Question

Mayor Mullens wants to repair $4\frac{2}{3}$ miles of road in his city. Workers can repair $\frac{9}{13}$ miles per week. If “W” represents the required number of weeks to repair the road, choose the correct value for W.

Multiplication equation: $4\frac{2}{13}=W\times \frac{9}{13}$
Related division equation: $4\frac{2}{13}÷\frac{9}{13}=W$

• A. $3$
• B. $6$
• C. $\frac{1}{13}$
• D. $2\frac{4}{13}$

Answer 1

The correct option is B $6$

Required number of weeks to repair the road = W

Length of the road repaired per week by workers $=\frac{9}{13}$ mi

Total length of the road to be repaired = length of the road repaired per week by workers $\times$ required number of weeks to repair the road

$4\frac{2}{13}=\frac{9}{13}\times W$

Express $4\frac{2}{13}$ as a fraction: $\frac{4\times 13+2}{13}=\frac{54}{13}$

$\frac{54}{13}=\frac{9}{13}\times W$

Choose W = 6 to make the numerator 54.
$\frac{9}{13}\times 6=\frac{54}{13}$

So, the multiplication equation is $\frac{9}{13}\times 6=\frac{54}{13}$

Division equation is $4\frac{2}{13}÷\frac{9}{13}=W$

Hence, the value of W is 6.