Order of Operations

Problem: Evaluate the following arithmetic expression:

3 + 4 x 2

Solution:

It seems that each student interpreted the problem differently, resulting in two different answers. Student 1 performed the operation of addition first, then multiplication; whereas student 2 performed multiplication first, then addition. When performing arithmetic operations there can be only one correct answer. We need a set of rules in order to avoid this kind of confusion. Mathematicians have devised a standard order of operations for calculations involving more than one arithmetic operation.

Rule 1: First perform any calculations inside parentheses.

Rule 2: Next perform all multiplications and divisions, working from left to right.

Rule 3: Lastly, perform all additions and subtractions, working from left to right.

The above problem was solved correctly by Student 2 since she followed Rules 2 and 3. Let’s look at some examples of solving arithmetic expressions using these rules.

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