Unit 2: Real Numbers

Resource: Unit 2 Real Numbers


1. Equal, Less than or Greater than sign
  • > Greater than 
    • 5 > -12
    • n > 20 where n is a prime number. 
      • Then n = 23, 29, 31, 37, 41, etc...
  • ≥ Greater than or equal
    • n ≥ -1 where n is an integer. It means include -1 if it satisfies the given condition
      • Then n = -1 (i.e. including the number), 0, 1, 2, 3, 4....
  • < Less than
    • 20 < 23
    • n < 20 where n is a  natural number
      • Then n = 1, 4, 9, 16
  • ≤ Less than or equal
    • n ≤ 25 where n is a multiple of 3. It means include 25 if it satisfies teh given condition.
      • Then n = 24, 21, 18, 15, 12, 9, 3, 0, -3, -6, ...




Watch the following clip for a Preview of what we will be doing in the next few lessons.




1. Number Lines




2. Real Numbers



3. Operations of Numbers
Integers - Zero Pairs (Basic Concept)

The sum of an integer and its opposite is ZERO
  • E.g. 1: - 20 + 20 = 0
  • E.g. 2: 56 + (-56) = 0
  • E.g. 3: -28 + 28 = 0

Integers - Addition of Integers (Basic Concepts)
Evaluate - 3 + (-2)

RuleTo add two negative numbers, add their absolute values and take the negative sign for the answer
  • E.g. 1: -25 + (-17) = -42
  • E.g. 2: -21 + (-21) = -42
  • E.g. 3: -18 + (-11) = -29
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Evaluate 3 + (-7)



Rule: To add 2 integers of different signs such that the negative integer has a larger absolute value, we find the difference between their absolute value and take the negative sign for the answer.
  • E.g. 1: -17 + 12 = -5
  • E.g. 2: 52 + (-67) = -15
  • E.g. 3: -88 + 85 = -3
  • E.g. 4: 28 + (-82) = -54
Rule: To add 2 integers of different signs such that the positive integer has a larger absolute value, we find the difference between their absolute value and take the positive sign for the answer.
  • E.g. 1: -12 + 17 = 5
  • E.g. 2: -63 + 68 = 5
  • E.g. 3: 86 + (-53) = 33
  • E.g. 4: -38 + 83 = 45



Using Number Line to Explain...
(A) Adding and Subtracting Negative Numbers


(B) Adding Negative Numbers:
Find: -45 + (-46) + (-29)


(C) Adding Integers of Different Signs
Find: 15 + (-46) + 29



4. Properties of Operations

Commutative & Associative Properties



Commutative Property of Multiplication






5. Recurring Decimals
Converting Repeating Decimals (Recurring Number) to Fraction







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