Question

find the volume of the rectangular prism. write your answer in simplest form. \\(\frac{9}{10}\\) yd, \\(\frac{1}{8}\\) yd, \\(\frac{5}{7}\\) yd, \\(\square\text{yd}^3\\)

Explanation:

Step1: Recall Volume Formula

The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height. Here, \( l = \frac{9}{10} \) yd, \( w = \frac{1}{8} \) yd, \( h = \frac{5}{7} \) yd.

Step2: Multiply the Fractions

Substitute the values into the formula: \( V = \frac{9}{10} \times \frac{1}{8} \times \frac{5}{7} \). First, multiply \( \frac{9}{10} \) and \( \frac{1}{8} \): \( \frac{9}{10} \times \frac{1}{8} = \frac{9}{80} \). Then multiply by \( \frac{5}{7} \): \( \frac{9}{80} \times \frac{5}{7} \). Simplify by canceling 5 and 80 (80 ÷ 5 = 16): \( \frac{9}{16} \times \frac{1}{7} = \frac{9}{112} \).

Answer:

\(\frac{9}{112}\)