Order Of Operations

Let's start this off with one that I see cause many debates on Facebook no matter how many different problems I have seen put up for people to answer. Here is the proper way to think about any arithmetic problem whether variables are involved or not.

1. Work all parenthesis or other grouping symbols before proceeding with any other operations. A grouping symbol can be a set of braces {}, brackets [], parenthesis (), the radical sign √, or the division bar also known as the fraction bar (expression)/(expression). Sometimes, there will be grouping symbols inside another set of grouping symbols. Always work from the inside out in this case.

2. Compute all exponents including roots or radicals from left to right.

3. Perform all multiplication and division from left to right. This is a single step. You do not do all multiplication followed by all division.

4. Perform all addition and subtraction from left to right. As above, this is a single step.

Now, let's see how this works with a typical Facebook problem. Consider the following expression: 12 + 6 × 5 - 3 × 4. This would become 12 + 30 - 12 = 42 - 12 = 30.

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