When to Use PEMDAS and When Not to (Everything you need to Know!)

PEMDAS, or Parentheses, Exponents, Multiplication, Division, and Addition and Subtraction, is an arithmetic algorithm used in solving complex mathematical equations. Generally, many students learn PEMDAS while in elementary or middle school, but not all are able to apply it effectively.

So, when to use PEMDAS? The best time to use PEMDAS is generally when there is more than one operation in a mathematical expression. PEMDAS is a useful tool for remembering the order of operations when solving complex math problems.

However, misusing PEMDAS can lead to numerous errors, which is why it is essential to understand when and when not to use PEMDAS. Read on to explore when to use PEMDAS and when not to. You might also enjoy reading: 17 Maths Websites the Best High School Students Use to Get Ahead.

What Does PEMDAS Stands For, and How Does It Work to Solve Mathematical Equations?

PEMDAS is an acronym used to help remember the order of operations. Parentheses, Exponents, Multiplication, and Division are performed from left to right, and Addition and Subtraction are also performed from left to right.

If you wonder how to use the order of operations (PEMDAS) effectively, I wrote a whole article that I encourage you to read.

However, the key to understanding PEMDAS is knowing when to use it in the first place, and here is when to use PEMDAS and when not to.

When to Use PEMDAS and When Not to?

Understanding when to use PEMDAS and when to veer off will ensure that you solve problems correctly. One common mistake that students make is using PEMDAS to solve all mathematical equations. Generally, PEMDAS only applies to complex equations with multiple operations. For simple equations such as 6 + 4, you do not need to use PEMDAS because there are no multiple operations.

However, for more complicated equations such as (2 + 3) * 4, PEMDAS is essential because there are multiple operations that need to be performed.

Another mistake that students commonly make is not grouping expressions correctly. For example, in the equation 9 + 2 * 3, some students may solve it as 9 + 6, while others may solve it as 11 * 3. The correct way to solve the equation is by performing multiplication before addition, giving you the answer 15. You can easily avoid this mistake by grouping the correct expressions together and then applying PEMDAS.

One exception to using PEMDAS is when dealing with exponents higher than 2. In this case, you would use Power Rule suggests that when you multiply two exponents with the same base, you add their powers. For example, 2³ * 2⁴ = 2⁽³⁺⁴⁾ = 2⁷ = 128. Knowing when to use the Power Rule instead of PEMDAS is crucial in solving higher-level mathematical equations.

Also, when dealing with square roots, the order of operations can change. You want to start with the numbers inside the square root, then exponents, followed by all other operations in order. In this case, you’d use Square Root, Exponents, Multiplication/Division, and finally, Addition/Subtraction.

Also, if there are no parentheses or exponents in the equation, you don’t need to apply the PEMDAS.

Another situation where you don’t need to use PEMDAS is when dealing with problems that involve fractions. Instead of using PEMDAS, you can apply multiplication rules for fractions. For instance, when dividing fractions, flip the second fraction and multiply. When multiplying fractions, multiply the numerators together and then the denominators together.

Moreover, understand that PEMDAS doesn’t always apply when solving trigonometric problems. In these cases, you might need to memorize the trigonometry ratios and apply the appropriate formula.

Remember to use PEMDAS when solving simple math problems that don’t require much practice or thought, such as basic algebra, arithmetic operations, and simple geometry problems. Using PEMDAS ensures that you solve basic math problems correctly and efficiently.

Read this article from Khan Academy if you are looking for worked examples of PEMDAS, or watch this video or the video below.

What to read next:

• How to solve quadratic equations by factoring: a quick and helpful guide.
• What is the FOIL Method? (With examples!)
• What a tangent line is, how to find it, and why is it important?

Wrapping Up

I believe that knowing when to use PEMDAS is essential to solving math problems correctly. While PEMDAS is often a handy guide to solving problems correctly and efficiently, it is crucial to know when to use it and when not to.

By knowing when to use PEMDAS and when not to, you can avoid common mistakes and confidently tackle any mathematical equation.