Order Of Operations
The Order of Operations is the agreed-upon sequence for evaluating mathematical expressions: Parentheses, Exponents, then Multiplication and Division (left to right), then Addition and Subtraction (left to right) — often remembered as PEMDAS. For example, 3 + 4 x 2 = 3 + 8 = 11, not 14, because multiplication comes before addition. This 7th grade math rule from Saxon Math Course 2 is universal: every calculator and algebra system follows it, making it one of the most critical conventions in all of mathematics.
Key Concepts
Property 1. Simplify within parentheses (or other symbols of inclusion). 2. Simplify powers and roots. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right.
Examples $2 + 4 \times 3 4 \div 2 = 2 + 12 2 = 12$ $5 + 5 \cdot 5 5 \div 5 = 5 + 25 1 = 29$ $50 8 \cdot 5 + 6 \div 3 = 50 40 + 2 = 12$.
Explanation Think of 'Please Excuse My Dear Aunt Sally' as the ultimate rulebook for math! Following this sequence prevents mathematical chaos and ensures everyone arrives at the same correct answer. It is the essential guide to solving expressions correctly, no matter how complicated they might look at first.
Common Questions
What is the order of operations?
The order of operations specifies the sequence for evaluating expressions: Parentheses first, then Exponents, then Multiplication and Division left to right, then Addition and Subtraction left to right. Remember with PEMDAS.
What does PEMDAS stand for?
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It is a memory aid for the standard order of operations.
Why does order of operations matter?
Without a standard order, the expression 3 + 4 x 2 could equal either 11 or 14 depending on which operation you do first. The order of operations eliminates ambiguity so everyone gets the same answer.
What grade learns the order of operations?
Order of operations is introduced in earlier grades and reinforced in 7th grade Saxon Math Course 2, where it applies to more complex expressions involving fractions, decimals, and exponents.
Do multiplication and division have equal priority?
Yes. Multiplication and division have the same priority and are performed left to right. For 12 / 4 x 3: first 12 / 4 = 3, then 3 x 3 = 9 — not 12 / 12 = 1.
What is a common mistake with order of operations?
Treating PEMDAS as strictly left-to-right for all operations. Multiplication and division are performed left to right as a pair, and addition and subtraction are performed left to right as a pair — not multiplication before division always.