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Gina wants to ship three books that weigh 2$\frac{7}{16}$ pounds, 1$\frac{7}{8}$ pounds and $\frac{1}{2}$ pound. Which is the best estimate for the total weight of the three books?

(A) $3 \frac{1}{2}$ pounds
(B) 4 pounds
(C) 5 pounds
(D) 6 pounds

Solution

VerifiedFirst, those weights in pounds we need to be fractions, so, we have the following:

$\begin{align*} 2\dfrac{7}{16}&=\dfrac{39}{16}\\ 1\dfrac{7}{8}&=\dfrac{15}{8} \end{align*}$

Because now we have fractions $\dfrac{39}{16}, \dfrac{15}{8}$ and $\dfrac{1}{2}$, we have to add them in order to find their sum and the best estimate for the total weight of those three books.

$\begin{align*} \dfrac{39}{16}+\dfrac{15}{8}+\dfrac{1}{2}&=\dfrac{39+15\cdot2+1\cdot8}{16}\\ &=\dfrac{77}{16}\\ &=4\dfrac{13}{16} \end{align*}$

So, $\textbf{conclusion is the best estimate is $5$ pounds.}$

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