# At a Glance - Parentheses

When evaluating algebraic expressions, we evaluate things inside parentheses first. Think of the parentheses as two bananas that are quickly ripening, and you need to down them before they turn brown and go bad. You can think of them as apples, too, but they look much more like bananas. When translating from English into math, we need to be careful to put parentheses in the correct places. If anyone else ever tells you they know where you can put your parentheses, they're probably being rude.

If an English phrase says to perform first one operation and then another, we can put parentheses around the operation that's performed first. We need to take care of our browning bananas, you see.

### Sample Problems

If we triple a number and then add eight, we get (3x) + 8.

This is an example of a situation where we can get away with ditching the parentheses, since multiplication is performed before addition anyway. The answer 3x + 8 is also fine. The parentheses just make it look so much more official.

If we add eight to a number and then triple it, we get 3(x + 8).

Here we do need the parentheses, or we would get 3x + 8 again, which is different from 3(x + 8).

Often, a problem won't come right out and say "first you do this, then you do this other thing.'' Some of them are quite shy and will be tight-lipped even when you plead with them to tell you. Therefore, we need to reason out for ourselves which operation is performed first. Thanks a lot, problem. Some help you are.

#### Example 1

 How do we translate the following phrase into a mathematical expression?"Quadruple the sum of eleven and a number."

#### Example 2

 How do we translate the following phrase into a mathematical expression?"Four together with one-fifth of x."

#### Example 3

 How do we translate the following phrase into a mathematical expression?"Three times the sum of four and the quotient of x and two."

#### Example 4

 How do we translate the following phrase into a mathematical expression?"The triple of the double of the difference of 5 and 3."