# Question #21119

Oct 17, 2017

$- \frac{10}{21}$

#### Explanation:

Write the fractions like this:

$\frac{- 5}{6} \cdot \frac{4}{7}$

Neither fraction can be simplified any more, since 5 and 6 have no common factors, and 4 and 7 have no common factors (other than 1). However, when combining fractions, you can remove a factor from the top of one fraction if the same factor can be removed from the bottom of the other fraction.

In this case, the bottom of the first fraction and the top of the second fraction both have a common factor of $2$, so we can get rid of that factor:

$\frac{- 5}{3 \times 2} \cdot \frac{2 \times 2}{7}$

$\frac{- 5}{3 \times \cancel{2}} \cdot \frac{\cancel{2} \times 2}{7}$

$\frac{- 5}{3} \cdot \frac{2}{7}$

Now, we have no more common factors to get rid of, so just multiply the tops and bottoms of the two fractions together to get the answer:

$\frac{- 5 \times 2}{3 \times 7}$

$\frac{- 10}{21}$