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 you use, leading to confusion and errors.

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

These rules ensure that operations are performed in the correct order, regardless of the complexity of the expression.

Why Do We Need Order of Operations?

When solving an expression, everyone must follow the same rules to arrive at the same answer. Otherwise, different interpretations can lead to incorrect results.

Consider this expression: $$ 2 + 3 \times 4 $$

Some might first add: $$ 2 + 3 = 5 \ 5 \times 4 = 20 $$

But according to order of operations, multiplication comes before addition: $$ 3 \times 4 = 12 \ 2 + 12 = 14 $$

✅ Correct answer: 14

This rule becomes even more important with complex equations. In real-world applications like finance or engineering, following the order of operations ensures consistent and accurate calculations.

What Is the Order of Operations?

When solving algebraic expressions, use PEMDAS/BODMAS to remember:

1. Parentheses / Brackets
   Always simplify expressions inside parentheses/brackets first.

2. Exponents / Orders
   Solve powers and square roots next.

3. Multiplication and Division
   From left to right.

4. Addition and Subtraction
   Also from left to right.

For example: $$ 5 + (3 \times 2)^2 \div 3 $$ Step-by-step:

• Inside parentheses: $3 \times 2 = 6$
• Exponent: $6^2 = 36$
• Division: $36 \div 3 = 12$
• Addition: $5 + 12 = 17$

✅ Final answer: 17

Common Mistakes to Avoid

Here are common errors and how to prevent them:

• ❌ Not following the order of operations
  Always apply PEMDAS/BODMAS rules in sequence.

• ❌ Forgetting to distribute
  Example: $2(x + 3) \Rightarrow 2x + 6$ (not just $2x + 3$)

• ❌ Incorrectly combining like terms
  Only combine terms with the same variables and exponents.
  $3x + 2x = 5x$ ✅
  $3x + 2x^2$ ≠ $5x^2$ ❌

Double-check your work and follow the process carefully.

Conclusion

Now that you understand the order of operations, you’re ready to simplify complex algebraic expressions with confidence.

Recap:

1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication & Division (left to right)
4. Addition & Subtraction (left to right)

These rules are a universal convention in maths. By mastering them, you’ll avoid confusion and consistently arrive at the correct answer.

With regular practice, applying these rules will become second nature—setting you up for success in algebra and beyond.