A. Subsets of Real Numbers
whole numbers - positive numbers beginning with zero such as 0, 1, 2, 3, 4, . . .
integers - positive and negative whole numbers such as . . . -3, -2, -1, 0, 1, 2, 3, . . .
rational numbers - numbers when written as decimals either terminate OR repeat such as ¾, ½, 1/3, 2/3
irrational numbers - numbers when written as decimals do not terminate AND do not repeat such as 2, p
C. Properties of Addition and Multiplication where a, b, c are Real Numbers
zero - the origin of the number line
graphing or plotting - drawing the point
coordinate - the number corresponding to a point
opposites - numbers that are the same distance from zero, but on opposite sides of zero such as -5 and 5 OR ¾ and -¾.
reciprocal - to reciprocate a fraction, exchange the numerator and denominator and any number multiplied by its reciprocal is equal to 1.
D. The Four Basic Operations
||a + b is a real #
||a·b is a real #
||a + b = b + a
||a·b = b·a
||(a+b)+c = a+(b+c)
||(ab)c = a(bc)
||a + 0 = a and 0 + a = a
||a·1 = a and 1·a = a
||a + (-a) = 0
||a·(1/a) =1, a¹0
||a(b + c) = ab + ac
- sum - means to add
- difference - means to subtract
- product - means to multiply
- quotient - means to divide