# 0.1.1 - Order of Operations

0.1.1 - Order of OperationsWhen performing a series of mathematical operations, begin with those inside parentheses or brackets. Next, calculate any exponents or square roots. This is followed by multiplication and division, and finally, addition and subtraction.

## Example: Standard Error for Two Proportions

This is a formula that you will see in Lesson 9: \( \sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}\)

\(p\) is a proportion and \(n\) is a sample size. Let's look at an example of working through this formula with the following values:

\(p_1=0.60\)

\(p_2=0.35\)

\(n_1=40\)

\(n_2=80\)

We can begin by plugging these values into the formula:

\( \sqrt{\frac{0.60(1-0.60)}{40}+\frac{0.35(1-0.35)}{80}}\)

The first operations that we perform are the ones in the parentheses:

\( \sqrt{\frac{0.60(0.40)}{40}+\frac{0.35(0.65)}{80}}\)

Though not typically shown, the values under the square root symbol in the fractions are treated as if they are in parentheses:

\(\sqrt{\left ( \frac{0.60(0.40)}{40}\right )+ \left ( \frac{0.35(0.65)}{80}\right ) } \)

Working within each set of parentheses, are next step is to multiply in the numerators:

\(\sqrt{\left ( \frac{0.24}{40} \right ) + \left ( \frac{0.2275}{80}\right ) } \)

Then, the division (i.e., the fractions):

\( \sqrt{0.006+0.00284375}\)

The addition underneath the square root:

\( \sqrt{0.00884375}\)

And finally, we take the square root:

\(0.0940\)