Free Order of Operations Worksheets
Students work through a number of basic worksheets and then advance to four and five step operations.
The Basics
PEMDAS - A great reference sheet to have handy when learning this process. his is great to have handy through out the entire unit. You can even turn it into a quiz.
Order of Operations Guide to Simple Problems - A 3 page step-by-step walk through. Great for new learners. This two page worksheet walks students through the entire process of three and four step problems.
Step By Step Operations (Larger Numbers) - We use much larger numbers here. We start to walk you through much larger problems.
Addition and Subtraction Only - We focus on specific operations in this column. Addition before subtraction. Sums before differences.
Addition and Multiplication Only - Sums and products give us a bit of a challenge. Multiplication before addition. Products before sums.
Addition and Division Only - Practice with just sums and quotients. Divide and then multiply a wise man one said.
Division and Subtraction Only - For some odd reason, we find that children have the most problems with these operations. Make sure that you remember DAS: Division before subtraction.
Multiplication and Subtraction Only - Products and differences only. his is the part that you need to remember: MDAS: Products before differences.
Division and Multiplication Only - They seem to fly through this one. Put the middle of PEMDAS to work for you.
Finding the Solution to Your Problems (Simple) - Match the outcome to the problem by drawing a line. This is a neat way, we thought, to challenge students just a bit more and add an element of fun to it.
Circle or Square (Simple Operations) - You draw figure based on the operations you work with. his is one that we dreamed up while writing following directions worksheets, you'll see why.
Create your Own Order of Operations Worksheet - This is a fun cooperative activity for your students. This is fun activity for a pair of students in class. They can also peer grade it. This helps a great deal.
Advanced Level
Order of Operations Puzzle - Figure out which equation matches the outcome. A fun puzzle that can help students really grasp the concept and practice their PEMDAS.
Decimals with No Negative Numbers - We go all decimal on you. Decimals are introduced for the first time to add a new level of difficulty to the problems. We start to walk you through much larger problems.
Order of Operations (Decimals with No Negative Outcomes) - If this is your first time with decimals, start here.
All Operations; No Parenthesis or Exponents - This is an all out no holds barred sheet. This is a quick and simple rewind of operations practice. There are 3 versions and answers in this file, so 6 pages in all.
Order of Operations with Exponents - This does not include all parts of the system. This is a really big one. 10 printable pages in all. 3 versions that are well spaced out for you.
Order of Operations with Parenthesis - Great for practicing with brackets. We work with the old ( ) for the first time. The top of PEMDAS food chain, if you will.
Order of Operations with Parenthesis and Exponents - We include all operations in this one. The go deep on this one. Just about every level skill is covered here.
Finding the Solution to Your Problems (Complex) - Match the solution to the starting problem. The problems get a bit tricker and the arrows start to fly even more.
Circle or Square (Complex Operations) - We're on the hunt for operations below 16. Another neat way to keep them motivated and paying attention when working with operations.
Order of Operations with Fractions - We introduce fractions to work with. Believe it or not, students usually pick this skill up quickly; since it really is two skills that should already be mastered.
Crazy Order of Operations (Decimals and Fractions) - This is about as difficult as it gets in this section. You might want to use calculators for this one. Otherwise get ready to round, big time!
Order of Operations Related Teacher Resources
Here is a wide range of resources for a deeper understanding of this topic.- Basic Math Operations Lesson Plans
- Order of Operations Lesson Plans
- Sequence: Order of Events Worksheets
- Teacher Curriculum For Math
What are the Order of Operations?
The order of operations refers to a series of rules that are enforced in a certain order when answering a mathematical equation. The method of assessing any arithmetic statement using mathematical operations such as addition, multiplication, subtraction, and division is referred to as operations in mathematics. Let us go through the sequence of operations in detail and see how we can recall them by employing simple techniques.
In mathematics, the order of operation specifies how numerous operations in a mathematical equation should be addressed.
PEMDAS is a term used to describe this sequence in which each letter represents an arithmetic operation. It is a good strategy to recall the sequence of the operational processes.
Symbol | Operation | |
P | (), [], {} | Parenthesis |
E | (^) | Exponents |
M | x | Multiplication |
D | ÷ | Division |
A | + | Addition |
S | - | Subtraction |
The PEMDAS rules governing the sequence in which processes in an equation must be performed are as follows:
PEMDAS Rule # 1: They have priority above other operations. The very first step is to solve all the functions that are included in the parenthesis. Work through all the groups from within. (Anything in parentheses is a group.)
PEMDAS Rule # 2: Complete all of the exponential equations.
PEMDAS Rule # 3: Then, cater to the multiplication and/or division operations from left to right, depending on what occurs first.
PEMDAS Rule # 4: Finally, solve the addition and/or subtraction operations from left to right, whichever one occurs first.
In simple words, while solving a mathematical equation, you should first calculate the parenthesis, then perhaps the exponents if present in the equation, then multiplication and division, and lastly addition and subtraction. Calculate from left to right for functions within the same category. For example, if your issue has more than one exponent, you would start answering from the first left, and subsequently, make your way to the right.
Using Order of Operations
To demonstrate the precision of the rules employed in order of operations, consider the following example.
8 + 9 x (4 x 5) + 2^{3} - 2 ÷ 1
As per the order of operations, let's solve the parentheses first:
(4 x 5) = 20
Solving the parenthesis will leave us with the equation:
8 + 9 x 20 + 2^{3} - 2 ÷ 1
Next, we'll solve the exponential expression within the equation:
2^{3} = 8
The equation will then be as follows:
8 + 9 x 20 + 8 - 2 ÷ 1
We'll now cater to all the multiplication and division operations from left to right
9 x 20 = 180
2 ÷ 1 = 1
The equation:
8 + 180 + 8 - 2
Now we'll solve the equation from left to right adding or subtracting the values:
Addition: 8 + 180 + 8 = 196
Subtraction: 196 - 2 = 194
The answer as per the order of operation for the equation 8 + 9 x (4 x 5) + 2^{3} - 2 ÷ 1 is 194
How to Remember Order of Operations?
Having just learned about a word (PEMDAS) that will almost certainly be tough to recall, here is the most effective method for remembering the order. The catchphrase "Please Excuse My Dear Aunty Susan" is used to recall PEMDAS. It signifies "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction" in the order of operations.
The simplest method to understand the order is to follow the instructions below:
Begin by simplifying phrases within the brackets.
Calculate the exponential terms.
Divide or multiply the numbers.
Carry out addition or subtraction operations.
The Importance of the Order of Operations
Students will struggle to address increasingly sophisticated problems in mathematics that incorporate several operations if they do not understand the order. For instance, with this equation: (3 × 10) + (6 ÷ 3).
The brackets (or parentheses) represent the initial order of action, thus we must solve them first., leaving us with 30 + (6÷3). We'll then solve the equation in the other bracket, which will give us 30 + 2, and finally, the answer will be 32.
A student may arrive at a range of solutions if they do not know the right order. They'd get a lengthy (and wrong) decimal response if they tackled the addition before the brackets. Students will learn how to fix these issues if they follow the sequence of operations properly.
The Origin
The first reference to there being a specific sequence of operations that had to occur appeared with the introduction of academic books in the 19th century. There was more of a mutual understanding about whatever came first while solving an equation among mathematicians.
We don't put everything in brackets when it comes to solving all the aspects of a mathematical problem. This was the notion on which the order of operations was built.
More Examples...
To better understand PEMDAS, well mention below a few more examples:
5 + (2 x 4) - 3
Solving the parentheses first:
2 x 4 = 8
Leaving us with the equation
5 + 8 - 3
Solving the equation left to
5 + 8 = 13
13 - 3 = 10
The answer for the equation 5 + (2 x 4) - 3 is 10
10 + 6 x 5^{2} ÷ 3 - 6
As per the PEMDAS rules, we'll solve the exponential expression first
5^{2} = 25
Giving us the equation = 10 + 6 x 25 ÷ 3 - 6
Next we'll cater to all the multiplication and division operations from left to right in the equations:
6 x 25 = 150
150 ÷ 3 = 50
The equation will now become = 10 + 50 - 6
Now we'll add and subtract from left to right
10 + 50 = 60
60 - 6 = 54
Wrapping Up
The order of operations is one of the most basic principles in mathematics. However, students must learn this rule of solving a mathematical equation at a young age. This sequence can help solve basic equations to hard-to-solve word problems. Therefore, learn and understand it now to become an expert in solving arithmetic problems.