Order of Operations
Apply PEMDAS/BODMAS rules to evaluate mathematical expressions correctly — parentheses, exponents, multiplication, division, addition, subtraction in Grade 9 math.
Key Concepts
Property Operations in mathematical expressions must be evaluated in a systematic order, which can be simplified using the acronym PEMDAS : P (arentheses) E (xponents) M (ultiplication) and D (ivision) A (ddition) and S (ubtraction).
To simplify an expression using the order of operations: 1. Simplify any expressions within grouping symbols. 2. Simplify any expressions containing exponents or radicals. 3. Perform any multiplication and division in order, from left to right. 4. Perform any addition and subtraction in order, from left to right.
Examples Evaluate $(4 \cdot 3)^2 5(4 + 2)$: First, solve inside parentheses to get $(12)^2 5(6)$. Then, handle the exponent: $144 5(6)$. Next, multiply: $144 30$. Finally, subtract to get $114$. Evaluate $\frac{4^2 6}{5} + \sqrt{21 5}$: Simplify the numerator and under the radical first: $\frac{16 6}{5} + \sqrt{16} = \frac{10}{5} + 4$. Then divide: $2 + 4 = 6$. Evaluate $15 |6 10| + 4(5 2)$: Handle absolute value and parentheses: $15 | 4| + 4(3) = 15 4 + 12$. Add and subtract from left to right: $11 + 12 = 23$.
Common Questions
What is the order of operations in mathematics?
The order of operations (PEMDAS/BODMAS) dictates the sequence for evaluating expressions: Parentheses first, then Exponents, then Multiplication and Division left to right, then Addition and Subtraction left to right. Following this order ensures every mathematician gets the same answer.
Why does order of operations matter?
Without a consistent order of operations, the same expression could produce different answers. For example, 2 + 3 × 4 equals 14 using correct order (multiply first) but 20 if you add first. The PEMDAS rules create a universal standard so mathematical communication is unambiguous.
How do parentheses affect order of operations?
Parentheses have the highest priority in the order of operations. Any expression inside parentheses must be evaluated first before performing operations outside. Nested parentheses are evaluated from innermost to outermost, giving mathematicians control over the computation sequence.