How to Calculate Mathematical Problems Using the Order of Operations

Calculating mathematical problems that involve multiple operations can be very confusing. When working out a formula, it's very important to follow the order of operations to calculate the formula. Remember these simple steps when working with complex problems involving multiple operations.

Instructions

1. Simplify all operations inside parentheses. Any operations contained in parentheses are answered first. This also applies to these enclosure symbols { } and [ ].

2. Work from the inside-out IF parentheses are enclosed within other parentheses.

3. Simplify all exponents, working from left to right. Remember that the exponent goes with the thing to which it is closer.

4. Treat any square root as an exponent.

5. Perform all multiplications and divisions working from left to right.

6. Perform all additions and subtractions working from left to right.

Tips & Warnings

• There is no particular significance in the use of square brackets or parentheses. It's more a personal preference than a requirement.

• The most important things to remember with Order of Operations is to work from the inside out, and to do each step completely and separately.

• Do not try to complete two steps at once, nor try to do stuff in your head, as you will be much more likely to make mistakes.

Resources

• Find examples of orders of operations at Mathgoodies.com.
• Here are more great examples of orders of operations at Purplemath.com.