College Algebra & Trigonometry Asian College of Aeronautics AVT 1

NUMBERS & THIER PROPERTIES REAL NUMBERS Are numbers that are either rational or irrational. RATIONAL NUMBERS Are numbers that can be represented as a quotient of two integers a and b where b is not equal 0. IRRATIONAL NUMBERS Are numbers that can not be represented as a quotient of two numbers. Its decimal expression of these numbers do not repeat themselves. INTEGERS Are rational numbers which is composed of whole numbers and the set of negatives of the natural numbers. NON - INTEGERS Are numbers that do not belong to the set of integers such as: fraction, decimal and percent. The decimal expression are terminating and repeating. NATURAL NUMBERS Also known as counting numbers. Composed of numbers beginning from 1. WHOLE NUMBERS Are numbers beginning with 0. It combines 0 and natural numbers.

PROPERTIES OF REAL NUMBERS CLOSURE The sum and product of any two real numbers are also real numbers. COMMUTATIVE The order of the addends or factors does not affect the result. 2+3 =3+2 p*q=q*p ASSOCIATIVE When you add or apply any three real numbers, the grouping or association does not affect the result. (a+b)+c = a+(b+c) (p*q)*r = p*(q*r) IDENTITY For addition, a + 0 = a and 0 + a = a. For multiplication, a * 1 = a and 1* a = a. INVERSE For addition, a + (-a) = 0. For multiplication, a * (1/a) = 1. DISTRIBUTIVE a (b + c) = ab + ac.

OPERATIONS ON SIGNED NUMBERS ADDIION To add numbers having like signs, add their absolute values and prefix their common sign. To add numbers having unlike signs, subtract the smaller absolute value from the greater absolute value and prefix to the difference, the sign of the number having the greater absolute value. SUBTRACTION To subtract one number from another, change the sign of the number to be subtracted and proceed to addition. MULTIPLICATION / DIVISION The product / quotient of two numbers having the same signs is positive. The product / quotient of two numbers having different signs is negative. ORDER OF OPERATIONS PEMDAS – Parentheses and Exponents, Multiplication and Division, Addition and Subtraction