How do you solve \frac { 8} { 12} = \frac { n } { 3}?

Jul 4, 2017

$n = 2$

Explanation:

1. Cross multiply.

Multiply the numerator of the first fraction by the denominator of the second fraction, and set that equal to the numerator of the second fraction times the denominator of the first fraction. For example:

$\frac{a}{b} = \frac{c}{d}$

$a d = b c$

$\frac{8}{12} = \frac{n}{3}$

$8 \left(3\right) = 12 n$

$24 = 12 n$

2. Divide both sides by 12 to find n.

$\frac{24}{12} = \frac{\cancel{12} n}{\cancel{12}}$

$n = 2$

Hope this helps!

Jul 4, 2017

$2$

Explanation:

There is another way to do this question, however, it is a lot more dependant on the question, while the answer earlier shows a universal way of doing it which will work for all proportions.

You can simplify $\frac{8}{12}$ by dividing the numerator and the denominator both by the greatest common factor of $4$.

$\frac{8 \div 4}{12 \div 4} = \frac{2}{3}$

Now you have $\frac{2}{3} = \frac{n}{3}$

Logically, the only possible value for $n$ would be $2$