Order of operations

The order of operations is a very simple, but a very important rule. So important, in fact, that you will have to obide by it in every math problem you encounter – ever! It concernes the order in which these operations need to be performed. The order of operations lists mathematical operations in order in which they should be performed in a mathematical expression, from highest to lowest priority. Here is that list:

The first letters of these operations (P-E-M-A) are often used as a mnemonic device to help you remember the order in which they should be performed. As you can see, operations inside parentheses have the highest priority, then exponents, then multiplication and, with the lowest priority, addition. To explain how this translates to problem solving, we will use this example:

(8 – 10)2 – (-9) * (-3)

This is a fairly complex example, but it contains all the elements needed to properly explain the order of operations . The first step we have to do is to get rid of the parentheses where it is possible. That can be done by solving the expressions inside the parentheses.

(-2)2 – (-9) * (-3)

Notice that we left -9 and -3 inside their parentheses. That is because there are no operations to perform there and we will get rid of them a bit later. We will leave them be to avoid clutter. Now we need to perform the exponentation, as it is second on the list of priorities. Since (-2)2 equals 4, we get:

4 – (-9) * (-3)

The next operation on the order of operations is multiplication, so let us do it. The result of multiplying (-9) and (-3) is 27, so we are left with:

4 – 27

The only operation left to perform now is subtraction, which has the lowest priority. The end result is:

-23

It is important to adhere to this order as it affects the end result. If we performed the operations in a different order, we could have gotten the wrong result.

If you wish to practice the order of operations, you can use the free worksheets below.

Order of operations exams for teachers

 Exam Name File Size Downloads Upload date Non positive numeric expression Order of operations – non positive integers 725.4 kB 6143 September 3, 2019 Order of operations – non positive decimals 602.6 kB 2541 September 3, 2019 Order of operations – non positive fractions 901.4 kB 2485 September 3, 2019 Order of operations – non positive mixed numbers 933.8 kB 2214 September 3, 2019 Order of operations – non positive improper fractions 857.5 kB 2057 September 3, 2019 Positive numeric expression Order of operations – positive integers 662.2 kB 6406 September 3, 2019 Order of operations – positive decimal 732.4 kB 2447 September 3, 2019 Order of operations – positive fractions 848.8 kB 3154 September 3, 2019 Order of operations – positive mixed numbers 878.5 kB 2453 September 3, 2019 Order of operations – positive improper fractions 794.9 kB 1980 September 3, 2019 Non positive algebraic expression Order of operations – non positive integers 897.4 kB 3078 September 3, 2019 Order of operations – non positive decimals 897.4 kB 1876 September 3, 2019 Order of operations – non positive fractions 1.2 MB 1624 September 3, 2019 Order of operations – non positive mixed numbers 1 MB 1845 September 3, 2019 Order of operations – non positive improper fractions 1020.2 kB 1700 September 3, 2019 Positive algebraic expression Order of operations – positive integers 865.7 kB 3608 September 3, 2019 Order of operations – positive decimals 982.5 kB 2014 September 3, 2019 Order of operations – positive fractions 1.2 MB 2178 September 3, 2019 Order of operations – mixed fractions 1 MB 2080 September 3, 2019 Order of operations – improper fractions 981.2 kB 1974 September 3, 2019

Order of operations worksheets for students

 Worksheet Name File Size Downloads Upload date Order of operations – Positive numeric expressions 781.9 kB 6017 September 3, 2019 Order of operations – Non positive numeric expressions 843.8 kB 3880 September 3, 2019 Order of operations – Positive algebraic expressions 924.8 kB 3398 September 3, 2019 Order of operations – Non positive algebraic expressions 1.4 MB 3080 September 3, 2019