Elementary Math: Learning the Order of Operations

What You Need to Know about the Order of Operations

Master the Details

The order of operations does not have to be difficult or complicated; it just requires practice and memorization. However, before you can master the order of operations, you must understand each operation separately. If you're having difficulty comprehending ordered operations, the problem might be that you do not know how to complete some of the individual steps involved.

Some of the common elements in a multi-step equation are multiplication of negative numbers, arithmetic involving variables (like 2a x 5) and subtraction of negative integers. Ask your teacher or a parent to go over any of these parts of long math expressions that you're struggling with.

How to Solve Multi-Step Problems

When a mathematical expression has more than one operation, that is, when more than one calculation has to be made to find the solution, you have to follow a specific order of operations. Here are the rules for the order of operations:

1. Perform any operations that are inside parentheses before performing any other calculations.
2. When all operations contained inside parentheses are complete, do any work involving exponents or radicals.
3. Next, work from left to right and complete all multiplication and division.
4. Finally, working from left to right, perform any addition or subtraction.

You can create a poster or a decorated, personalized list of these order of operations rules to hang above your study desk while you are still learning them. Just be careful to take down the list well before test time, or you may find yourself unable to remember the proper order when it really counts.

Learn by Making Mistakes

To make it easier to understand the importance of the order of operations, try working out a problem in the wrong order. Here's an example: 8 - ( 7 + 3 ) = -2.

If you ignore the parentheses and just go in order from left to right, you get 4 as your answer. But if you start inside the parentheses (adding 7 and 3 to get 10), you get the correct answer of -2. Following these steps in the correct order makes the rest of the problem easier to solve.