Question

find the volume of the rectangular prism. write your answer in simplest form. \\(\frac{4}{7}\\) ft \\(\frac{1}{5}\\) ft \\(\frac{7}{9}\\) ft

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a rectangular prism is given by the product of its length, width, and height. So, \( V = l \times w \times h \), where \( l=\frac{4}{7}\) ft, \( w = \frac{1}{5}\) ft, and \( h=\frac{7}{9}\) ft.

Step2: Multiply the three fractions

Substitute the values into the formula: \( V=\frac{4}{7}\times\frac{1}{5}\times\frac{7}{9}\). First, multiply the numerators together and the denominators together: \( \frac{4\times1\times7}{7\times5\times9}\).

Step3: Simplify the fraction

Notice that the 7 in the numerator and the 7 in the denominator can be canceled out. So we have \( \frac{4\times1\times\cancel{7}}{\cancel{7}\times5\times9}=\frac{4\times1}{5\times9}=\frac{4}{45}\).

Answer:

\(\frac{4}{45}\) cubic feet