Algebra II Recipe: Real Numbers and Number Operations

A. Subsets of Real Numbers

1. whole numbers - positive numbers beginning with zero such as 0, 1, 2, 3, 4, . . .
2. integers - positive and negative whole numbers such as . . . -3, -2, -1, 0, 1, 2, 3, . . .
3. rational numbers - numbers when written as decimals either terminate OR repeat such as ¾, ½, 1/3, 2/3
4. irrational numbers - numbers when written as decimals do not terminate AND do not repeat such as 2, p

B. Definitions

1. zero - the origin of the number line
2. graphing or plotting - drawing the point
3. coordinate - the number corresponding to a point
4. opposites - numbers that are the same distance from zero, but on opposite sides of zero such as -5 and 5 OR ¾ and -¾.
5. reciprocal - to reciprocate a fraction, exchange the numerator and denominator and any number multiplied by its reciprocal is equal to 1.

C. Properties of Addition and Multiplication where a, b, c are Real Numbers

1.	closure	a + b is a real #	a·b is a real #
2.	commutative	a + b = b + a	a·b = b·a
3.	associative	(a+b)+c = a+(b+c)	(ab)c = a(bc)
4.	identity	a + 0 = a and 0 + a = a	a·1 = a and 1·a = a
5.	inverse	a + (-a) = 0	a·(1/a) =1, a¹0
6.	distributive	a(b + c) = ab + ac

D. The Four Basic Operations

1. sum - means to add
2. difference - means to subtract
3. product - means to multiply
4. quotient - means to divide

Practice Problems