Easy Algebra Step-by-Step

8 Easy Algebra Step-by-Step

Problem Graph the real numbers − 42 − 5

3

4

,. 2 3 ,

4

, 0 3 eand 3.6.

Solution

Step 1. Draw a number line.

–4 –3 –2 –1 0 1 2 3 4

Step 2. Mark a large dot at each of the points corresponding to − 4 , − 25 ., 0,

3

4

, 3 , e, and 3.6. (Use 31. 73 and e≈ 27. 1 .)

–4 –3 –2 –1 1 2 3 4

3 e 3.

3

–4 –2.5 0 4

0

Properties of the Real Numbers

For much of algebra, you work with the set of real numbers along with the

binary operations of addition and multiplication. A binary operation is one

that you do on only two numbers at a time. Addi-

tion is indicated by the + sign. You can indicate

multiplication a number of ways: For any two real

numbers a and b, you can show a times b as a · b,

ab, a(b), (a)b, or (a)(b).

The set of real numbers has the following 11

fi eld properties for all real numbers a, b, and c under the operations of addi-

tion and multiplication.

1. Closure Property of Addition. (a + b) is a real number. This property
   guarantees that the sum of any two real numbers is always a real number.
   Examples
   (4 + 5) is a real number.
   1
   2

⎝⎝⎛⎛⎛⎝⎛⎛⎛⎛⎛⎛ + ⎠⎠⎞⎞⎞⎞⎞⎠⎞⎞⎞⎞

3

4

is a real number.

(0.54 + 6.1) is a real number.

() is a real number.

2. Closure Property of Multiplication. (a · b) is a real number. This property
   guarantees that the product of any two real numbers is always a real
   number.

Generally, in algebra, you do not

use the times symbol × to indicate

multiplication. This symbol is used

when doing arithmetic.