MATHEMATICS 7

• Set


  A well-defined selection of objects
• Element


  An object/s in a set
• Ellipses


  '...' used to make writing down elements shorter
• Cardinality


  The number of elements a set contains
• Cardinality notation


  Can be written as 'n ()' or |_| = number
• Intersection of sets


  Written as 'A ∩ B = {_}', the set of elements that are in both sets A & B
• Union of sets


  Written as 'A U B = {_}', the set of elements that are in both A & B
• Difference of sets


  The difference between Set A & B is written as 'A - B', the set of elements in A that are not in B & vice versa
• Complement of a set


  Written as " A' " (said as 'A prime'), the set of elements in the universal set that are not in A
• 'OR'


  Means union
• 'AND'


  Means intersection
• 'ONLY'


  Means found in a set but not in any intersection
• Subsets of Real Numbers


  • Z = { …-3, -2, -1… 0, +1, +2, +3… } / integers
  • W = {0, 1, 2, 3, 4, 5, 6, 7, 8…} / whole numbers
  • N = {1, 2, 3, 4, 5…} / Counting/Natural numbers
• Real numbers


  Contain rational and irrational numbers
• Imaginary numbers


  The square roots of negative numbers
• Rational numbers (Q)


  Are fractions, decimals, & integers. Fractions with 0 as the denominator are not allowed. Have repeating digits.
• Irrational numbers (Q' or 'Q prime')


  Numbers that are not rational, such as non-repeating decimals like pi.
• Whole numbers (W)


  Are counting numbers, but includes 0
• Natural/Counting numbers (N)


  From 1 & above
• Integers (Z)


  Includes whole & counting/natural numbers
• Addition of integers


  Add as is. If they're different symbols, subtract & give the final answer the larger number's symbol
• Subtraction of integers


  Keep, Change, Change (KCC)
• Multiplication & Division of integers


  Multiply/divide as is. Same sign: Positive. Different sign: Negative
• Commutative Property of Addition (CPA)


  Change of order in addition DOES NOT AFFECT THE SUM
• Commutative Property of Multiplication (CPM)


  Change of order in multiplication DOES NOT CHANGE THE PRODUCT
• There is no commutative property for division & subtraction
• Associative Property of Addition (APA)


  Change in grouping DOES NOT AFFECT THE SUM. Different groups do not mean a different sum when adding.
• Associative Property of Multiplication (APM)

  Change of grouping when multiplying DOES NOT CHANGE THE PRODUCT
• Identity Property of Addition (IdPA)

  Adding 0 to a number does not affect the value AT ALL. Applies to fractions, decimals, integers, or any real number.
• Identity Property of Multiplication (IdPM)


  Multiplying 1 to any real number DOES NOT CHANGE THE PRODUCT. Multiplying a real number by 1 is always equal to its original product.
• Inverse Property of Addition (InvPA)


  When adding the same numbers with different symbols (negative and positive) they will result to 0.
• Inverse Property of Multiplication (InvPM)


  Multiplying any real number to its reciprocal (switching the numerator and denominator) will result to 1.
• Zero Property of Multiplication (ZPM)


  Any number multiplied by 0 equals to 0
• There is no Zero Property of Addition (ZPA)
• Distributing Property of Multiplication over Addition (DPMA)


  Multiplying any real number to a sum of numbers is the same as multiplying the real number to each of the addends.
• Measurement


  Obtaining quantitative information
• Types of measurement systems

  • Nonstandard - using body parts to measure
  • English/Imperial - has set values for each of its units and is still used in the US
  • Metric or the International System of Measurement (SI) - its units are found through the power of 10
• Metric Conversion Line


  Kilo, Hecta, Deck, Unit, Deci, Centi, Milli
• Units


  Could be either meters, grams, or liters
• Metric conversion


  From the unit point, you move the decimal point depending on which unit you'll be converting your measurements to. To the Left; Kilo: ÷ 1000, Hekto: ÷100, Deka: ÷10. To the Right; Deci: x10, Centi: x100, Mili: x1000