Order of Operations (PEMDAS)
In short: Order of operations is the shared priority list that tells which calculation in a long expression goes first, so that everyone lands on the same value.
6th GradeNumbers and Operations6.EE.A.2c
What is Order of Operations?
The order of operations removes doubt from lines like \(8 + 6 \times 5\), which could be read as 70 or as 38. Multiplication outranks addition here, so the value is 38, and every careful student agrees on it, whatever calculator or notebook they use.
Remember it as PEMDAS. Work inside Parentheses first, then handle Exponents, then do Multiplication and Division as one tier, moving left to right, and finally Addition and Subtraction as the last tier, again left to right.
How to spot it
- An expression mixes several operations, such as addition, multiplication and a power.
- Parentheses or fraction bars group part of the work and must be finished first.
- Two classmates get different answers from the same line of calculation.
- A calculator result looks wrong because the expression was typed without grouping.
The method
- Scan for grouping symbols and simplify what sits inside each one first, using these same rules.
- Evaluate every power next.
- Sweep across the line for times and divide signs, taking whichever appears first.
- Sweep once more for plus and minus signs, again taking whichever appears first.
Order of Operations: solved example
Problem
Evaluate \(8 + 6 \times (9 – 4)^2 \div 5\).
Solution
Inside the parentheses: \(9 – 4 = 5\). The power: \(5^2 = 25\). Then \(6 \times 25 = 150\), and \(150 \div 5 = 30\).
Last, add: \(8 + 30 = 38\). The value is 38.
Try it
Question 1
Evaluate \(40 – 12 \div 4 + 3^2\).
Show the answer
Exponent: 9. Divide: \(12 \div 4 = 3\). Then \(40 – 3 + 9 = 46\).
Question 2
Evaluate \(24 \div 6 \times 2\) and explain the order.
Show the answer
Neither sign outranks the other, so the leftmost goes first: \(24 \div 6 = 4\), then \(4 \times 2 = 8\).
Order of Operations vs. Inverse Operations
The order of operations tells you which step to do first when evaluating an expression. Inverse operations are pairs that undo each other, like adding 7 and subtracting 7, and they are used to solve equations, not to decide priority.
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Whole dictionary: A–Z · 6th Grade · Numbers and Operations