Question

Alex spend $5\frac{2}{3}h$ studying. By how many fewer hours he can study so that the total time is a whole number?

• A. $\frac{2}{3}h$
• B. $2\frac{2}{3}h$
• C. $1\frac{2}{3}h$
• D. $\frac{1}{3}h$

Answer 1

Answer: (A), (B), (C)

$1\frac{2}{3}h$

Solution:
Time spend by Alex on studies $=5\frac{2}{3}h$
Now, $5\frac{2}{3}$ is a mixed number. Convert it into a fraction greater than 1.
$5\frac{2}{3}=5+\frac{2}{3}=\frac{5\times 3}{1\times 3}+\frac{2}{3}=\frac{15}{3}+\frac{2}{3}=\frac{17}{3}h$
If Alex reduces the time by $\frac{2}{3}h$:
$\frac{17}{3}-\frac{2}{3}=\frac{15}{3}=5h$ (Whole number)
Hence, Option A is correct.

If Alex reduces time by $1\frac{2}{3}h$.
Now, $1\frac{2}{3}=\frac{5}{3}h$
$\frac{17}{3}-\frac{5}{3}=\frac{12}{3}=4h$ (Whole number)
Hence, Option B is correct.

If Alex reduces the time by $2\frac{2}{3}h:$
Now, $2\frac{2}{3}=\frac{8}{3}h$
$\frac{17}{3}-\frac{8}{3}=\frac{9}{3}=3h$ (Whole number)
Hence, Option C is correct.

If Alex reduces the time by $\frac{1}{3}h$:
$\frac{17}{3}-\frac{1}{3}=\frac{16}{3}$ (Not a whole number)
Hence, Option D is incorrect.