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Appetizers and Lessons for Mathematics and Reason
  online logic chapters  - the best starting point for further site exploration.  Bon Appetite.

4. Fractions & Proporitionality
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Section Entrance ] Fractions Revisited ] Fractions with Units ] Ratios & Fractions ] Proportionality Forwards and Backwards ] Links ]


Section Topics

 
Fraction, Fraction with Units, Fractions &  Ratios; and Proportionality forwards & backwards.

Section Pages

1. What is Proportionality
2. Examples of Proportionality
3. Multiple Ratios & Proportionality
4. Fractions & Proporitionality
5. More Examples


Would you like to show yourself or others how to be  algebra power users

 

Numerator is Proportional to Denominator in Equivalent Fractions

Equivalent Fractions:

  A fraction M/N equals 3/4, that is

M
N
= 3
4

when and only when

4M
4N
= 3N
4N

when and only when

4M = 3N  or  the numerator M =  (¾ ) N is proportional to the numerator N.

In general a pair of fractions

M
N
= A
B

are equal when and only when the numerator M of the first

M = ( A
B
) N  = kN

is proportional to the denominator M of the first with proportionality constant k = the second fraction  A/B

 

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Parents: Help your Child/Teen Learn covers  Speaking Skills, Reading & Writing Preparing for Science Having Patience, etc

Math How-TOs
1. Arithmetic   2. Algebra   3.  More Algebra  4.  Geometry 5 More Geometry 6.  Calculus
>> densely written 
>> use as skill checklists

Online Volumes (orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3 .Why.Slopes.&
.More.Math.1995

Skill & Concept 
Review or  Development 

 1. Decimal Arith - Video Based ]
2   Fractions  
3.  Fractions  with Units  
3. Solving Linear Equations  - 
making alg easier
4. Formulas forwards & Backwards - unifying theme for Algebra
5.  Proportionality, Back- & For-wards - theme at work.
6.  Logic - Math Free, good for precision in  work & studies 
7. Euclidean-Geometry  (leanly)
8. Slopes and Lines 
9. Why Study Slopes - a context 
10.  Quadratics
11  Polynomials
12  Factored Polys - a context
13 Functions - For-& Back -wards
14  Number Theory, Richly
15. Exponents, Radicals & logs.  
16   Calculus - Examples & Advice 
17.   Real  Analysis 
18  Electric Circuits Etc (So So)
19 Maps, Similarity & Trig, (alt view)
20 Complex numbers  

21 Logic with Symbols+truth tables

22  Consistent Story Telling
23. Even More Logic

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