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Chapter 6: Rational Number Operations and Properties
6.2 Adding and Subtracting Rational Numbers
6.2.1. Modeling Addition and Subtraction of Fractions
6.2.1.1. Modeling Adding and Subtracting: Fractions with like denominators
6.2.1.1.1. Generalization about addition and subtraction of fractions: In general, for
a
b a b a  b 
a b a  b 
rational numbers
and ,  
and  
c
c c c
c
c c
c
a
6.2.1.1.2. mixed number: Z , where Z is an integer and b > a
b
c
6.2.1.1.3. improper fraction: , where c  d
d
6.2.1.1.4. Your turn p. 296: Do the practice and the reflect
6.2.1.1.5. Using integer rods to add and subtract fractions with like denominators
6.2.1.1.6. http://arcytech.org/java/
6.2.1.2. Modeling Adding and Subtracting: Fractions with unlike denominators
6.2.1.2.1. Using integer rods to add and subtract fractions with unlike denominators
6.2.1.2.2. http://arcytech.org/java/
6.2.1.2.3. Using paper folding method
6.2.1.2.4. Your turn p. 298: Do the practice and the reflect
6.2.2. Adding and Subtracting Fractions
6.2.2.1. Procedure for adding and subtracting rational numbers represented by
a
c a c ad cb ad  cb 


fractions: For rational numbers
and ,  
and
b
d b d bd bd
bd
a c ad cb ad  cb 
 


b d bd bd
bd
6.2.2.1.1. Your turn p. 299: Do the practice and the reflect
6.2.3. Properties of Rational Number Addition and Subtraction
6.2.3.1. Definition of rational number subtraction in terms of addition: For rational
a
c a c e
e
numbers
and ,   if and only if
is the unique rational number such that
f
b
d b d f
e c a
 
f d b
6.2.3.2. Properties of Addition of rational numbers
a
c a c
 Closure property – For rational numbers
and ,  is a unique rational
b
d b d
number
a a
a
 Identity property – A unique rational number, 0, exists such that 0    0 
b b
b
a
for every rational number ; 0 is the additive identity element
b
a
c a c c a
 Commutative property – For rational numbers
and ,   
b
d b d d b
a c
e
 Associative property – For rational numbers , , and ,
f
b d
a c e a c e
      
b d f b  d f 

Additive Inverse Property – For every rational number
a
, a unique rational
b
a
a  a
a a
exists such that         0
b  b
b b
b
6.2.4. Estimation Strategies
6.2.4.1. See techniques practiced in chapter 3
6.2.4.1.1. rounding
6.2.4.1.2. front-end estimation
6.2.4.1.3. substitution of compatible numbers
6.2.4.1.4. clustering
6.2.4.1.5. Your turn p. 301: Do the practice and the reflect
6.2.5. Problems and Exercises p. 301
6.2.5.1. Home work: 3abc, 4ab, 5, 9acd, 10, 11, 18
number 