Florida Teacher Certification Examinations (FTCE) Subject Area Practice Test

What rule determines the order in which operators are applied in a mathematical expression?

1. Associative property

2. Commutative property

3. Order of operations

4. Distributive property

The correct answer is: Order of operations

The order in which operators are applied in a mathematical expression is dictated by the order of operations. This rule is crucial for ensuring that expressions are interpreted correctly and consistently. The order of operations typically follows the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (also from left to right). This hierarchy determines which calculations are performed first, thus leading to the correct outcome of the expression. Understanding the order of operations is fundamental for solving mathematical problems accurately. It prevents ambiguity in expressions that might otherwise be interpreted in multiple ways. For example, in the expression 3 + 4 × 2, the multiplication is performed before the addition, leading to a different result than if the addition were performed first. The other concepts listed—associative property, commutative property, and distributive property—do not dictate the order of operations but rather describe different properties of numbers and operations. The associative property concerns how numbers are grouped when adding or multiplying, the commutative property focuses on the rearranging of numbers when adding or multiplying, and the distributive property outlines how multiplication interacts with addition. None of these properties impact the sequence in which operations are executed in