# Proportional Reasoning

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```					                      Proportional Reasoning
Proportional reasoning is one of the four types of mathematical reasoning that we
discussed in Unit 1 of this course. O’Daffer states, “Proportional reasoning involves drawing
conclusions or solving problems with either the formal or informal use of proportions” (2002, p.
29). When two rational expressions are equal to one another, they form a proportion. So the
problem with solving and working with proportions is two fold: 1) rational numbers and 2)
rational number equivalencies.

Rational Numbers
Rational numbers are discussed in chapter 6 of the O’Daffer text.
 Modeling Q numbers
 Rational Numbers
a
o      ; a  Z, b  Z , b  0
b
o Why can’t b be zero?
o Dividing by zero is undefined
 Expanded notation: 100 . 10-1 10-2 10-3 …
 Decimals
o Terminating: 5, 2.5, 3.1254689, …
o Repeating: 2.3 ; 0.56 ; 23.18 568 ; …
o Irrational numbers: , e, 2 ; 3 ;       5 ;   6 ;    non - squarenumber , 1.2121121112…, …
   Decimal  Rational
   Rational  Decimal

Rational Number Equivalents  Proportions
Proportional reasoning is discussed in chapter 7 of the O’Daffer text.
 Equivalent fractions
a c
o       iff ad = bc ; a  Z, b  Z, c  Z, d  Z , b  0 , d  0
b d
4 ? 20
o           example
7 35
5 ? 30
o           non-example
9 45
 Fundamental Law of Fractions
a                                                    a ac
o      , a  Z, b  Z, c  Z , b  0 , c  0, exists, then 
b                                                    b bc

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