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Question

# Short Response Mari bought 3 packages of colored paper. She used $\frac{3}{4}$ of a package to make greeting cards and used $1 \frac{1}{6}$ packages for an art project. She gave $\frac{2}{3}$ of a package to her brother. How much colored paper does Mari have left? Show the steps you used to find the answer.

Solution

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Step 1
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Determine the sum of the packages used.

\begin{align*} &= \dfrac{3}{4} + 1\dfrac{1}{6} + \dfrac{2}{3} && \text{Write an expression}\\ &= \dfrac{3}{4} + \dfrac{7}{6} + \dfrac{2}{3} && \text{Write the mixed number as improper fraction}\\ &= \dfrac{9}{12} + \dfrac{14}{12} + \dfrac{8}{12} && \text{Write as equivalent fractions}\\ &= \boldsymbol{\dfrac{31}{12}} && \text{Add the fractions} \end{align*}

The package of colored paper used and given away is $\dfrac{31}{12}$. Determine the package of colored paper left.

\begin{align*} &= 3 - \dfrac{31}{12} && \text{Write an expression}\\ &= \dfrac{36}{12} - \dfrac{31}{12} && \text{Write 3 as fraction with the same denominator}\\ &= \boldsymbol{ \dfrac{5}{12}} && \text{Subtract the fractions} \end{align*}

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