Welcome to the order of operations worksheets page at Math-Drills.com where we definitely follow orders! This page includes Order of Operations worksheets using whole numbers, decimals and fractions.
Elementary and middle school students generally use the acronyms PEMDAS or BEDMAS to help them remember the order in which they complete multi-operation questions. The 'P' or 'B' in the acronym stands for parentheses or brackets. All operations within brackets get completed first. The 'E' refers to any exponents; all exponents are calculated after the parentheses. The 'M' and 'D' are interchangeable as one completes the multiplication and division in the order that they appear from left to right. The fourth and final step is to solve for the addition and subtraction in the order that they appear from left to right.
More recently, students are being taught the acronym, PEMA, for order of operations, to avoid the confusion inherent in the other acronyms. For example, in PEMDAS, multiplication comes before division which some people incorrectly assumes means that multiplication must be done before division in an order of operations question. In fact, the two operations are completed in the order that they occur from left to right in the question. This is recognized in PEMA which more correctly shows that there are four levels to complete in an order of operations question.
Unless you want your students doing something different than the rest of the world, it would be a good idea to get them to understand these rules. There is no discovery or exploration needed here. These are rules that need to be learned and practiced and have been accepted as the standard approach to solving any multi-step mathematics problem.
Order of Operations with All Operations
Even though this is the first option on the page, we've only put it here because this is what most people will look for. If you want to easy your students into order of operations questions, you might want to scroll down and bit and take it a bit at a time.
Order of Operations with Addition & Multiplication
This is a good starting point where only addition and multiplication is involved (with a few parentheses thrown in). These worksheets will help students to recognize that multiplication is done before addition unless there are parentheses involved. It's always nice if you can think up a few examples to illustrate what some of these questions mean. For example, 2 + 7 × 3 could refer to the number of days in two days and three weeks. (9 + 2) × 15 could mean the total amount earned if someone worked 9 hours yesterday and 2 hours today for $15 an hour.
Order of Operations with Addition, Subtraction, & Multiplication
Order of Operations with Addition, Subtraction, Multiplication, & Division
Decimals Order of Operations Worksheets
These worksheets are actually quite sophisticated as they require a stong foundation in a number of skills. Basic math facts, operations with decimals, exponents, and, of course, order of operations. They are not for the faint of heart, but they are also really not that complicated if students have the prerequisite knowledge. We've made them work out to nice numbers, so you won't have to deal with non-repeating decimals or such overwhelming concepts that take students forever to complete the questions. If you find students are having difficulty with these questions, ask yourself whether they have enough background knowledge to complete these questions. Like we said, it requires a lot to be successful on these pages, so spend the time backing up and going over these concepts again before proceeding.
Fractions Order of Operations Worksheets
As with the decimals order of operation worksheets, the fractions order of operations worksheets require quite a bit of pre-requisite knowledge. If your students struggle with these questions, it probably has more to do with their ability to work with fractions than the questions themselves. Observe closely and try to pin point exactly what pre-requisite knowledge is missing then spend some time going over those concepts/skills before proceeding.
Otherwise, the worksheets below should have fairly straight-forward answers and shouldn't result in too much hair loss.
Order of Operations with Fractions & Decimals