tests as 1

Let total tests = $1$

Step2: Calculate graded portion first

First graded: $\frac{1}{3}$, remaining after first: $1 - \frac{1}{3} = \frac{2}{3}$

Step3: Calculate second graded portion

He graded $\frac{1}{3}$ of remaining: $\frac{1}{3} \times \frac{2}{3} = \frac{2}{9}$

Step4: Sum total graded tests

Total graded = $\frac{1}{3} + \frac{2}{9} = \frac{3}{9} + \frac{2}{9} = \frac{5}{9}$

Step5: Calculate ungraded portion

Ungraded = $1 - \frac{5}{9} = \frac{4}{9}$

Answer:

D. $\frac{4}{9}$