Question

6 5/6 x 1 4/7

Answer 1

To multiply the mixed numbers \(6 \frac{5}{6}\) and \(1 \frac{4}{7}\), we first need to convert them into improper fractions.

**Step 1: Convert the mixed numbers to improper fractions.**

For \(6 \frac{5}{6}\):
\[
6 \frac{5}{6} = \left(6 \times 6 + 5\right) / 6 = (36 + 5) / 6 = 41 / 6
\]

For \(1 \frac{4}{7}\):
\[
1 \frac{4}{7} = \left(1 \times 7 + 4\right) / 7 = (7 + 4) / 7 = 11 / 7
\]

**Step 2: Multiply the improper fractions together.**
\[
\frac{41}{6} \times \frac{11}{7} = \frac{41 \times 11}{6 \times 7} = \frac{451}{42}
\]

**Step 3: Simplify the fraction if possible.**
451 and 42 do not have common factors (451 is a prime number), so the fraction \(\frac{451}{42}\) is already in its simplest form.

**Step 4: Convert back to a mixed number.**
To convert \(\frac{451}{42}\) to a mixed number, we divide 451 by 42:
\[
451 \div 42 = 10 \quad \text{(the whole number part)}
\]
\[
451 - (42 \times 10) = 451 - 420 = 31 \quad \text{(the remainder)}
\]
Thus,
\[
\frac{451}{42} = 10 \frac{31}{42}
\]

Therefore, the final result of multiplying \(6 \frac{5}{6}\) by \(1 \frac{4}{7}\) is:
\[
\boxed{10 \frac{31}{42}}
\]