Easy Algebra Step-by-Step

4 Easy Algebra Step-by-Step

Step 2. The number that is 4 units to the right of 0 is 4. Therefore, 4 is the

opposite of − 4.

Problem Graph the integers −5, −2, 3, and 7.

Solution

Step 1. Draw a number line.

–8 –7 –6 –5 –4 –3 –2 –1 041 2 3 5 678

Step 2. Mark a large dot at each of the points corresponding to −5, −2, 3,

and 7.

–8 –7 –6 –5 –4 –3 –2 –1 041 2 3 5 678

Rational, Irrational, and Real Numbers

You can add, subtract, or multiply any two integers, and your result will

always be an integer, but the quotient of two integers is not always an inte-

ger. For instance, 622 = 3 is an integer, but 141

4

4 = is not an integer. The

number^1

4

is an example of a rational number.

A rational number is a number that can be expressed as a quotient of an

integer divided by an integer other than 0. That is,

the set of rational numbers (usually denoted Q) is

Q =

p

q

, wherepqpand are integers,q≠

⎧

⎨

⎧⎧

⎩

⎨⎨

⎫

⎬

⎫⎫

⎭

(^0) ⎬⎬
Fractions, decimals, and percents are ratio-
nal numbers. All of the natural numbers, whole
numbers, and integers are rational numbers as well because each number n
contained in one of these sets can be written as
n
1
, as shown here.

...,,,−= ,,,,,...

−

−=

−

−=

−

3 ==== =

3

1

2

2

1

1

1

1

0

0

1

1

1

1

2

2

1

3

3

1

The decimal representations of rational numbers terminate or repeat. For

instance,

1

4

= 02. 5 is a rational number whose decimal representation termi-

The number 0 is excluded as a

denominator for pq because division

by 0 is undefi ned, so p 0 has no

meaning, no matter what number

you put in the place of p.