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 is 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 (3*x*) + 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 3*x* + 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 3*x* + 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.

## Parentheses Practice:

Quadruple the sum of eleven and a number. | |

4(11 + *x*) We can infer from the problem that 11 and *x* must be added first, since we need to find their sum before we can quadruple it. That's called putting the horse before the cart, because when you put the cart before the horse, it's easy for all of your groceries to spill out. | |

Four together with one-fifth of *x*. | |

In order to add 4 and , we must find first. We don't need to write more parentheses, since multiplication is performed before addition. Oh, good. Our parenthesis finger was getting tired. | |

Three times the sum of four and the quotient of *x* and two. | |

Here we have three operations. That would be a busy day for a brain surgeon. "The quotient of...'' must be the first thing we do, since the quotient is needed for the sum. Multiplying the sum by three is the last operation performed. | |

The triple of the double of the difference of 5 and 3. | |

3(2(5-3)) Wow, what a horribly worded sentence. However, you need to be able to know how to read, understand and solve something like this, no matter how much it may make the English-lover in you cringe. And you thought Faulkner took liberties with language. The nested parentheses show the order in which the operations are performed: first we find a difference (green bananas), then we double it (yellow bananas), then we triple it (yellowish-brownish bananas). Better hurry, they're fading fast... | |