MathBasics

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Author:
dsouthgate
ID:
63716
Filename:
MathBasics
Updated:
2011-02-02 20:39:29
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Math basics algebra
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Description:
Algebra basics for precalc study
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  1. What is the set of natural or counting numbers?
    [1, 2, 3 ...] Notice that the set of natural numbers doesn't include 0.
  2. What is the set of whole number?
    (0, 1, 2, 3...) The set of whole numbers does include the number 0.
  3. What is the set of integers?
    [... -3, -2, -1, 0, 1, 2, 3 ...] The set of integers includes positives, negatives and 0. It's like dealing with money: THis of positives as having it and negatives as owing, an important point when operating on numbers.
  4. What is the set of rational numbers?
    Numbers that can be expressed as a fraction where the numberator and the denomintor are both integers.
  5. What kind of number is this?
    1/2, -1/7, 0.23?
    They are all examples of integers.
  6. What is the key to adding or subtracting fractions?
    • 1. You must find a common denominator.
    • 2. And the roots must be like terms in order to add or subtract them.
  7. What is the set of irrational numbers?
    • 1. Rational numbers cannot be expressed as fractions.
    • Examples or irrational numbers are:
    • √2,
    • √21
    • π
  8. What is the set of all real numbers?
    • A natural number
    • A whole number
    • An interger
    • A rational number
    • An irrational number
  9. What numbers are not real?
    • Examples:
    • 4/0 (a fraction with the denominator of 0)
    • √-2 (a square root of a negative number)
    • ∞ (infinity)
  10. What is the set of imaginary numbers?
    • These are numbers which are square roots of negative numbers.
    • They have an imaginary unit, such as:
    • i
    • 4i
    • -2i
    • DEFINED AS i=√-1
  11. What is the set of complex numbers?
    • These are numbers that are the sum and difference of a real number and an imaginary number.
    • examples:
    • 3 + 2i,
    • 2 - √2i
    • 4 - 2/3i
  12. Why is the set of numbers that is the most complete set of numbers in the math vocabulary?
    The set of complex numbers is the most complete set, because it includes real numbers, imaginary numbers, and any combination of the two.
  13. In what or should fundamental operations be performed?
    • Parenthese (and other grouping device)
    • Exponents
    • Multiplication and Division (whichever is first, from LEFT to RIGHT)
    • Addition and subtraction (whichever is first, from LEFT to RIGHT)
  14. What is the mnemoic device used to remember the order of the fundamental operations you can perform on numbers?
    • PEMDAS
    • Parenthese
    • Exponents 2^2
    • Multiplication and Division
    • Addition and Subtraction
  15. What is the Reflexive Property of numbers?
    • a = a
    • for example: 10 = 10
  16. What is the Symmetric Property of numbers?
    • If a = b, then b = a
    • for example: if 5 + 3 = 8, then 8 = 5 + 3
  17. What is the Transitive Property of numbers?
    • If a = b and b = c, then a = c
    • for example, if 5 + 3 = 8 and 8 = 4 * 2,
    • then 5 + 3 = 4 * 2
  18. What is the Commutative Property of Addition?
    • a + b = b + a
    • for example 2 + 3 = 3 + 2
  19. What is the Commutative Property of Multiplication?
    • a * b = b * a
    • for example: 2 * 3 = 3 * 2
  20. What is the Associative Property of Addition?
    • (a + b) + c = a + (b + c)
    • for example:
    • (2 + 3) + 4 = 2 + (3 + 4)
  21. What is the Associative Property of Multiplication?
    • (a * b) * c = a * (b * c)
    • for example:
    • (2 * 3) * 4 = 2 * (3 * 4)
  22. What is Additive Identity (as the property of numbers)?
    • a + 0 = a
    • for example 0 + -3 = -3
  23. What is the Multiplicative Identity (of properties of numbers)?
    • a * 1 = a
    • for example: 4 * 1 = 4
  24. What is the Additive Inverse Property of numbers?
    • a + (-a) = 0
    • example:
    • 4 + (-4) = 0
  25. What is the Multiplicative Inverse Property of numbers?
    • a * (1/a) = 1
    • for example:
    • 2 * (1/2) = 1
  26. What is the Distributive Property of numbers?
    • a(b + c) = a * b + a * c
    • for example:
    • 10(2 + 3) = 10 * 2 + 10 * 3 = 50
  27. What is the Multiplicative Property of Zero?
    • a * 0 = 0
    • for example:
    • 5 * 0 = 0
  28. What is the Zero Product Property of numbers?
    • If a * b = 0, a = 0 or b = 0
    • for example:
    • if x(x + 2) = 0, then x = 0 or x + 2 = 0

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