![]() Solution: This problem includes a fraction bar (also called a vinculum), which means we must divide the numerator by the denominator. This is done in Example 4 below.Įxample 4: Evaluate 150 ÷ (6 + 3 x 8) - 5 using the PEMDAS.Įxample 5: Evaluate the arithmetic expression below: When two or more operations occur inside a set of parentheses, these operations should be evaluated according to Rules 2 and 3. Similarly, addition and subtraction were evaluated from left to right, according to Rule 3. In Examples 2 and 3, you will notice that multiplication and division were evaluated from left to right according to Rule 2. Let's look at some examples that involve more than two operations.Įxample 2: Evaluate 3 + 6 x (5 + 4) ÷ 3 - 7 using PEMDAS.Įxample 3: Evaluate 9 - 5 ÷ (8 - 3) x 2 + 6 using PEMDAS. In Example 1, each problem involved only 2 operations. Let's look at some examples of solving arithmetic expressions using these rules.Įxample 1: Evaluate each expression using the rules for PEMDAS. The above problem was solved correctly by Student 2, since she followed Rules 2 and 3. Rule 3: Lastly, perform all additions and subtractions, working from left to right.Īn easy way to remember this order is to use the acronym PEMDAS (parentheses, exponents, multiplication and division, addition and subtraction). Rule 2: Next perform all multiplications and divisions, working from left to right. Rule 1: First perform any calculations inside parentheses. Mathematicians have devised a standard order of operations for calculations involving more than one arithmetic operation. We need a set of rules in order to avoid this kind of confusion. When performing arithmetic operations there can be only one correct answer. Student 1 performed the operation of addition first, then multiplication whereas student 2 performed multiplication first, then addition. It seems that each student interpreted the problem differently, resulting in two different answers. Problem: Evaluate the following arithmetic expression:
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