Multiplication and division have the same level of priority in the standard order of operations.
This means that when multiplication and division appear together, you must evaluate them strictly from left to right.
Example 1
Consider the expression: 24 ÷ 6 × 3
Start with the operation on the far left:
- First step: 24 ÷ 6 = 4
- Second step: 4 × 3 = 12
Therefore, 24 ÷ 6 × 3 = 12.
A Common Wrong Approach
Some students see multiplication written before division in the PEMDAS acronym (or division before multiplication in BODMAS) and assume multiplication must always come first.
That is not how the rule works. Multiplication and division share equal priority.
Example 2
Consider the expression: 48 × 2 ÷ 8
Work from left to right as the operations appear:
- First step: 48 × 2 = 96
- Second step: 96 ÷ 8 = 12
The correct answer is 12.
Why Does Left to Right Matter?
Mathematical operations at the same priority level require a consistent tie-breaking rule to ensure predictable results. The left-to-right convention provides that exact consistency.
The same identical principle applies to addition and subtraction when they appear together.
Remember This
Do not read PEMDAS as a strict linear sequence where every M must happen before every D.
Instead, think of operational priority in levels:
- Parentheses and grouping symbols
- Exponents and radicals
- Multiplication and division (from left to right)
- Addition and subtraction (from left to right)
This tiered structure makes the rules much easier to apply accurately.