# How do you solve 9/c=27/39?

Feb 3, 2017

$c = 13$.

#### Explanation:

We can solve this by way of Cross Multiplication.

There are two sets of factors that will be multiplied with each other: 9 and 39, c and 27. It doesn't really matter on which side of the equation we will put the product of each sets. But for now, let's put the product of 9 and 39 on the left side, the product of c and 27 on the right side. Multiplication will be done simultaneously, that is, at the same time.
$\frac{9}{c} = \frac{27}{39}$ becomes...

$351 = 27 c$.
See how cross multiplication works? We multiply the left side's numerator with the right side's denominator (9 and 39, respectively), and multiply the left side's denominator with the right side's numerator (c and 27, respectively).

Now we are going to simplify the equation. Since we need to isolate the $c$ (because we are looking for its value), we will divide both sides by 27.
$\frac{351}{27} = \frac{27 c}{27}$ becomes...

$13 = c$. Hope this helps.

Feb 3, 2017

$c = 13$

#### Explanation:

$\frac{9}{c} = \frac{27}{39}$

cross multiply

$27 \times c = 9 \times 39$

$27 c = 351$

$c = 13$

substitute $c = 13$

$\frac{9}{13} = \frac{27}{39}$

$\frac{9}{13} \left(\frac{3}{3}\right) = \frac{27}{39}$

$\frac{27}{39} = \frac{27}{39}$