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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
Companion Exercises Practice Problems


G Redden

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