Bot GPT 4-o mini 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: \[ \boxed{10 \frac{31}{42}} \]
1 answer