# 0.1.1 - Order of Operations

When 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 Section

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:

$$0.0940$$