Algebra Basics: What is the Order of Operations?

If you’re studying algebra, you’ve likely come across the concept of the order of operations. This is a set of rules that tells you the order in which to perform mathematical operations within an equation. Without these rules, you could end up with different answers depending on the order in which you perform the operations, which could lead to confusion and errors.

The order of operations is typically abbreviated as PEMDAS or BODMAS, which stands for:

P arentheses B rackets
E xponents O rder
M ultiplication & D ivision D ivision & M ultiplication
A ddition & S ubtraction A ddition & S ubtraction
The acronyms PEMDAS and BODMAS and what each letter means when performing math operations.

These rules ensure that you always perform the operations in the correct order , regardless of the complexity of the equation.

By following the order of operations, you can simplify even the most complicated equations and arrive at the correct answer every time.

Why Do We Need Order of Operations?

When solving a mathematical expression, it is important to follow a set of rules to ensure that everyone arrives at the same answer.

The order of operations is a set of rules that dictate how mathematical operations should be performed.

Without these rules, different people may arrive at different answers, leading to confusion and errors.

Consider the expression 2 + 3 \times 4 . Without the order of operations, different people may interpret this expression in different ways.

Here are some answers you could get from this expression:

2 + 3 \times 4 \\ 5 \times 4 \\ 20

In the example above the numbers 2 and 3 were added first, and then the result of that sum 5 was multiplied to 4 giving a result of 20 .

Here is another way to answer the expression (using the PEMDAS/BODMAS order):

2 + 3 \times 4 \\ 2 + 12 \\ 14

In this example above the numbers 3 and 4[katex] were multiplied first, and the result of that was then added to [katex]2 , resulting in an answer of 14 .

By following the order of operations, however, everyone will arrive at the same answer of 14 .

The order of operations is especially important when dealing with more complex expressions involving multiple operations and parentheses.

Additionally, the order of operations is essential in real-world applications of mathematics. In fields such as finance and science, formulas and calculations must be performed consistently and accurately to ensure the correct results are obtained. By using the order of operations, we can guarantee that everyone follows the same rules and arrives at the same answer, making it easier to compare and evaluate calculations.

What Is the Order of Operations?

When solving algebraic expressions, following the order of operations is important to ensure a correct answer. The order of operations is known as PEMDAS or BODMAS which is an acronym used to help you remember the order in which you should perform operations.

Common Mistakes to Avoid

When it comes to solving algebraic equations, there are a few common mistakes that many students make.

Here are some of the most common mistakes to avoid:

  • Not following the order of operations: The order of operations is crucial when solving algebraic equations. Remember to always perform operations in the correct order: parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
  • Forgetting to distribute: When there is a number outside of a set of parentheses, you need to distribute that number to every term inside the parentheses. This is a common mistake that can lead to incorrect solutions.
  • Combining like terms incorrectly: When combining like terms, make sure you are adding or subtracting the coefficients (the numbers in front of the variables), not the variables themselves.

It's important to take your time when solving algebraic equations and double-check your work to avoid these common mistakes. Remember, practice makes perfect!


Now that you have a good understanding of the order of operations in algebra, you'll be able to simplify complex expressions with ease. Remember to always start with parentheses and work your way out, evaluating exponents before multiplication and division before then using multiplication and division (in order from left to right) before finishing with any addition and subtraction (again, from left to right).

It's important to keep in mind that the order of operations is a universally accepted convention, designed to ensure that mathematical expressions are evaluated consistently and accurately. By following these rules, you can avoid confusion and arrive at the correct answer every time.

While the order of operations may seem daunting at first, with practice and repetition, it will become second nature. You'll be able to tackle even the most complex algebraic expressions with confidence, knowing that you're following the correct order of operations every step of the way.