Resource: Unit 2 Real Numbers


The Story of One
(clip inserted on 5 Feb 2017)

Having worked with the Decimal System for years, and with the introduction of the Binary System in the recent Alternative Assessment Practice, you would probably able to appreciate this documentary better now, when the "1"s and "0"s are the core actors in the documentary.

Enjoy!



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)

Rule: To 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

Integers - Subtraction (Basic Concepts)
Evaluate - 2 - 6
Note: Zero Pairs are introduced.


Evaluate - 5 - (-3)



Evaluate 5 - (-7)
Note: Zero Pairs are introduced.


Multiplication (Basic Concepts)
Draw comparison between 2 x 3 (i.e. 2 groups of positive 3)
and 2 x (-3) (i.e. 2 groups of negative 3)




2 x 3 = 6
2 x (-3) = -6

Division (Basic Concepts)
Draw comparison between 8 ÷ 2

and (-8) ÷ 2



8 ÷ 2 = 4

(-8) ÷ 2 = -4



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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