Algebra I All-in-One For Dummies. Mary Jane Sterling

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      11 Which is larger, –2 or –8?

      12 Which has the greater value, –13 or –1?

      13 Which is bigger, –0.003 or –0.03?

14 Which is larger, or

Going in for Operations

      Operations in algebra are nothing like operations in hospitals. Well, you get to dissect things in both, but dissecting numbers is a whole lot easier (and a lot less messy) than dissecting things in a hospital.

      Algebra is just a way of generalizing arithmetic, so the operations and rules used in arithmetic work the same for algebra. Some new operations do crop up in algebra, though, just to make things more interesting than adding, subtracting, multiplying, and dividing. I introduce three of those new operations after explaining the difference between a binary operation and a nonbinary operation.

      Sorting out types of operations

      Operations in mathematics come in all shapes and sizes. There are the basic operations that you first ran into when you started school, and then you have the operations that are special to one branch of mathematics or another. The operations are universal; they work in all languages and at all levels of math.

      Breaking into binary operations

      Bi means two. A bicycle has two wheels. A bigamist has two spouses. A binary operation involves two numbers. Addition, subtraction, multiplication, and division are all binary operations because you need two numbers to perform them. You can add , but you can’t add 3 + if there’s nothing after the plus sign. You need another number.

      Introducing nonbinary operations

      A nonbinary operation needs just one number to accomplish what it does. A nonbinary operation performs a task and spits out the answer. Square roots are nonbinary operations. You find by performing this operation on just one number (see Chapter 6 for more on square roots). Another important nonbinary operation is absolute value. It will be used in the upcoming sections, where you subtract numbers. And two other important nonbinary operations are factorial and greatest integer. It gets better and better!

      Getting it absolutely right with absolute value

      The absolute value operation, indicated by two vertical bars around a number, , is greatly related to the number line, because it tells you how far a number is from 0 without any regard to the sign of the number. The absolute value of a number is its value without a sign. The absolute value doesn’t pay any attention to whether the number is less than or greater than 0; it just determines how far it is from 0.

      The formal definition of the absolute value operation is:

      So, essentially, if a number is positive or 0, then its absolute value is exactly that number. If the number you’re evaluating is negative, then you find its opposite — or you make it a positive number.

      Getting the facts straight with factorial

      The factorial operation looks like someone took you by surprise. You indicate that you want to perform the operation by putting an exclamation point after a number. If you want 6 factorial, you write “6!”. Okay, I’ve given you the symbol, but you need to know what to do with it.

      To find the value of n!, you multiply that number by every positive integer smaller than n.

      There’s one special СКАЧАТЬ