## Related questions with answers

Ms. Augello is making tie dye shirts with her students. Each gallon of hot water needs

$\frac{2}{3}$

cup of tie dye. If Ms. Augello has

$5\frac{1}{4}$

cups of tie dye, how many batches of solution will she be able to make?

Solution

VerifiedThe conditions of the problem translate to the expression

$\begin{align*} 5\dfrac{1}{4}\div\dfrac{2}{3} .\end{align*}$

Converting to fraction results to

$\begin{align*} 5\dfrac{1}{4} &\Rightarrow \dfrac{5(4)+1}{4} \\\\&= \dfrac{20+1}{4} \\\\&= \dfrac{21}{4} .\end{align*}$

Thus the expression $5\dfrac{1}{4}\div\dfrac{2}{3}$ is equivalent to

$\begin{align*} \dfrac{21}{4}\div\dfrac{2}{3} .\end{align*}$

Since $\dfrac{a}{b}\div\dfrac{c}{d}$ implies $\dfrac{a}{b}\cdot\dfrac{d}{c}$, the expression $\dfrac{21}{4}\div\dfrac{2}{3}$ implies

$\begin{align*} & \dfrac{21}{4}\cdot\dfrac{3}{2} .\end{align*}$

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