Free Order of Operations Worksheet, Definition, and Examples

How to do Order of Operations

Order of operations is a set of rules used to determine the sequence of operations to be performed in a mathematical expression. It is also known as PEMDAS, BODMAS, BEDMAS, or BIDMAS, depending on the country. The order of operations is essential in ensuring that everyone gets the same answer when solving a mathematical expression.

The order of operations is as follows:

1. Parentheses or Grouping Symbols: Perform operations inside parentheses or grouping symbols first.
2. Exponents: Perform any exponents or powers next.
3. Multiplication and Division: Perform multiplication and division in order from left to right.
4. Addition and Subtraction: Perform addition and subtraction in order from left to right.

It is essential to follow the order of operations to avoid confusion and ensure the correct answer.

When dealing with nested parentheses, start with the innermost parentheses and work your way out.

For example, in the expression:

(10 + 2) x 3 - 8 ÷ 4 

First, solve the parentheses:

12 x 3 - 8 ÷ 4 

Then, solve the division:

12 x 3 - 2 

Finally, solve the multiplication and subtraction:

36 - 2 = 34 

It is essential to note that different calculators may have different ways of interpreting the order of operations. However, as long as you follow the standard order of operations, you will always get the same answer.

In summary, the order of operations is crucial in solving a mathematical expression. Always start with parentheses or grouping symbols, followed by exponents, multiplication and division, and finally addition and subtraction. When dealing with nested parentheses, start with the innermost parentheses and work your way out. Following these rules will ensure that you get the correct answer every time.

Order of Operations Rules

When solving mathematical expressions, it is important to follow the correct order of operations to obtain the correct result. The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed. The most commonly used order of operations is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Addition and Subtraction

Addition and subtraction have the same priority and should be performed from left to right. For example, in the expression 10 + 5 – 3, the addition of 10 and 5 should be performed first, resulting in 15. Then, the subtraction of 3 should be performed, resulting in a final answer of 12.

Multiplication and Division

Multiplication and division also have the same priority and should be performed from left to right. For example, in the expression 12 ÷ 3 x 4, the division of 12 by 3 should be performed first, resulting in 4. Then, the multiplication of 4 and 4 should be performed, resulting in a final answer of 16.

The Role of Parentheses, Brackets, and Braces

Parentheses, brackets, and braces are used to group operations and indicate which operations should be performed first. Operations inside parentheses should be performed first, followed by operations inside brackets, then operations inside braces. If there are multiple sets of parentheses, brackets, or braces, they should be evaluated from the innermost set to the outermost set.

For example, in the expression 2 x (3 + 5) – 4, the addition inside the parentheses should be performed first, resulting in 2 x 8. Then, the multiplication of 2 and 8 should be performed, resulting in 16. Finally, the subtraction of 4 should be performed, resulting in a final answer of 12.

Remembering the order of operations is crucial when solving mathematical expressions. By following the rules of PEMDAS and prioritizing parentheses, brackets, and braces, one can ensure that they arrive at the correct answer.

Order of Operations Definition

Order of operations is a set of rules that dictate the order in which mathematical operations should be performed in an expression. It is also known as the operator precedence rule. The order of operations is essential to ensure that mathematical expressions are evaluated accurately and consistently.

The order of operations is usually abbreviated as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. The order of operations is as follows:

1. Parentheses: Evaluate expressions within parentheses first.
2. Exponents: Evaluate exponents (powers and square roots, etc.).
3. Multiplication and Division: Evaluate multiplication and division from left to right.
4. Addition and Subtraction: Evaluate addition and subtraction from left to right.

It is important to note that the order of operations is not optional and must be followed strictly to obtain the correct answer. Failure to follow the order of operations can result in incorrect answers.

For example, consider the expression 6 + 4 x 2. If one does not follow the order of operations, they may perform the addition operation first and get the incorrect answer of 20. However, if they follow the order of operations, they will perform the multiplication operation first and get the correct answer of 14.

In summary, the order of operations is a set of rules that dictate the order in which mathematical operations should be performed in an expression. It is essential to follow the order of operations to obtain accurate and consistent answers.

 Here are some examples that illustrate the application of the Order of Operations:

Example 1:

Simplify the expression: 4 + 3 x 2

According to the Order of Operations, multiplication should be done before addition. Therefore, we first multiply 3 and 2, which gives us 6. Then we add 4 to 6, which gives us the final answer of 10.

Example 2:

Simplify the expression: 8 – 4 x (6 ÷ 3)

The expression contains both multiplication and division, which have equal priority. Therefore, we perform division first, followed by multiplication, and finally subtraction.

First, we divide 6 by 3, which gives us 2. Then we multiply 4 and 2, which gives us 8. Finally, we subtract 8 from 8, which gives us the final answer of 0.

Example 3:

Simplify the expression: 3 + 4 x (5 – 2)^2

This expression contains both addition, subtraction, multiplication, and exponents. According to the Order of Operations, we perform the operations inside the parentheses first, then exponents, followed by multiplication, and finally addition.

First, we perform the subtraction inside the parentheses, which gives us 3. Then we square 3, which gives us 9. Next, we multiply 4 and 9, which gives us 36. Finally, we add 3 and 36, which gives us the final answer of 39.

Example 4:

Simplify the expression: 12 ÷ 2(3)

This expression contains both division and multiplication. According to the Order of Operations, we perform multiplication before division. Therefore, we first multiply 2 and 3, which gives us 6. Then we divide 12 by 6, which gives us the final answer of 2.

These examples demonstrate how the Order of Operations is used to solve mathematical expressions and ensure that the correct sequence of operations is followed.

Order of Operations Worksheet Video Explanation

Watch our free video on how to solve Order of Operations Examples. This video shows how to solve problems that are on our free Order of Operation Worksheet that you can get by submitting your email above.

Watch the free Order of Operations Worksheet video on YouTube here: Order of Operations Video

Video Transcript:

This video is about answering the question what is the order of operations. You can get this pemdas worksheets for free by clicking on the link in the description below.

Before we do some order of operations practice problems, I want to first go over what exactly the order of operations are. Typically, when we talk about order of operations, we refer to it as PEMDAS. These are the order that you need to perform the operations in a problem. Each one of these stands for something different. The P stands for parentheses, which would be the parentheses symbols if there are any.

The e stands for exponents. You would do those next and those are the little numbers up here like this two, right here would be an exponent. The M stands for multiplication, the d stands for division, A stands for addition and finally the S stands for subtraction. Now the only other thing I need to make mention of is that a lot of times people get confused around the M the d the a and the S. This is because it seems like you should always do multiplication first or always do division first.

In reality these two go together and these two go together. You always perform these two from left to right as well as addition and subtraction from left to right. That means that sometimes you’ll do division before you do multiplication and you’ll do subtraction before you do addition. It just depends on which one is on the left and which one is on the right in your problem.

Let’s do the first order of operations problems on our pemdas worksheet. Now the first problem we’re going to go over is number two, which is three plus five times four. In order to determine which operation, you should perform first you have to remember the order of operations, or PEMDAS, as a cheat. For this problem we don’t have any parentheses so we’re going to go past that step.

Then we check for exponents, we also don’t have any exponents so we skip that step. The next step is multiplication and division. If you look, we do have a multiplication part of this problem. The first thing we’re going to do is we’re going to perform that multiplication part. We’re going to do 5 times 4. We bring down this 3 and we do 3 plus and then 5 times 4 is 20. That turns into that then the next step is to just perform the last operation. 3 plus 20 is 23. Our final answer has to be 23.

Moving on to number 3 showing you guys what is the order of operations, we have negative 2 plus four in parenthesis times 10. For this pemdas problems we’re still going to follow the order of operations. The first thing we have to check for is parentheses, that’s what P is. If we look we do have a set of parentheses here. The first thing we have to do is we have to perform the operations inside of the parentheses.

In this case we have to add negative 2 plus 4. We’re going to add those two together first because they’re in the parentheses. When we add negative 2 plus 4 you will get positive 2, then you bring down the x and the 10. Now we have positive 2 times 10. Our parentheses are done, now we don’t have any exponents so we can cross that off and we’re all into multiplication. Right here we do 2 times 10 and 2 times 10 is 20 and that’s going to be our answer.

Moving on to our next order of operations example number 6 gives us 4 minus 10 divided by 5 times 7. The first thing we have to do is we have to determine which is the first part of the pemdas practice problems that we need to complete according to our order of operations. We’re going to just go down the list. P stands for parentheses, there are no parentheses so we can ignore that and we’re going to skip it. E stands for exponents, there are no exponents in this one so we’re going to skip it.

M stands for multiplication and we have a multiplication part right here. Five times seven and D stands for division and we have a division component right here. M and D go from left to right. They are actually the same step and you perform them from left to right. A very common mistake is to always complete multiplication before division. Now in this problem the division is on the left of the multiplication symbol which is on the right. That means that you’re going to perform this part first and then you’re going to do this multiplication part second. We’re going to do ten divided by five 10 divided by 5 is 2 then we’re going to simplify that and just make it 2. Next we have to bring down the other parts of the problem.

This 4 comes down this minus comes down and this multiplication and 7 come down. For the second step we have 4 minus 2 times 7 now and for this one, 2 times 7 comes first because this is multiplication. We know that multiplication comes before subtraction. This multiplication is going to get done before this subtraction so we’re going to do 2 times 7 first before we do the subtraction part. 2 times 7 is 14 and then we bring down this 4 again and this minus sign again. Now we’re left with 4 minus 14 and 4 minus 14 is negative 10. Our solution is going to be negative 10.

The last order of operations example that we’re going to do on our order of operations worksheet is number 8. This problem gives us 2 to the 4th plus 5 times 6 divided by 3. In parentheses in order to complete these in the correct order we just follow our order of operations. The first thing we’re going to do is anything in parentheses. If you look, we have a set of parentheses here which has 6 divided by 3 inside.

The very first thing we need to do is this part, six divided by three is two and then you bring the rest of the problem down. Two to the fourth comes down here this plus five comes down and then this multiplication symbol also comes down. The next thing we have to check for is exponents. In this case we have a term that has an exponent, that’s going to be our second step for this problem. Two to the fourth power is two times two times two times two, this would be 2 times 2 is 4 4 times 2 is 8 8 times 2 is 16. That’s going to be 16.

Then we bring down the rest of our problem. Now the problem is 16 plus 5 times 2. The next thing we need to look for is multiplication and division. We have 5 times 2, this multiplication symbol goes before this addition symbol so we’re going to multiply those two together. 16 comes down plus 5 times 2 and 5 times 2 is 10. Finally, we do 16 plus 10, that’s our last step, and that’s going to give us 26 as our final answer. You can try all the practice problems by downloading the free order of operations worksheets with answers above.