Order of Operations: Groups > Parentheses

Students usually know to do what is in the “parentheses” first. And yet, there are many nuances to consider. So, let’s propose we use the word “Groups” rather than “Parentheses” so that we can make things easier (on all of us) to learn the rules.

Why Groups?

The reason is simple: parentheses is too limiting of a term. A set of parentheses, brackets, braces or fraction lines can all represent groups. These groups indicate which operations need to be given priority attention before other operations in a problem. When using the term groups, students will know to look for each type of group first as a top priority. Let’s explain how this can be useful when dealing with fractions.

Numerator and denominators represent their own groups. This means you can simplify the numerator before simplifying the denominator and vice versa. When the numerator or denominator has an addition or subtraction operator, that numerator or denominator should be treated as a group because it now has limitations. Simplifying that numerator or denominator can be treated as a priority before simplifying or solving for the rest of the problem.

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