Question

Nancy worked for some hours and did $3\frac{2}{9}$ of her homework. If she did $1\frac{1}{3}$ of the homework every hour, calculate the number of hours she worked.

• A. $\frac{39}{8}$
• B. $\frac{29}{8}$
• C. $\frac{29}{12}$
• D. $\frac{39}{12}$

Answer 1

The correct option is C $\frac{29}{12}$

Total homework = $3\frac{2}{9}$
Nancy completed $1\frac{1}{3}$ of the homework every hour.
To find the number of hours, we need to divide $3\frac{2}{9}$ by $1\frac{1}{3}$.
To divide mixed fractions, first we have to convert them into improper fractions.
$3\frac{2}{9}=\frac{\left(3\times 9\right)+2}{9}=\frac{27+2}{9}=\frac{29}{9}1\frac{1}{3}=\frac{\left(1\times 3\right)+1}{3}=\frac{3+1}{3}=\frac{4}{3}$
Now, let's divide the two fractions.
$3\frac{2}{9}÷1\frac{1}{3}=\frac{29}{9}÷\frac{4}{3}=\frac{29}{9}\times \frac{3}{4}=\frac{29\times 3}{9\times 4}=\frac{29\times 3}{4\times 3\times 3}=\frac{29}{4\times 3}=\frac{29}{12}$
So, Nancy worked for $\frac{29}{12}$ hours.