Question

find the volume of the rectangular prism. 1\frac{2}{7} mi. 1\frac{1}{3} mi. \frac{2}{3} mi. write your answer as a whole number, a proper fraction, or a mixed number. cubic miles

Explanation:

Step1: Convert mixed - numbers to improper fractions

$1\frac{2}{7}=\frac{1\times7 + 2}{7}=\frac{9}{7}$; $1\frac{1}{3}=\frac{1\times3+1}{3}=\frac{4}{3}$

Step2: Apply the volume formula for a rectangular prism

The volume formula of a rectangular prism is $V = l\times w\times h$. Here, $l=\frac{4}{3}$, $w = \frac{2}{3}$, $h=\frac{9}{7}$. So $V=\frac{4}{3}\times\frac{2}{3}\times\frac{9}{7}$

Step3: Multiply the fractions

$\frac{4}{3}\times\frac{2}{3}\times\frac{9}{7}=\frac{4\times2\times9}{3\times3\times7}=\frac{72}{63}$

Step4: Simplify the fraction

$\frac{72}{63}=\frac{8}{7}=1\frac{1}{7}$

Answer:

$1\frac{1}{7}$