Evaluating algebraic expressions is a foundational skill in mathematics, and mastering it requires a clear understanding of the order of operations.

Without following this order, you might end up with incorrect answers, no matter how well you understand the individual steps involved.

In this guide, we’ll break down how to apply the order of operations.

Let’s explore helpful strategies like the P.E.M.D.A.S. mnemonic and walk through practical examples to make sure you’re solving algebraic expressions with confidence.

## What is P.E.M.D.A.S.?

P.E.M.D.A.S. stands for **Parentheses, Exponents, Multiplication, Division, Addition, **and** Subtraction**.

This acronym outlines the specific order in which you should evaluate different operations in an expression.

Without a consistent order, the same expression could yield different results depending on how it’s interpreted, which is why P.E.M.D.A.S. is so critical to mathematical accuracy.

This order of operations was established to ensure consistency and clarity across all mathematical problem-solving. It defines a hierarchy that must be followed.

For example, parentheses take priority because they group terms together, signaling that they should be solved first.

Exponents come next because they represent repeated multiplication, and their effect on the expression can be significant. Multiplication and division are treated equally, as are addition and subtraction, but both pairs must be solved from **left to right**.

Ignoring the P.E.M.D.A.S. sequence can lead to major errors.

### Why is the Order of Operations important?

The order of operations ensures consistency when solving algebraic problems.

Without it, the same expression could be interpreted in multiple ways, resulting in different answers.

By using P.E.M.D.A.S., mathematicians and students alike can follow a universal system, guaranteeing that everyone arrives at the same solution.

## Understanding the steps in P.E.M.D.A.S.

Let’s break down each step of the order of operations so you can better understand how to apply them:

**Parentheses**: First, solve any operations inside parentheses or brackets. These symbols group parts of an expression that should be evaluated first.- Example: In the expression
**3 * (5 + 8)**, you would solve**(5 + 8)**first, which equals 13.

- Example: In the expression
**Exponents**: After parentheses, solve any exponents or powers in the expression.- Example: If you encounter
**2^3**, calculate the exponent to get 8 before moving to the next step.

- Example: If you encounter
**Multiplication and Division**: These operations are solved from**left to right**, regardless of whether multiplication or division appears first. Treat them as equals and proceed in sequence.- Example: In
**3 * 13 – 22 / 4**, first calculate**3 * 13**and then**22 / 4**.

- Example: In
**Addition and Subtraction**: Like multiplication and division, these are also solved from**left to right**.- Example: In
**39 – 1 + 3**, subtract first to get**38**and then add to get the final answer**41**.

- Example: In

## A helpful mnemonic: “Please Excuse My Dear Aunt Sally”

If you’re ever unsure of the order, the phrase “Please Excuse My Dear Aunt Sally” can help you remember the correct sequence:

**Please**: Parentheses**Excuse**: Exponents**My Dear**: Multiplication and Division (from left to right)**Aunt Sally**: Addition and Subtraction (from left to right)

This simple mnemonic is easy to memorize and can serve as a quick reminder whenever you’re faced with a challenging algebraic expression.

## Example: Walking through a problem

Now, let’s solve the following algebraic expression step by step using P.E.M.D.A.S.:

### Expression:

**3 * ( 5 + 8 ) – 22 / 4 + 3**

**Parentheses**: Solve the operation inside the parentheses first.**5 + 8 = 13**

Now the expression becomes:

**3 * 13 – 22 / 4 + 3****Exponents**: There are no exponents in this example, so we move to the next step.**Multiplication and Division**: Perform multiplication and division from left to right.**3 * 13 = 39****22 / 4 = 5.5**

Now the expression is:

**39 – 5.5 + 3****Addition and Subtraction**: Finally, perform addition and subtraction from left to right.**39 – 5.5 = 33.5****33.5 + 3 = 36.5**

So, the final answer is **36.5**.

### Common pitfalls to avoid

Even though the steps seem straightforward, it’s easy to make mistakes if you’re not careful.

Many students, especially those new to algebra, often misinterpret the left-to-right rule for multiplication and division.

This can lead to errors in solving even simple expressions.

To avoid these mistakes, it’s essential to take your time and double-check that you’re following the order of operations correctly.

## Why left to right matters

Multiplication and division, as well as addition and subtraction, should always be performed from left to right.

This rule helps ensure consistency in your calculations.

For instance, in the expression **10 – 3 + 5**, solving from left to right gives you:

**10 – 3 = 7****7 + 5 = 12**

If you were to reverse the order and add first, you would incorrectly get:

**3 + 5 = 8****10 – 8 = 2**

And guess what?

The answer would be completely wrong!

This is why it’s critical to remember the left-to-right rule for these operations.

## The role of exponents in algebra

Exponents are a common stumbling block for many students when evaluating algebraic expressions.

If you encounter a term like **2^4**, remember that this means multiplying the base (2) by itself as many times as the exponent indicates (4). Therefore, **2^4 = 16**.

Ignoring exponents can lead to dramatically wrong results, so always handle them right after solving any parentheses.

Regular practice with exponent-related problems helps build a stronger foundation in algebra, boosting your confidence when tackling more complex expressions.

The more familiar you become with exponents, the more naturally you’ll handle challenging problems, improving your overall problem-solving skills in mathematics.

## Practice makes perfect

To truly master evaluating algebraic expressions using P.E.M.D.A.S., consistent practice is key.

Regularly solving different types of algebraic problems will help solidify your understanding of the order of operations and reduce the likelihood of errors.

It’s also helpful to explain your thought process as you solve each step, which can reinforce your understanding and make complex problems feel more manageable.

## Conclusion: Why P.E.M.D.A.S. matters

Evaluating algebraic expressions using the correct order of operations is critical for ensuring accurate results in mathematics.

By mastering P.E.M.D.A.S. and understanding how to apply each step, you can solve even the most complex expressions with ease.

Whether you’re preparing for a math test, tackling a homework problem, or exploring advanced algebra, following the order of operations will keep you on the right track.

Remember, it’s not just about solving problems — it’s about solving them correctly. So, take your time, follow P.E.M.D.A.S., and you’ll consistently get the right answer.