1 5/7 *6 1/8

To multiply the mixed numbers \(1 \frac{5}{7}\) and \(6 \frac{1}{8}\), we first convert them to improper fractions.

1. Convert \(1 \frac{5}{7}\): \[ 1 \frac{5}{7} = \frac{(1 \times 7) + 5}{7} = \frac{7 + 5}{7} = \frac{12}{7} \]

2. Convert \(6 \frac{1}{8}\): \[ 6 \frac{1}{8} = \frac{(6 \times 8) + 1}{8} = \frac{48 + 1}{8} = \frac{49}{8} \]

Now, we multiply the two improper fractions: \[ \frac{12}{7} \times \frac{49}{8} = \frac{12 \times 49}{7 \times 8} \]

Calculating the numerator: \[ 12 \times 49 = 588 \]

Calculating the denominator: \[ 7 \times 8 = 56 \]

Now we have: \[ \frac{588}{56} \]

Next, we simplify this fraction. To do this, we find the greatest common divisor (GCD): \[ \frac{588 \div 28}{56 \div 28} = \frac{21}{2} \]

Lastly, we can convert \(\frac{21}{2}\) back to a mixed number: \[ 21 \div 2 = 10 \quad \text{(whole number)} \quad \text{with a remainder of } 1 \] Thus, \[ \frac{21}{2} = 10 \frac{1}{2} \]

So, the product of \(1 \frac{5}{7}\) and \(6 \frac{1}{8}\) is: \[ 10 \frac{1}{2} \]