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Arithmetic

  1. A prime number is an integer that is divisible only by itself and 1.
  2. An even number is divisible by 2, and can be written as 2x.
  3. An odd number is not divisible by 2, and can be written as 2x + 1.
  4. Division by zero is undefined.
  5. Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81 . . .
  6. Perfect cubes: 1, 8, 27, 64, 125 . . .
  7. If the last digit of a integer is 0, 2, 4, 6, or 8, then it is divisible by 2.
  8. An integer is divisible by 3 if the sum of its digits is divisible by 3.
  9. If the last digit of a integer is 0 or 5, then it is divisible by 5.
  10. Miscellaneous Properties of Positive and Negative Numbers:
     
    • The product (quotient) of positive numbers is positive.
    • The product (quotient) of a positive number and a negative number is negative.
    • The product (quotient) of an even number of negative numbers is positive.
    • The product (quotient) of an odd number of negative numbers is negative.
    • The sum of negative numbers is negative.
    • A number raised to an even exponent is greater than or equal to zero.
       
       

      even × even = even

      odd × odd = odd

      even × odd = even

      even + even = even

      odd + odd = even

      even + odd = odd

  11. Consecutive integers are written as x, x + 1, x + 2, . . .
  12. Consecutive even or odd integers are written as x, x + 2, x + 4, . . .
  13. The integer zero is neither positive nor negative, but it is even: 0 = 2 × 0.
  14. Commutative property: x + y = y + x. Example: 5 + 4 = 4 + 5.
  15. Associative property: (x + y) + z = x + (y + z). Example: (1 + 2) + 3 = 1 + (2 + 3).
  16. Order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
  17. − xy = -xy = x-y Example: − 23 = -23 = 2-3
  18. 3313% = 13
    6623% = 23
    25% = 14
    50% = 12
    20% = 15
    40% = 25
    60% = 35
    80% = 45
  19. 1100 = .01
    150 = .02
    125 = .04
    120 = .05
    110 = .1
    12 = .5
    14 = .25
    13 = .333…….
    25 = .4
    12 = .5
    23 = .666….
    34 = .75
  20. Common measurements:

     

    1 foot = 12 inches

    1 yard = 3 feet

    1 mile = 5,280 feet

    1 quart = 2 pints

    1 gallon = 4 quarts

    1 pound = 16 ounces

    1 ton = 2,000 pounds

    1 year = 365 days

    1 year = 52 weeks

  21. Important approximations: 2 ≈ 1.4 3 ≈ 1.7 π ≈ 3.14
  22. "The remainder is r when p is divided by q" means p = qz + r; the integer z is called the quotient. For instance, "The remainder is 1 when 7 is divided by 3" means 7 = 3 × 2 + 1.
  23. Probability=number of outcomestotal number of possible outcomes




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