Question

find the volume of the rectangular prism. write your answer in simplest form. \\(\frac{4}{5}\\) yd \\(\frac{3}{5}\\) yd \\(\frac{3}{8}\\) yd

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a rectangular prism is given by the formula \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height. Here, \( l=\frac{4}{5}\) yd, \( w = \frac{3}{5}\) yd, and \( h=\frac{3}{8}\) yd. So we need to calculate \( \frac{4}{5}\times\frac{3}{5}\times\frac{3}{8} \).

Step2: Multiply the first two fractions

First, multiply \( \frac{4}{5} \) and \( \frac{3}{5} \). Using the rule for multiplying fractions \( \frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d} \), we get \( \frac{4\times3}{5\times5}=\frac{12}{25} \).

Step3: Multiply the result by the third fraction

Now, multiply \( \frac{12}{25} \) by \( \frac{3}{8} \). Again, using the fraction multiplication rule: \( \frac{12\times3}{25\times8}=\frac{36}{200} \).

Step4: Simplify the fraction

Simplify \( \frac{36}{200} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 4. So \( \frac{36\div4}{200\div4}=\frac{9}{50} \).

Answer:

\(\frac{9}{50}\)