Yes, in the context of the order of operations (commonly known as PEMDAS or BODMAS), multiplication and division are indeed considered to have the same priority. This means they are interchangeable in terms of their hierarchical level, and when both operations appear in an expression, you resolve them from left to right as they appear.
Understanding the PEMDAS Rule
PEMDAS is a widely used mnemonic to help remember the correct order of operations in mathematics. Each letter stands for a type of operation:
- Parentheses (or Brackets)
- Exponents (or Orders)
- Multiplication
- Division
- Addition
- Subtraction
While the M for multiplication comes before D for division in the acronym, this does not imply that multiplication must always be performed before division.
The Equal Standing of Multiplication and Division
Even though "M" for multiplication appears before "D" for division in PEMDAS, these two operations actually hold the same priority. This means neither operation takes precedence over the other simply because of its letter order in the acronym. Instead, when you encounter both multiplication and division in a mathematical expression, you complete them in the order they occur from left to right.
This rule is critical because performing these operations out of their left-to-right sequence can lead to incorrect results.
Why Left-to-Right Matters: A Practical Example
Consider the expression: 20 ÷ 5 × 2
If you strictly followed the order of the letters in PEMDAS and performed multiplication before division (which is incorrect for same-priority operations):
- Incorrect approach:
20 ÷ (5 × 2) 20 ÷ 10- Result:
2(This is incorrect)
Following the correct left-to-right rule for operations of equal priority:
- Correct approach: Start from the left. The first operation encountered is division.
(20 ÷ 5) × 24 × 2- Result:
8(This is the correct answer)
This example clearly demonstrates that while multiplication and division have the same priority, their position in the equation dictates which is performed first when moving from left to right.
The Same Rule Applies to Addition and Subtraction
Just like multiplication and division, addition and subtraction also share the same priority level. Although "A" for addition comes before "S" for subtraction in PEMDAS, they are also resolved from left to right as they appear in the expression.
Visualizing the Order of Operations
To solidify understanding, here's a table summarizing the correct order of operations and their priority levels:
| Order | Operation | Description |
|---|---|---|
| 1st | Parentheses | Simplify expressions inside parentheses (or brackets) first. |
| 2nd | Exponents | Evaluate powers and roots next. |
| 3rd | Multiplication & Division | Perform these operations from left to right as they appear. |
| 4th | Addition & Subtraction | Perform these operations from left to right as they appear. |
Key Takeaways
- Multiplication and division are on the same level of priority within the order of operations.
- You perform them from left to right as they appear in the equation, not strictly by the letter order in PEMDAS.
- The same left-to-right rule applies to addition and subtraction, which also share the same priority level.
- Understanding this "tiering" and the left-to-right rule for operations of equal priority is fundamental to accurately solving mathematical expressions.
