Mathematics: Order of Operations
This goal of this series is to share information on a topic that is a passion of mine: mathematics. There are so many different topics in math to learn and fascinate about. My goal is to create a series of puzzles that share these math topics, and some of their history, while also allowing you to use those skills to solve for the necessary coordinates. The goal is to provide puzzles that aren’t too difficult but can also offer a challenge.
In math, order of operations is a collection of rules that govern the order to which a problem with multiple steps is evaluated. This is done with a ranking, or precedence, of operations that are calculated in that specified order. Some operations carry equal precedence and are carried out left-to-right. The common order is as such:
- Parentheses
- Exponents (and Roots)
- Multiplication & Division
- Addition & Subtraction
There are many mnemonics to assist with performing these steps, but PEMDAS is the most used in the United States and France. Schools have even taught different sentences to remember this order such as Please Excuse My Dear Aunt Sally or Popcorn Everyday Monday Donuts Always Sunday. Other countries around the world use variations of this. The United Kingdom and its commonwealths use BOMDAS: Brackets Orders Division/Multiplication Addition/Subtraction. The “O” represents fractional multiplication and can sometimes be replaced by “I” (indices) resulting in BIMDAS. BEMDAS (Brackets Exponents Multiplication/Division Addition/Subtraction) is also common in Canada and other countries. GEMS (Groupings Exponents Multiplication/Division Subtraction/Addition) is also becoming more common as it addresses multiple variations of groupings such as parentheses, brackets, and braces.
In today’s technological world, we rely on calculators to perform those steps. Performing these operations is a lost art that most cannot perform accurately. I’ve seen countless students, parents, and others who perform these steps incorrectly. The expressions below can help you to locate this geocache, but only if performed according to the order of operations. Take your time with each step. It looks intimidating but is completely doable. If you find I made an error (totally possible), please reach out.
Please replace cache exactly as you find it for the next cacher to experience.