Chapter 5.3, Problem 40IP

To determine

To compare: Thewingspan of a moth and a butterfly if the wingspan of the butterfly is $3\frac{1}{4}\text{in}\text{.}$ and the mothis $3\frac{1}{2}\text{in}\text{.}$

Answer to Problem 40IP

The wingspan of the moth is $1\frac{1}{13}$ times larger than the wingspan of the butterfly.

Explanation of Solution

Given information:

The wingspan of the butterfly is $3\frac{1}{4}\text{in}\text{.}$ and the moth is $3\frac{1}{2}\text{in}\text{.}$

Calculation:

To compare the wingspan of the butterfly and the moth, divide the wingspan of the moth by the wingspan of the butterfly.

  $\begin{array}{c}\frac{3\frac{1}{2}\text{in}\text{.}}{3\frac{1}{4}\text{in}\text{.}}=\frac{\frac{7}{2}}{\frac{13}{4}}\left\{\text{Convert mixed fraction into improper fraction}\right\}\\ =\frac{7}{2}÷\frac{13}{4}\\ =\frac{7}{2}\cdot \frac{4}{13}\end{array}$

Simplify the fraction.

  $\begin{array}{c}\frac{3\frac{1}{2}\text{in}\text{.}}{3\frac{1}{4}\text{in}\text{.}}=\frac{7}{2}\cdot \frac{4}{13}\\ =\frac{7}{13}\cdot 2\\ =\frac{14}{13}\\ =1\frac{1}{13}\end{array}$

Therefore, the wingspan of the moth is $1\frac{1}{13}$ times larger than the wingspan of the butterfly.