To find the volume of a rectangular prism, you use the formula:
[tex]\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\][/tex]
Given the dimensions of the rectangular prism:
- Length ([tex]\( l \)[/tex]) = [tex]\(\frac{2}{3}\)[/tex] inch
- Width ([tex]\( w \)[/tex]) = [tex]\(\frac{3}{5}\)[/tex] inch
- Height ([tex]\( h \)[/tex]) = [tex]\(\frac{4}{7}\)[/tex] inch
You multiply these fractions together to find the volume:
[tex]\[
\text{Volume} = \left( \frac{2}{3} \right) \times \left( \frac{3}{5} \right) \times \left( \frac{4}{7} \right)
\][/tex]
First, multiply the numerators:
[tex]\[
2 \times 3 \times 4 = 24
\][/tex]
Then, multiply the denominators:
[tex]\[
3 \times 5 \times 7 = 105
\][/tex]
Thus, the product of the fractions is:
[tex]\[
\frac{24}{105}
\][/tex]
Now, simplify the fraction:
[tex]\[
\frac{24}{105} = \frac{24 \div 3}{105 \div 3} = \frac{8}{35}
\][/tex]
As a decimal, this results in approximately:
[tex]\[
0.22857142857142854
\][/tex]
Thus, the volume of the rectangular prism is [tex]\(\boxed{0.22857142857142854}\)[/tex] cubic inch.
