Question

Your friend’s goal is to practice table tennis for at least $2$ hours in one week.
Time spent on Monday: $\frac{3}{4}h$
Time spent on Wednesday: $\frac{1}{2}h$
Time spent on Friday: $\frac{2}{3}h$
Did she reach her goal?

• A. She did not reach her goal.
• B. She reached her goal

Answer 1

The correct option is A She did not reach her goal.

Solution:
Time spent on Monday $=\frac{3}{4}h$
Time spent on Wednesday $=\frac{1}{2}h$
Time spent on Friday $=\frac{2}{3}h$
Total time spent $=\frac{3}{4}+\frac{1}{2}+\frac{2}{3}$
$\frac{3}{4},\frac{1}{2},$ and $\frac{2}{3}$ are unlike fractions.
To add unlike fractions, first convert them into like fractions by finding the equivalent fractions with the same denominator.
$\frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12}$
$\frac{1}{2}=\frac{1\times 6}{2\times 6}=\frac{6}{12}$
$\frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12}$
$\frac{9}{12}+\frac{6}{12}+\frac{8}{12}=\frac{9+6+8}{12}=\frac{23}{12}$
Dividend $=23$
Quotient $=1$
Divisor $=12$
Remainder $=11$
$\text{Mixed number = Quotient}\frac{\text{Remainder}}{\text{Divisor}}$
Mixed number $=1\frac{11}{12}$ which is less than $2$ hours
She did not reach her goal.


PQ: How short did she fall?

• $2-\frac{23}{12}=\frac{24}{12}-\frac{23}{12}=\frac{1}{12}$
• She fell short of $\frac{1}{12}$ hour.