Parentheses Examples

How do we translate the following phrase into a mathematical expression?

"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.

How do we translate the following phrase into a mathematical expression?

"Four together with one-fifth of x."

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

How do we translate the following phrase into a mathematical expression?

"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.

How do we translate the following phrase into a mathematical expression?

"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...