Ordering Operations with Parentheses

As we mentioned in the introduction, this section is going to introduce two new symbols to your vocabulary. Parentheses are used in English to set aside a comment or an idea (like this). In math, parentheses set aside a few terms and operations. The whole point of parentheses is to say "Do this first!" Sometimes they might be very important to the order of operations and your answer totally depends on them. Sometimes they are there to help you see where to start, but don't play a role in coming up with the answer. Let's take a look at a few ways they might be used...

Examples:
(1 + 2) + 3 = 6
3 + (9 x 2) = 21
(3 x 6) + (5 - 2) = 21
(3 + 4 + 5 + (4 x 3) - 2 - 3) = 19

Multiplication and Division

So we've introduced parentheses. You need to do the math inside of parentheses first. Once you get all of that stuff out of the way, you move to the operations in the open areas. The first operations that need to be finished are multiplication and division. If you see "3 + 5 x 6" you need to do the "5 x 6" part of the equation first and then add the three (3) to your product. The same would be true for division. An equation like "16 - 4 ÷ 2" would have two steps. The division comes first with an answer of 2. The second step would have you subtracting that two from the 16.

Addition and Subtraction

The last steps when you have a variety of operations are the addition and subtraction. We told most of the story in the previous paragraph. Start with the parentheses, move to the multiplication and division, and finish off with the addition and subtraction.

Example:
3 x 2 x 5 + 5 x 6 + (11 - 3) = ?
Step1 - Parentheses: 3 x 2 x 5 + 5 x 6 + 8 = ?
Step 2 - Multiplication and Division: 30 + 30 + 8 = ?
Step 3 - Addition and Subtraction: 30 + 30 + 8 = 68

Bigger than Arithmetic Operations

We're here to help you with the basics. As you move forward with math, you will learn about other operations and symbols. Each one plays a specific role in solving any equation. There are symbols called "brackets" that are related to parentheses. They look like this [ and ]. They work the same way, but come before parentheses in the order. You will also discover square roots and other roots. They break apart larger numbers into smaller factors. We think the biggest thing you will find in math is the variable. Variables are symbols for unknown amounts. In many cases you will be finding out the value of variables and not coming up with the answer to an equation. We'll save that excitement for later.
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