No, division is not before multiplication. Multiplication and division have equal priority in the order of operations.
Understanding Order of Operations
The order of operations, often remembered by acronyms like PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) or BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction), dictates the sequence for evaluating mathematical expressions. A crucial point often misunderstood is the equal standing of multiplication and division (and similarly, addition and subtraction).
This means that when encountering both multiplication and division in an expression, you perform the operations from left to right. The same principle applies to addition and subtraction.
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Example 1: 6 ÷ 2 × 3 = ?
- Following the left-to-right rule: 6 ÷ 2 = 3, then 3 × 3 = 9. The correct answer is 9, not 1 (which would result from doing multiplication before division).
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Example 2: 10 - 4 + 2 = ?
- Following the left-to-right rule: 10 - 4 = 6, then 6 + 2 = 8. The correct answer is 8, not 4 (which would result from performing addition before subtraction).
Multiple sources confirm this:
- Reddit's r/askmath states explicitly that "Multiplication and division have equal priorities so we work with them left to right."
- Numerous other resources (Quora, Stack Overflow, Mathnasium) reiterate that multiplication and division are of equal precedence and should be evaluated from left to right.
Therefore, the statement "division before multiplication" is incorrect. The correct interpretation is that both operations are performed from left to right.
