Order of Operations
This page contains links to free math worksheets for Order of Operations problems. Click one of the buttons below to view a worksheet and its answer key. You can also use the 'Worksheets' menu on the side of this page to find worksheets on other math topics.
These order of operations worksheets mix basic arithmetic, including parentheses and exponents. If you are looking for order of operations worksheets that test your PEMDAS acumen, these math worksheets are a good start. You can also find order of operations worksheets with negative numbers and order of operations worksheets with comparisons on pages.
Order of Operations (PEMDAS)
The order of operations are set of conventions used in math to decide what order operations need to be evaluated in to consistently get to the answer to a problem. These are also called precedence rules, and the occur in math problems as well as computer programming languages. Students make errors related to order of operations because we train them to read left-to-right, and a natural tendency is simply to evaluate a math program the same way. Left-to-right processing of a mathematical expression is the short road to whatever you get when you divide by zero. Just call it bad.
Instead, check with dear Aunt Sally. PEMDAS is a mnemonic tool used to help remember what operations to perform in what order. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. We can remember this ordering with the phrase, 'Please excuse dear Aunt Sally.' By remembering this phrase, we know the order to evaluate terms in an expression. Anything inside parentheses is always evaluated first, even if it contains operations that are of lower precendence. Always work from the 'inside out' when dealing with expressions that have parentheses. Within a set of parathenses, the same rules for order of operations apply, so look for other parenthees and similarlly follow all the other rules below.Next, consider any terms that have exponents. The exponent is something that you might consider strongly attached to a term in an expression, much like a sign on a number. Following this, consider any multiplication or division operations. These operations are of equal precedence, so they can be evaluated in any order themselves. The same is true of the next set of operations, addition and subtraction. They can be evaluated in any order as long as you've done all of the preceding operations completely.
The order of operations worksheets in this section provide plenty of practice, and they gradually introduce each step in the PEMDAS mnemonic. If you work your way through all of them, you'll be an order of operations expert in no time. Aunt Sally would be proud.