# How do you solve \frac { 9} { 10} = \frac { 7} { a }?

Mar 5, 2018

See a solution process below:

#### Explanation:

Because both sides of the equation are pure fractions we can "flip" or invert the fractions and not impact the solution:

$\frac{10}{9} = \frac{a}{7}$

Now, multiply each side of the equation by $\textcolor{red}{7}$ to solve for $a$ while keeping the equation balanced:

$\textcolor{red}{7} \times \frac{10}{9} = \textcolor{red}{7} \times \frac{a}{7}$

$\frac{70}{9} = \cancel{\textcolor{red}{7}} \times \frac{a}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}}$

$\frac{70}{9} = a$

$a = \frac{70}{9}$