An exponent refers to the number of times a number is multiplied by itself. For example [katex] 7^2 = 7 \times 7 [/katex] or [katex] 4^3 = 4 \times 4 \times 4. [/katex]

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Order of op

Order of operations

Here you will learn about order of operations, including what it means and how to calculate and solve order of operations problems using PEMDAS.

Students will first learn about order of operations as a part of operations and algebraic thinking in elementary school.

What is the order of operations?

Order of operations refers to the rule that explains the sequence of steps necessary for correctly evaluating a mathematical expression or math problem.

You will use the acronym PEMDAS to help recall the correct order, or priority, in which you complete mathematical operations.

Mathematical operations such as multiplication and addition have to be completed in a specific order. This sequence of steps helps us to evaluate any mathematical expression, both with numerical values and algebraic expressions.

To evaluate an expression using PEMDAS, you need to understand what PEMDAS represents and be able to apply the PEMDAS rule to any calculation.

PEMDAS stands for:

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction

Parentheses have a higher priority than exponents, so we calculate what is inside a pair of parentheses first. Exponents have a higher priority than division and multiplication, so any exponent that can be evaluated is calculated next, and so on.

The order can be remembered using the mnemonic device for PEMDAS, ‘Please Excuse My Dear Aunt Sally.’

Order of operations

Priority of Operation	PEMDAS	Mathematical Symbol
$katex is not defined$	Parentheses
$katex is not defined$	Exponents
$katex is not defined$	Division Multiplication
$katex is not defined$	Addition Subtraction	$katex is not defined$

It is important to note that multiplication and division are given equal priority, and addition and subtraction are given equal priority.

When completing calculations that involve multiplication and division or addition and subtraction, you work from left to right.

For example,

Consider the following expression $katex is not defined$

$katex is not defined$ and then $katex is not defined$

For example,

Consider the following expression $katex is not defined$

$katex is not defined$ and then calculate $katex is not defined$

Visually you could represent PEMDAS as:

What is the order of operations?

Common Core State Standards

How does this relate to 5th grade math and 6th grade math?

Grade 5: Operations and Algebraic Thinking (5.OA.1)
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Grade 5: Operations and Algebraic Thinking (5.OA.2)
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

Grade 6: Expressions and Equations (6.EE.1)
Write and evaluate numerical expressions involving whole-number exponents.

How to evaluate using order of operations

In order to evaluate expressions using order of operations, you would use PEMDAS:

Solve any calculations within parentheses.
Solve for any exponents.
Solve any division and multiplication calculations.
Solve any addition and subtraction calculations.

[FREE] Order Of Operations Worksheet (Grade 5 and 6)

Use this worksheet to check your 5th and 6th grade students’ understanding of order of operations. 15 questions with answers to identify areas of strength and support!

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[FREE] Order Of Operations Worksheet (Grade 5 and 6)

Use this worksheet to check your 5th and 6th grade students’ understanding of order of operations. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREE

Order of operations examples

Example 1: PEMDAS with addition and multiplication

Evaluate $katex is not defined$

Solve any calculations within parentheses.

There are no parentheses.

2Solve for any exponents.

There are no exponents.

3Solve any division and multiplication calculations.

The multiplication that we need to calculate is $katex is not defined$

Replacing $katex is not defined$ with $katex is not defined$ gives us the calculation $katex is not defined$

4Solve any addition and subtraction calculations.

$katex is not defined$

So $katex is not defined$

Example 2: PEMDAS with division and subtraction

Evaluate $katex is not defined$

Solve any calculations within parentheses.

Show step

There are no parentheses.

Solve for any exponents.

Show step

There are no exponents.

Solve any division and multiplication calculations.

Show step

The division you need to calculate is $katex is not defined$

Replacing $katex is not defined$ with $katex is not defined$ gives us the calculation $katex is not defined$

Solve any addition and subtraction calculations.

Show step

$katex is not defined$

So $katex is not defined$

Example 3: PEMDAS with parentheses and multiplication

Evaluate $katex is not defined$

Solve any calculations within parentheses.

Show step

You have a pair of parentheses and so you need to resolve what is inside the set of parentheses first. This is the calculation $katex is not defined$

Using PEMDAS, multiplication comes before addition and subtraction so you need to solve the multiplication $katex is not defined$

Replacing $katex is not defined$ with $katex is not defined$ in the calculation, you have $katex is not defined$

Addition and subtraction should be completed from left to right and so you have $katex is not defined$ and $katex is not defined$ Therefore $katex is not defined$

As $katex is not defined$ and $katex is not defined$ means $katex is not defined$ you have the updated calculation $katex is not defined$

Solve for any exponents.

Show step

There are no exponents.

Solve any division and multiplication calculations.

Show step

$katex is not defined$

Solve any addition and subtraction calculations.

Show step

There is nothing else to solve, so the final answer is:

$katex is not defined$

Example 4: PEMDAS with an exponent and multiplication

Evaluate $katex is not defined$

Solve any calculations within parentheses.

Show step

There are no parentheses.

Solve for any exponents.

Show step

Here you have to resolve $katex is not defined$

Replacing $katex is not defined$ with $katex is not defined$ in the calculation, you now have:

$katex is not defined$

Solve any division and multiplication calculations.

Show step

The final step needed is to calculate $katex is not defined$

Solve any addition and subtraction calculations.

Show step

There is nothing else to solve, so the final answer is:

$katex is not defined$

Example 5: PEMDAS with brackets, an exponent and division

Evaluate $katex is not defined$

Solve any calculations within parentheses.

Show step

Within the set of parentheses, you have the calculation $katex is not defined$

You need to work from left to right.

Completing the division, you have $katex is not defined$

Next, $katex is not defined$

Therefore, $katex is not defined$

Replacing $katex is not defined$ with $katex is not defined$ you now have the updated calculation,

$katex is not defined$

Solve for any exponents.

Show step

You now have to solve $katex is not defined$

Updating the calculation, you now have $katex is not defined$

Solve any division and multiplication calculations.

Show step

There are no divisions or multiplications to solve.

Solve any addition and subtraction calculations.

Show step

$katex is not defined$ which gives us the final answer:

$katex is not defined$

Example 6: PEMDAS with everything

Evaluate $katex is not defined$

Solve any calculations within parentheses.

Show step

Within the brackets is the calculation $katex is not defined$

Updating the calculation by changing the value in the bracket to $katex is not defined$ you have

$katex is not defined$

Solve for any exponents.

Show step

As $katex is not defined$ you now have

$katex is not defined$

Solve any division and multiplication calculations.

Show step

Here you have to calculate $katex is not defined$ Working from left to right, you calculate $katex is not defined$ and then divide the solution by $katex is not defined$

$katex is not defined$

Updating the calculation, you now have $katex is not defined$

Solve any addition and subtraction calculations.

Show step

As $katex is not defined$ our final answer is:

$katex is not defined$

Teaching tips for order of operations

While PEMDAS is a great way for students to remember the order of operations, it’s important that the students understand how to solve for each of the operations required, not simply giving them the acronym to memorize.

It is important to find a way for students to practice outside of order of operations worksheets. The more practice a student gets, the better. For example you can physically separate word problems from the answer choices in the classroom. Students would have to walk around to discuss and solve the problem and then find the answer that matches.

Students could be given an expression without the symbols. They would have to then decide which operations/symbols would make the expression true.

Easy mistakes to make

Multiplication/division and addition/subtraction in the incorrect order
When you have a chain of multiplication and division calculations or a chain of addition and subtraction calculations, you work from left to right.
For example, If you put parentheses into the calculation $katex is not defined$ with the purpose of keeping the calculation exactly the same, you must place the parentheses around $katex is not defined$
This is because $katex is not defined$ and $katex is not defined$
If you placed parentheses around $katex is not defined$ you would have $katex is not defined$ which is a different answer that you would get without the parenthesis.

Exponents as multiplying a number by $katex is not defined$
When introducing exponents, some students will interpret $katex is not defined$ as $katex is not defined$ instead of $katex is not defined$ The use of a number line to represent this expression or using expanded notation when introducing the concept can help students internalize the learning.

Multiplying before exponents
Take $katex is not defined$ Because you would perform exponents before you perform multiplication within PEMDAS, you need to calculate the exponent term first, and then multiply the solution by $katex is not defined$ Inserting a pair of parentheses with the purpose of keeping the calculation exactly the same, $katex is not defined$ A common misconception is that the multiplication is carried out first, and then the value is raised to the power; here this would look like $katex is not defined$ and is equal to $katex is not defined$ which is the wrong answer.

Practice order of operations questions

katex is not defined

katex is not defined

katex is not defined

katex is not defined

To solve, follow the order of operations by using PEMDAS.

Order of Operations practice question 1

katex is not defined

katex is not defined

katex is not defined

katex is not defined

To solve, follow the order of operations by using PEMDAS.

Order of Operations practice question 2

katex is not defined

katex is not defined

katex is not defined

katex is not defined

To solve, follow the order of operations by using PEMDAS.

Order of Operations practice question 3

katex is not defined

katex is not defined

katex is not defined

katex is not defined

To solve, follow the order of operations by using PEMDAS.

Order of Operations practice question 4

katex is not defined

katex is not defined

katex is not defined

katex is not defined

To solve, follow the order of operations by using PEMDAS.

Order of Operations practice question 5

katex is not defined

katex is not defined

katex is not defined

katex is not defined

To solve, follow the order of operations by using PEMDAS.

Order of Operations practice question 6

Order of operations FAQs

Do you perform multiplication or division first in order of operations?

In the order of operations, multiplication and division are seen as equal and would be performed as they are stated within the expression, starting from left to right. The same is true with addition and subtraction.

Is PEMDAS or BODMAS correct?

Both PEMDAS and BODMAS are correct. The acronym BODMAS is the UK version of the same rules. It can also be referred to as BIDMAS or BEDMAS. The acronym in the UK would read as: Brackets, Indices, Division and Multiplication, Addition and Subtraction.

What is an exponent?

An exponent refers to the number of times a number is multiplied by itself. For example $katex is not defined$ or $katex is not defined$

Why do we use parentheses in math?

Parentheses are used within mathematical expressions to note a modification is the normal order of operations. In the expression, $katex is not defined$ because the addition is within parentheses, it is solved before the multiplication.

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