Question

10 2/5 x 8 1/2 x 6 1/4 simplest form

Answer 1

To solve the multiplication of the mixed numbers \(10 \frac{2}{5} \times 8 \frac{1}{2} \times 6 \frac{1}{4}\), we first convert each mixed number into an improper fraction.

1. Convert \(10 \frac{2}{5}\):
\[
10 \frac{2}{5} = \left(10 \times 5 + 2\right) / 5 = \frac{50 + 2}{5} = \frac{52}{5}
\]

2. Convert \(8 \frac{1}{2}\):
\[
8 \frac{1}{2} = \left(8 \times 2 + 1\right) / 2 = \frac{16 + 1}{2} = \frac{17}{2}
\]

3. Convert \(6 \frac{1}{4}\):
\[
6 \frac{1}{4} = \left(6 \times 4 + 1\right) / 4 = \frac{24 + 1}{4} = \frac{25}{4}
\]

Now we can multiply the improper fractions together:
\[
\frac{52}{5} \times \frac{17}{2} \times \frac{25}{4}
\]

Combine the fractions:
\[
\frac{52 \times 17 \times 25}{5 \times 2 \times 4}
\]

Calculating the denominator:
\[
5 \times 2 = 10 \quad \text{and} \quad 10 \times 4 = 40
\]
Thus, the denominator is \(40\).

Calculating the numerator:
1. First calculate \(52 \times 17\):
\[
52 \times 17 = 884
\]

2. Now multiply \(884 \times 25\):
\[
884 \times 25 = 22100
\]

Thus, we have:
\[
\frac{22100}{40}
\]

Now, we simplify \(\frac{22100}{40}\):
1. Divide both numerator and denominator by 20 (the greatest common divisor):
\[
\frac{22100 \div 20}{40 \div 20} = \frac{1105}{2}
\]

This fraction is already in its simplest form. If we want to express it as a mixed number:
\[
\frac{1105}{2} = 552 \frac{1}{2}
\]

So, the final answer in simplest form is:
\[
552 \frac{1}{2}
\]