Order of Operations

Fundamentals of Social Statistics by Adam J. McKee

When you’re solving a math problem, it’s like following a recipe. If you add ingredients in the wrong order or skip a step, the dish might not turn out right. In the same way, math has its own recipe, called the “order of operations.” This order ensures you get the correct answer every time. Let’s dive deeper into these rules and offer some tips to remember them better.

Rule One: Prioritize Parentheses

Whenever you see parentheses, they’re like a flashing neon sign saying, “Start here!” Anything inside these curved brackets should be your top priority.

Tip: Picture parentheses as a fence, keeping certain numbers and operations contained. You must address what’s inside the fence before dealing with anything outside of it.

If you encounter parentheses within parentheses, known as “nested parentheses,” don’t panic. Just remember to start from the innermost set and work your way out.

Tip: Imagine these nested parentheses like opening a set of Russian nesting dolls. Start with the smallest doll in the center and work your way out to the larger dolls.

Rule Two: Examine Exponents and Roots

Once you’ve taken care of the parentheses, it’s time to tackle any exponents (numbers that indicate how many times a number should be multiplied by itself) and roots (which find the original number from a number’s power).

Tip: Think of exponents like climbing a ladder — each step multiplies the number. Roots, on the other hand, are like descending the ladder. Always start with the leftmost exponent or root and make your way to the right.

Rule Three: Master Multiplication and Division

Now, onto multiplication and division. These two are partners in the order of operations, and you must address them from left to right. If you have both in a single problem, don’t always multiply before dividing. Instead, handle them in the order they appear.

Tip: Imagine a seesaw, with multiplication on one side and division on the other. Whichever operation you encounter first, that’s the side of the seesaw you start with.

Rule Four: Address Addition and Subtraction

Lastly, we come to addition and subtraction. Similar to their multiplication and division counterparts, you’ll handle these operations from left to right.

Tip: Think of addition and subtraction like reading a book. You start from the leftmost operation and move to the right, just like reading from the beginning to the end of a sentence.

A Helpful Mnemonic: PEMDAS

A popular way to remember the order of operations is the acronym PEMDAS, which stands for:

  • Parentheses
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction

Tip: People often use the phrase “Please Excuse My Dear Aunt Sally” as a fun mnemonic device. Each word in this sentence starts with the letter corresponding to a step in the order of operations.

By following and remembering these rules, math problems become much more approachable. Remember, math is like a puzzle — and the order of operations is your guide to placing each piece in the right spot.

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Last Modified:  08/18/2023

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