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Rational Numbers, By - Om Mahendra Ahire - Coggle Diagram

- - - - Subtraction
        
        For any two rational numbers a and b, a - b ≠ b - a. So, Subtraction is not commutative for rational numbers
        
        Example:- 2 / 3 - 5 / 7 ≠ 5 / 7 - 2 / 3
      - Multiplication
        
        For any Two rational numbers a and b, a x b = b x a So, Multiplication is commutative for rational numbers
        
        Example:- 2 / 3 x 5 / 7 = 5 / 7 x 2 / 3 = 10 / 21
      - Addition
        
        For any Two rational numbers a and b, a + b = b + a So, Addition is commutative for rational numbers
        
        Example:- 2 / 3 + 5 / 7 = 5 / 7 + 2 / 3 = 29 / 21 or 1 8 / 21
      - Division
        
        For any Two rational numbers a and b, a / b = b / a So, Division is not commutative for rational numbers
        
        Example:- 2 / 3 ÷ 5 / 7 ≠ 5 / 7 ÷ 2 / 3
  - - - Distributivity of Addition over Multiplication
        
        For Any Three Rational Numbers a, b and c a (b + c) = ab + ac
        
        Example:- 3 / 4 x ( 2 / 3 + 5 / 6 ) = (3 / 4 x 2 / 3) + (3 / 4 x 5 / 6)
      - Distributivity of Subtraction over Multiplication
        
        For Any Three Rational Numbers a, b and c a (b - c) = ab - ac
        
        Example:- 3 / 4 x ( 2 / 3 - 5 / 6 ) = ( 3 / 4 x 2 / 3 ) - ( 3 / 4 x 5 / 6 )
  - - - Closure Property of Rational Numbers
        
        Subtraction
        
        Example: -5 / 7 - 2 / 3 = - 29 / 21
        
        For an two rational Numbers a and b, a - b is also a rational number
        
        Multiplication
        
        Example: - 2 / 3 x 4 / 5 = - 8 / 15
        
        For an two rational Numbers a and b, a x b is also a rational number
        
        Addition
        
        For an two rational Numbers a and b, a + b is also a rational number
        
        Example: - 3 / 8 + (- 5 / 7) = -19 / 56
        
        Division
        
        a ÷ 0 is not defined for rational numbers a and 0. Thus, rational numbers are not closed under division.
  - - - Addition
        
        According to the associative property of addition, the sum of three or more numbers remains the same regardless of how the numbers are grouped.
        
        Example:- ( 2 / 4 + 3 / 4 ) + 4 / 4 = 2 / 4 + ( 3 / 4 + 4 / 4 )
      - Multiplication
        
        For any three Rational Numbers a , b and c, a x (b x c) = ( a x b ) x c
        
        Example:- ( 2 / 4 x 3 / 4 ) x 4 / 4 = 2 / 4 x ( 3 / 4 x 4 / 4 )
      - Subtraction
        
        For any three Rational Numbers a , b and c, a - (b - c) ≠ ( a - b ) - c
        
        Example:- ( 2 / 4 - 3 / 4 ) - 4 / 4 ≠ 2 / 4 - ( 3 / 4 - 4 / 4 )
      - Division
        
        For any three Rational Numbers a , b and c, a ÷ (b / c) ≠ ( a / b ) ÷ c
        
        Example:- ( 2 / 4 ÷ 3 / 4 ) ÷ 4 / 4 ≠ 2 / 4 ÷ ( 3 / 4 ÷ 4 / 4 )