Arithmetic order of operations

When using arithmetic operators, it's important to understand the order of operations, as the compiler uses a specific format to determine this order.

So, what does this order mean for a problem/equation?

Let's say that we need to run an equation with all these operators, but in a different order. For example: 5 + 15 * 20 - 2 / 6 ** 3 - (3 + 1).

In the preceding problem, we have all the six operations included. If we run this code, it gives a value of 301.

To break it down, the compiler first looked for the parentheses, so it computed the value (3+1), which is 4. Then, it handled the exponent 6**3, which is 216. Next is multiplication, so 15 * 20 is 300. Now, for division, 2/216 will be equal to 0 (it's not really zero, but we'll discuss this in the next section). Next, it focuses on addition, 5 + 300 which equals 305. And lastly subtraction: 305 - 4 which equals 301.

You can see the step-by-step path here:

5 + 15 * 20 - 2 / 6 ** 3 - (3 + 1)  # parenthesis
5 + 15 * 20 - 2 / 6**3 - 4          # exponents
5 + 15 * 20 - 2 / 216 - 4           # multiplication
5 + 300 - 2 / 216 - 4               # division
5 + 300 - 0 - 4                     # addition
305 - 0 - 4                         # subtraction
301

A good way to remember this order is with the acronym PEMDAS or with the sentence Please Excuse My Dear Aunt Sally.

What this stands for is as follows:

• P: Parentheses
• E: Exponent
• M: Multiplication
• D: Division
• A: Addition
• S: Subtraction

Now, this format is not just for numbers but also for other programming components such as conditionals (which we will cover in a future section). Consider this example, where you have a conditional like the following:

if (x > 7 && y < 19) || z == 5 

The value inside the parentheses will get executed first.