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Test PrepACTMathOrder of Operations

ACT Math Skill Review: Order of Operations

The order in which we apply operations is extremely important and the ACT will frequently test your knowledge of it. There is a simple mnemonic device, “PEMDAS,” that will assist you in remembering the proper order. Students are often taught to remember the phrase “Please Excuse My Dear Aunt Sally,” to help keep the order of operations straight.

The letters stand for:

Parentheses
Exponents
Multiplication and Division
Addition and Subtraction

Consider the problem:

3(24 – 2 • 3)2 – 2 • 3

We begin by evaluating everything inside the parentheses, remembering the correct order of operations when doing so.

3(24 – 2 • 3)2 – 2 • 3 = 3(16 – 2 • 3)2 – 2 • 3
= 3(16 – 6)2 – 2 • 3
= 3(10)2 – 2 • 3

Now that we have evaluated everything inside the parentheses, we proceed to evaluate the exponents, followed by all multiplication and division. Finally, we complete all necessary addition and subtraction.

3(10)2 – 2 • 3 = (3 • 100) – (2 • 3) = 300 – 6 = 294

Although the above example used integers, please note that the rules concerning the order of operations should also be applied  to any of the classes of numbers we have already discussed.

Example

  1. (6.31 - 2.42) × 1.75 - 0.25 =

    A. 26.504175
    B. 0.7125
    C. 0.55
    D. 22.932215
    E. 0.825

Answer and Explanation

  1. The correct answer is B. You must tackle what’s in the parentheses first. Within the parentheses, first calculate the exponent, then subtract from 6.31. Multiple the result by 1.75 and then subtract 0.25. Do the steps in the wrong order and you could end up with one of the other answer choices!
     


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