Question

In cubic feet, what’s the volume of a toy box with a length of 4 1/5 ft, a width of 2 1/3 ft, and a height of 3 1/2 ft, the answer will be a mixed fraction in cubic feet

Answer 1

To find the volume of the toy box in cubic feet, we can use the formula for volume:

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]

First, we need to convert the mixed fractions into improper fractions.

1. **Convert Length (4 1/5 ft) to an improper fraction:**
\[
4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5}
\]

2. **Convert Width (2 1/3 ft) to an improper fraction:**
\[
2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}
\]

3. **Convert Height (3 1/2 ft) to an improper fraction:**
\[
3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}
\]

Now we can calculate the volume:

\[
\text{Volume} = \left( \frac{21}{5} \right) \times \left( \frac{7}{3} \right) \times \left( \frac{7}{2} \right)
\]

Multiplying the numerators and the denominators:

\[
\text{Numerator} = 21 \times 7 \times 7 = 21 \times 49 = 1029
\]

\[
\text{Denominator} = 5 \times 3 \times 2 = 30
\]

Thus, the volume in improper fraction form is:

\[
\text{Volume} = \frac{1029}{30}
\]

Next, we will convert this improper fraction back into a mixed fraction. To do this, we divide 1029 by 30.

\[
1029 \div 30 = 34 \text{ (whole number)} \quad \text{with a remainder of } 9
\]

This means:

\[
1029 = 30 \times 34 + 9
\]

Therefore, the mixed fraction is:

\[
34 \frac{9}{30}
\]

We can simplify \(\frac{9}{30}\):

\[
\frac{9}{30} = \frac{3}{10}
\]

So the volume of the toy box is:

\[
\boxed{34 \frac{3}{10}} \text{ cubic feet}
\]