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

Two other signs related to the greater-than and less-than signs are the greater-than-or-equal-to sign (≥) and the less-than-or-equal-to sign (≤).

So, putting the numbers 6, –2, –18, 3, 16, and –11 in order from smallest to largest gives you –18, –11, –2, 3, 6, and 16, which are shown as dots on a number line in Figure 2-3.

FIGURE 2-3:Positive and negative numbers on a number line.

Q.Write the description using math notation: is greater than .

A. . The point of the arrow is always in the direction of the smaller of the two numbers.

Q.Write the description using math notation: is less than or equal to 0.

A. . You could also write the inequality as , which is read, “0 is greater than or equal to .”

6 Write the description using math notation: is less than 1.

7 Write the description using math notation: is greater than .

8 Write the description using math notation: is less than or equal to 11.

9 Write the description using math notation: is greater than or equal to .

10 Write the description using math notation: is greater than or equal to .

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.

Q.Which number is larger, –3 or –13?

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 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

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.

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.

Bi means two. A bi cycle has two wheels. A bi gamist has two spouses. A bi nary 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.

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 6for 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!