text: # Properties of Rational Numbers - Negative Or Additive Inverse of Rational Numbers
  
  ## Notes
  
  ### Negative Or Additive Inverse of Rational Numbers:
  
  2 + (– 2) = (– 2) + 2 = 0.
  
  So, we say 2 is the negative or additive inverse of – 2 and vice-versa.
  
  In general, for an integer a, we have, a + (– a) = (– a) + a = 0; so, a is the negative of – a and – a is the negative of a.
  
  11/7 + (-11/7) = (-11/7) + 11/7 = 0
  
  So we say 11/7 is the negative or additive inverse of -11/7 and vice-versa.
  
  In general, for a rational number a/b, "we have", a/b + (-a/b) = (-a/b) + a/b = 0
  
  We say that (- a)/b "is the additive inverse of" a/b and a/b "is the additive inverse of" (- a)/b.
  
  ## Example
  
  Write the additive inverse of the following: (-7)/19
  
  7/19 "is the additive inverse of" (- 7)/19 "because" (- 7)/19 + 7/(19) = (- 7 + 7)/19 = 0/19 = 0.
  
  ## Example
  
  Write the additive inverse of the following:  21/112.
  
  The additive inverse of (21)/(112) "is" (-21)/112.
  
  ## Example
  
  Verify that – (-x) is the same as x for "x" = 13/17.
  
  x = 13/17
  
  The additive inverse of x = 13/17  "is" - x = (-13)/17 "since" 13/17 + ((-13)/17) = 0.
  The same equality 13/17 + ((-13)/17) = 0,
  shows that the additive inverse of (-13)/17  "is"  13/17 "or" -((-13)/17) = 13/17 i.e., -(- x) = x.
  
  ## Example
  
  Verify that – (-x) is the same as x for x = (-21)/31.
  
  Additive inverse of "x" = (-21)/31 "is -x" = 21/31 "since" (-21)/31 + 21/31 = 0.
  
  The same equality (-21)/31 + 21/31 = 0,
  
  shows that the addiditive inverse of 21/31 "is" (-21)/31, i.e., -(-x) = x.
  
  If you would like to contribute notes or other learning material, please submit them using the button below.
explanation: The document contains notes and examples related to the properties of rational numbers, specifically focusing on the concept of negative or additive inverses. It includes several examples that both pose questions and provide answers to those questions.
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distilabel_metadata.content: # Properties of Rational Numbers - Negative Or Additive Inverse of Rational Numbers
  
  ## Notes
  
  ### Negative Or Additive Inverse of Rational Numbers:
  
  2 + (– 2) = (– 2) + 2 = 0.
  
  So, we say 2 is the negative or additive inverse of – 2 and vice-versa.
  
  In general, for an integer a, we have, a + (– a) = (– a) + a = 0; so, a is the negative of – a and – a is the negative of a.
  
  11/7 + (-11/7) = (-11/7) + 11/7 = 0
  
  So we say 11/7 is the negative or additive inverse of -11/7 and vice-versa.
  
  In general, for a rational number a/b, "we have", a/b + (-a/b) = (-a/b) + a/b = 0
  
  We say that (- a)/b "is the additive inverse of" a/b and a/b "is the additive inverse of" (- a)/b.
  
  ## Example
  
  Write the additive inverse of the following: (-7)/19
  
  7/19 "is the additive inverse of" (- 7)/19 "because" (- 7)/19 + 7/(19) = (- 7 + 7)/19 = 0/19 = 0.
  
  ## Example
  
  Write the additive inverse of the following:  21/112.
  
  The additive inverse of (21)/(112) "is" (-21)/112.
  
  ## Example
  
  Verify that – (-x) is the same as x for "x" = 13/17.
  
  x = 13/17
  
  The additive inverse of x = 13/17  "is" - x = (-13)/17 "since" 13/17 + ((-13)/17) = 0.
  The same equality 13/17 + ((-13)/17) = 0,
  shows that the additive inverse of (-13)/17  "is"  13/17 "or" -((-13)/17) = 13/17 i.e., -(- x) = x.
  
  ## Example
  
  Verify that – (-x) is the same as x for x = (-21)/31.
  
  Additive inverse of "x" = (-21)/31 "is -x" = 21/31 "since" (-21)/31 + 21/31 = 0.
  
  The same equality (-21)/31 + 21/31 = 0,
  
  shows that the addiditive inverse of 21/31 "is" (-21)/31, i.e., -(-x) = x.
  
  If you would like to contribute notes or other learning material, please submit them using the button below.
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distilabel_metadata.raw_output_q_a_detector_0: The document contains notes and examples related to the properties of rational numbers, specifically focusing on the concept of negative or additive inverses. It includes several examples that both pose questions and provide answers to those questions.
  
  Label: multiple-question-and-answer