Question

Volume of rectangular prism with a length of 3 2/3, a height of 4 1/3, and a width of 2 1/4, the answer needs to be a mixed number or improper fraction

Answer 1

To find the volume of a rectangular prism, you multiply its length, width, and height. In this case, we have:

- Length: \(3 \frac{2}{3}\)
- Height: \(4 \frac{1}{3}\)
- Width: \(2 \frac{1}{4}\)

First, we convert these mixed numbers to improper fractions:

1. **Convert \(3 \frac{2}{3}\)**:
\[
3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}
\]

2. **Convert \(4 \frac{1}{3}\)**:
\[
4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3}
\]

3. **Convert \(2 \frac{1}{4}\)**:
\[
2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}
\]

Now, we have:
- Length: \(\frac{11}{3}\)
- Height: \(\frac{13}{3}\)
- Width: \(\frac{9}{4}\)

Next, we calculate the volume \(V\):
\[
V = \text{Length} \times \text{Height} \times \text{Width} = \frac{11}{3} \times \frac{13}{3} \times \frac{9}{4}
\]

Now, we multiply these fractions together:
\[
V = \frac{11 \times 13 \times 9}{3 \times 3 \times 4}
\]

Calculating the numerator:
\[
11 \times 13 = 143
\]
\[
143 \times 9 = 1287
\]

Calculating the denominator:
\[
3 \times 3 = 9
\]
\[
9 \times 4 = 36
\]

Thus, we have:
\[
V = \frac{1287}{36}
\]

Now we simplify \(\frac{1287}{36}\). First, we find the greatest common divisor (GCD) of 1287 and 36. Both numbers can be divided by 3.

Calculating:
\[
\frac{1287 \div 3}{36 \div 3} = \frac{429}{12}
\]

Now, we convert the improper fraction \(\frac{429}{12}\) to a mixed number. Dividing 429 by 12 gives:
\[
429 \div 12 = 35 \quad \text{(with a remainder of 9)}
\]

Thus,
\[
\frac{429}{12} = 35 \frac{9}{12}
\]

We can also simplify \(\frac{9}{12}\) to \(\frac{3}{4}\). So, the mixed number becomes:
\[
35 \frac{3}{4}
\]

Therefore, the volume of the rectangular prism is:
\[
\boxed{35 \frac{3}{4}}
\]