Left-to-Right for Multiplication and Division
When a mathematical expression contains only multiplication and division, with no other operations, the calculation proceeds strictly from left to right. In Grade 6 Saxon Math Course 1 (Chapter 1: Number, Operations, and Algebra), students apply this left-to-right rule as part of the order of operations. For 24 / 4 x 2: first 24 / 4 = 6, then 6 x 2 = 12. Reversing the order (doing multiplication first) would give 24 / 8 = 3, which is incorrect. Neither multiplication nor division takes priority over the other; the order of appearance in the expression determines which is performed first.
Key Concepts
Property When there is more than one multiplication or division step within a problem, we take the steps in order from left to right.
Examples $24 \div 6 \times 2 = 4 \times 2 = 8$.
$100 \div 10 \div 2 = 10 \div 2 = 5$.
Common Questions
What is the rule for expressions with both multiplication and division?
Perform operations from left to right in the order they appear. Neither multiplication nor division has priority over the other.
Evaluate 24 / 4 x 2.
Left to right: 24 / 4 = 6, then 6 x 2 = 12. Answer: 12.
Evaluate 3 x 8 / 4.
Left to right: 3 x 8 = 24, then 24 / 4 = 6. Answer: 6.
Why is it wrong to always do multiplication before division?
The order of operations says multiplication and division are equal in precedence. Only their left-to-right position determines which is performed first.
How does this rule fit into the full order of operations (PEMDAS)?
In PEMDAS, the M and D (multiplication and division) are on the same step and resolved left to right. Similarly, A and S (addition and subtraction) are resolved left to right.