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

A. Imaginary.Even though 9 is a perfect square, so you can write the number as and then simplify it to read or , this number stays imaginary.

1 Identify which of the following numbers are natural numbers:

2 Identify which of the following numbers are integers:

3 Identify which of the following numbers are rational numbers:

4 Identify which of the following numbers are irrational numbers:

5 Identify which of the following numbers are prime numbers:

6 Identify which of the following numbers are imaginary numbers:

A number line is labeled with numbers that increase as you move from left to right. And numbers are listed with an equal amount or value between any two consecutive numbers.

Numbers are placed on a number line to give you a visual picture of how they compare, how far apart they are, and what is missing between them. The two number lines shown here are examples of some versions that are possible. In Figure 1-1, you see the half-way mark indicated between units. And in Figure 1-2, the negative and positive integers are shown, with 0 in the middle.

FIGURE 1-1:A number line from 0 to 5 with half-unit increments.

FIGURE 1-2:A number line from –10 to 10 with one-unit increments.

Q.Place the numbers on a number line.

A.

Note that the marks representing these numbers on the number line are marked with dots or points. The points for the fraction and decimal numbers are approximated, because the tickmarks for these numbers aren’t on the number line to make them exact.

7 Place the following numbers on the number line:

8 Place the following numbers on the number line:

Algebra and symbols in algebra are like a foreign language. They all mean something and can be translated back and forth as needed. It’s important to know the vocabulary in a foreign language; it’s just as important in algebra.

The words used in algebra are very informative. You need to know their exact meaning, because they convey what is happening.

An expression is any combination of values and operations that can be used to show how things belong together and compare to one another. is an example of an expression. Think of an expression as being the equivalent of a phrase or part of a sentence; you have some subjects and conjugates, but no verbs. You see how items are distributed over expressions in Chapter 9.

A term, such as 4 xy , is a grouping together of one or more factors (variables and/or numbers) all connected by multiplication or division. In this case, multiplication is the only thing connecting the number with the variables. Addition and subtraction, on the other hand, separate terms from one another. For example, the expression has three terms.

An equation uses a sign to show a relationship — that two things are equal. By using an equation, tough problems can be reduced to easier problems and simpler answers. An example of an equation is . See Chapters 14through 18for more information on equations.

An operation is an action performed upon one or two numbers to produce a resulting number. Operations include addition, subtraction, multiplication, division, square roots, and so on. See Chapter 7for more on operations.

A variable is a letter representing some unknown; a variable always represents a number, but it varies until it’s written in an equation or inequality. (An inequality is a comparison of two values. For more on inequalities, turn to Chapter 19.) Then the fate of the variable is set — it can be solved for, and its value becomes the solution of the equation. By convention, mathematicians usually assign letters at the end of the alphabet to be variables to be solved for in a problem (such as x , y , and z ).

A constant is a value or number that never changes in an equation — it’s constantly the same. The number 5 is a constant because it is what it is. A letter can represent a constant if it is assigned a definite value. Usually, a letter representing a constant is one of the first letters in the alphabet. In the equation , c is a constant and x is the variable.