Question

Nancy left a bin outside in her garden to collect rainwater. She notices that 1 over 2 gallon of water fills 2 over 3 of the bin. Write and solve an expression to find the amount of water that will fill the entire bin. Show your work. Explain your answer in words

Answer 1

The entire bin can take up to 3/3, meaning, one whole, thus

$\bf \begin{array}{ccllll} gallons&\textit{portion of whole}\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ \frac{1}{2}&\frac{2}{3}\\\\ x&\frac{3}{3} \end{array}\implies \cfrac{\frac{1}{2}}{x}=\cfrac{\frac{2}{3}}{\frac{3}{3}}$

solve for "x"

Answer 2

Answer: Expression would be,

$\frac{3}{2}\times \frac{1}{2}$

The amount of water that will fill the entire bin is $\frac{3}{4}$ gallon.

Step-by-step explanation:

Given,

The quantity of water needs to fill $\frac{2}{3}$ part of the bin = $\frac{1}{2}$ gallon,

Thus, the quantity of water needs to fill 1 part of the bin = $\frac{3}{2}\times \frac{1}{2}$

Which is the required expression,

By fraction multiplication,

We get,

The amount of water that will fill the entire bin is $\frac{3}{4}$ gallon.