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Chapter 5: Rational Numbers as Fractions
5.2 Addition and subtraction of rational numbers
5.2.1. Vocabulary
5.2.1.1. mixed numbers – numbers made up of an integer and a fractional
part of an integer
5.2.2. Addition of rational numbers
a
c
5.2.2.1. Definition of addition of rational numbers: If
and
are
b
b
a c ac
rational numbers, then  
b b
b
a
c
5.2.2.2. Property: If
and
are any two rational numbers, then
b
d
a c ad  bc
 
b d
bd
5.2.3. Mixed numbers
5.2.3.1. 2 34  2  34
5.2.3.2.  2 34  (2  34 )  2  34
5.2.3.3. Calculators and fraction keys: Where is the fraction key on the TI83+????
5.2.3.4. Now Try This 5-8 p. 280: Work on in your groups
5.2.4. Properties of addition for rational numbers
5.2.4.1. Property: Additive inverse property of the rational numbers: For
any rational number ba , there exists a unique rational expression  ba ,
the additive inverse of
5.2.4.2.
 ( ba ) 
a
b
, such that
a
b
  ba    ba   ba  0
a
b
5.2.4.3.
 ba  cd  
5.2.4.4.
Property: Addition property of equality: If
a
b

numbers such that
c
d
a
c
and
are any rational
b
d
a c
e
 , and if
is any rational number, then
b d
f
a e c e
  
b f d f
5.2.5. Subtraction of rational numbers
a
c
and
are
b
d
a c
a c
any rational numbers, then   x if, and only if,   x , where x
b d
b d
is a rational number
5.2.5.1.
Definition of subtraction of rational numbers: If
5.2.5.2.
Definition of subtraction of rational numbers in terms of
a c
a
c
addition: If
and
are any rational numbers, then  is the
b
d
b d
e
a c e
unique rational number
such that  
f
b d f
a
c
5.2.5.3. Theorem 5-4: If
and
are any rational numbers, then
b
d
a c a c
  
b d b
d
a
c
5.2.5.4. Theorem 5-5: If
and
are any rational numbers, then
b
d
a c ad  bc
 
b d
bd
5.2.6. Estimation with rational numbers
5.2.6.1. rounding to the nearest integer
5.2.6.2. rounding to the nearest convenient fraction
5.2.6.3. Now Try This 5-9 p. 286: Work on in your groups
5.2.7. Ongoing Assessment p. 287
5.2.7.1. Home work: 1a, 1c, 1e, 2a, 2c, 3a, 3c, 5a, 9a, 24a, 29a, 29c