Praxis Core Prep: The Order of Operations
For any math question you will face on the Praxis Core, you will need to know the order of operations. After you have the basic mathematical principles down, you’re ready to tackle the order of operations.
When multiple computations are involved in finding a value represented by multiple numbers and operations signs, the rules concerning the order in which the operations are to be worked must be applied. Doing them in the wrong order can cause answers to be false, which is not the ideal situation. To avoid such examination misfortune, you must follow the order of operations, or the correct procedure for working multiple computations.
Think about how you would determine the value of the following expression:
3 + 23 + 5(4 – 7)
What would you do?
The acronym “GEMDAS” is formed by the initials of the order of operations, in order:
G: Grouping symbols (such as parentheses, brackets, and fraction bars)
MD: Multiplication and Division in order from left to right
AS: Addition and Subtraction in order from left to right
Notice that multiplication and division are represented together, as are addition and subtraction. That indicates that you must do those operations in the order in which they appear. For example, you don’t want to add all the way from left to right and then go back and do all the subtraction from left to right.
Okay, an unresolved issue is still waiting for an answer. How do you find the value of 3 + 23 + 5(4 – 7)? Well, the first step is to find the value within the grouping symbols, the parentheses. Then the exponent needs to be used. Next comes the indicated multiplication, and then the addition.
Using the order of operations within itself
What should you do if the issue of operations order arises within a step of the order of operations? Don’t worry. The order of operations is a principle of its word. It applies even within steps of itself. If multiple operations are needed within parentheses, for example, apply the order of operations inside the parentheses.
[(8 – 3)2 + 2 × 5] – 7 + 4 × 6 =
The correct answer is Choice (D). The value within the parentheses must be determined first, and then it must be squared because exponents come next in the order of operations. The product of 2 and 5 should be added to the value.
At this point, the value within the brackets can be determined. Then, you need to find the product of 4 and 6 and add it to the result of subtracting 7 from the value within the brackets. Here’s how the math looks when you work it out: