We use parentheses. A lot!.

We use parentheses so much, that we use them when we aren’t using them.

We use parentheses so much, that we use them by not using them.

Sometimes we use parentheses with arithmetic and there are arithmetic rules available.

Sometimes we use parentheses and there is no arithmetic implied.

It can be confusing.

There is more to using parentheses than just using parentheses.

Boundaries

Parentheses are mathematical fences. They identify designated areas, that each keep to themselves.

• You think inside the parentheses.
• You think outside the parentheses.

The inside and the outside do not interact.

We have two exceptions to this rule, function notation and the distributive property.

Distributive Property

If the inside is a sum or a difference and there is a number immediately to the left of the left parenthesis, then we have an arithmetic option.

The distributive property tells us that multiplication distributes over addition. You can distribute the factor across the addition.

Function Notation

If there is a function name immediately to the left of the left parenthesis, then the parentheses are surrounding a domain number.

The function name and the parentheses are actually one symbol, not two.

You cannot distribute function evaluation. You can distribute number multiplication.

The following two examples will illustrate how confusing it can be to react to written symbols without taking into account the context.

It isn’t just the symbols. It is how they are being used.

If you are just reacting to written symbols regardless of what they represent, then you are heading down a frustrating road.