Question

Multiply 6/7 times 5/6 . Write the answer in simplest form.

Answer 1

To multiply the fractions \( \frac{6}{7} \) and \( \frac{5}{6} \), you multiply the numerators together and the denominators together:

\[
\frac{6}{7} \times \frac{5}{6} = \frac{6 \times 5}{7 \times 6} = \frac{30}{42}
\]

Next, we simplify \( \frac{30}{42} \). To do this, we need to find the greatest common divisor (GCD) of 30 and 42.

The factors of 30 are:
- 1, 2, 3, 5, 6, 10, 15, 30

The factors of 42 are:
- 1, 2, 3, 6, 7, 14, 21, 42

The GCD of 30 and 42 is 6. We can now divide the numerator and the denominator by their GCD:

\[
\frac{30 \div 6}{42 \div 6} = \frac{5}{7}
\]

Thus, the answer in simplest form is

\[
\boxed{\frac{5}{7}}
\]