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7 Write the description using math notation:
8 Write the description using math notation:
9 Write the description using math notation:
10 Write the description using math notation:
Zeroing in on Zero
But what about 0? I keep comparing numbers to see how far they are from 0. Is 0 positive or negative? The answer is that it’s neither. Zero has the unique distinction of being neither positive nor negative. Zero separates the positive numbers from the negative ones — what a job! When using the number line to determine the order of numbers — which one is larger — you look at how far the number is from 0. You already know that a positive number is going to be larger than a negative number, but comparing two negative numbers can be a bit more challenging. You put the two negative numbers on the number line. The negative number that’s farthest from 0 is the smaller of the two numbers.
A. –3. Look at the following number line. You see that –3 is to the right of –13. In terms of distance from 0, –13 is much farther away, so it is smaller than –3.
11
12 Which has the greater value, –13 or –1?
13 Which is bigger, –0.003 or –0.03?
14 Which is larger,
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
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
Getting it absolutely right with absolute value
The absolute value operation, indicated by two vertical bars around a number,
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
