Math 2 - College Algebra

Real Numbers

• is a value that represents a quantity along a continuous line. Includes all the rational numbers, such as the integer -5 and the fraction ⁴⁄₃, and all the irrational numbers, such as √ 2  (1.414214), and π (3.14159265).

Rational Numbers

• is any number that can be expressed as the quotient or fraction of two integers, with the denominator not equal to zero (0).

Example:

Integers = -3, -2, -1, 0, 1, 2, 3, ...

Whole Numbers = 0, 1, 2, 3, 4, 5, ...

Natural/Counting Numbers = 1, 2, 3, 4, 5, 6, ...

Terminating Numbers = ⁵⁄₄, 1.25, ¾, 0.75, ...

Non-terminating Numbers = ¹⁄₁₆, ⁴⁄₃

Irrattional Number

• the decimal expansion of an irrational numbers continuous without repeating. Irrational numbers is any real numbers that cannot be expressed as a ratio of integers.
• cannot be represented as a simple fraction.
• are those real numbers that cannot be represented as terminating or repeating decimals.

Example:

√ 2  = 1.414214

√ 3  = 1.7320508

π      = 3.141592654

ADDITION OF REAL NUMBERS
Note: if same sign do addition and copy the sign, otherwise do subtraction and copy the sign of highest number.

  23
+ 49
  72
  -42
+ -68
 -110

SUBTRACTION OF REAL NUMBERS
Note: always change the signs of the subtrahend and do the addition process.

  23
- 49
 -26
  -42
- -68
   26

ORDER OF OPERATIONS - PEMDAS
P - parenthesis
E - exponent
M - multiplication
D - division
A - addition
S - subtraction

Example: 7 + (6 x 5² + 3)

                    = Start with parentheses
   7 + (6 x 25 + 3) = Then multiplication
   7 + (150 + 3)    = Then add
   7 + (153)        = Parentheses completed
   7 + 153          = Last operation is add.
   160              Done.