Order of Operations

When expressions combine addition, subtraction, multiplication, division, exponents, and parentheses, the order of operations tells you which steps to perform first so everyone simplifies in the same way. Remember PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) or BODMAS in some regions; skipping this order can lead to errors and confusion.

This rule matters whenever you see nested structures, such as 3 + 2 × (5 – 2)2. If you ignore the parentheses or do addition before multiplication, you’ll get the wrong result. By following PEMDAS, you break down the problem in a logical, systematic way.

Example: Simplify 3 + 2 × (5 – 2)2.

1. Parentheses: 5 – 2 = 3 ⇒ 3 + 2 × 32
2. Exponents: 32 = 9 ⇒ 3 + 2 × 9
3. Multiplication: 2 × 9 = 18 ⇒ 3 + 18
4. Addition: 21
   The correct simplified value is 21.

Hints and tips

• Annotate parentheses: Number nested brackets (( )₁​)₂​ to expand or simplify in the correct sequence.
• Underline exponents early: Before distributing or multiplying, mark any powers so you don’t forget to handle them.
• Convert division to fraction form: Writing a ÷ b helps you see exactly what gets multiplied or exponentiated.
• Work one layer at a time: Don’t jump ahead – fully simplify each operation level (PEMDAS/BODMAS) before moving on.
• Re-check ambiguous expressions: If you see something like 8 / 2(2 + 2), rewrite it unambiguously (e.g. 8 / 2 × (4)) before calculating.