# N14

QUESTION: Evaluate $\dfrac{12}{7}\div\dfrac{9}{20}$.

ANSWER: To divide these fractions, we need to keep the first fraction the same, change the $\div$ to a $\times$, and flip the second fraction. Doing so, we get

$\dfrac{12}{7}\div\dfrac{9}{20}=\dfrac{12}{7}\times\dfrac{20}{9}$

Then, we do the multiplication:

$\dfrac{12}{7}\times\dfrac{20}{9}=\dfrac{12\times20}{7\times9}=\dfrac{240}{63}$

240 and 63 both have 3 as a factor, so we can simplify our fraction to get

$\dfrac{240}{63}=\dfrac{80}{21}$

80 and 21 have no common factors, so we are done.