# How do you apply PEMDAS for expressions with fraction bars?

Nov 16, 2014

That depends on how much the fraction bar expands throughout the expression.
If it is the entire expression:

$\frac{\left(6 + 2\right) - 2 \cdot \left(3 - 7\right)}{3 \left(6 - 5\right)} = \frac{16}{3}$

Naturally, the way to go about this is to solve the numerator first, then the denominator. Eventually, when you get the final result, you divide.

But if the division only goes through only individual elements:

$\left(\frac{6 + 2 \cdot 3}{10 - 4}\right) \cdot {\left(3 - 1\right)}^{2} + 3 - 4 = 7$

You would follow PEMDAS normally, left to right, check parenthesis and exponents, multiply and divide, then add and subtract. When experiencing a fraction bar, you have to go through numerator first, then denominator before moving on to the next element.