Math Study Cards

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Author:
relkins
ID:
301593
Filename:
Math Study Cards
Updated:
2015-04-26 21:18:17
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Math
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Math
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  1. Natural or Counting Numbers
    1, 2, 3, 4...
  2. Whole Numbers
    0, 1, 2, 3,4...
  3. Integers
    -2, -1, 0, 1, 2, 3...
  4. Rational Numbers
    • Fractions
    • Real numbers can be written as fractions:
    • 5 = 5/1
    • Thus all integers are rational numbers
    • Terminating (.5) and repeating numbers (.333) decimals are rational numbers as they can be written as fractions
  5. Irrational Numbers
    • They cannot be written as a fraction
    • i.e. Pi or the square root of 3
  6. Properties (axioms) of addition
    • Closure
    • Commutative
    • Associative
    • Identity Element
    • Additive Inverse
  7. Closure
    Is when all answers fall into the original set:

    (2 + 4 = 6) the set of even numbers is closed

    (3 + 5 = 8) two odds equal even, thus it is open
  8. Commutative
    Means that the order does not make any difference:

    a + b = b + a

    Does not hold for subtraction
  9. Associate
    Means that the grouping does not make any difference:

    (a + b) + c = a + (b + c)

    Does not apply to subtraction
  10. Identity Element
    Any number added to zero equals the original number:

    a + 0 = a
  11. Additive Inverse
    Is the opposite (negative) of the number

    3 and -3
  12. Properties (axioms) of multiplication
    • Closure
    • Commutative
    • Associative
    • Identity Element
    • Multiplicative Inverse
    • Distributive Property
  13. Closure
    Is when all answers fall into the original set:

    2 x 4 = 8 (closed)

    3 x 5 = 15 (closed)
  14. Commutative
    Means that the order does not matter:

    a x b = b x a
  15. Associative
    Means that the grouping does not make any difference:

    (a x b) x c = a x (b x c)

    Does not hold for division
  16. Identity Element
    For multiplication is 1. Any number multiplied by 1 gives the original number.

    a x 1 = a
  17. Multiplicative Inverse
    Is the reciprocal of the number. Any number multiplied by its reciprocal equals 1.

    a x 1/a = 1; a and 1/a are multiplicative inverses or reciprocals (provide that a does not equal zero)
  18. A Property of Two Operations: Distributive Property
    Is the process of distributing the number on the outside of the parentheses to each term on the inside: a(b + c) = a(b) + a(c)

    Note: You cannot use the distributive property with only one operation: a(bcd) does not equal a(b) x a(c) x a(d)

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