Three Skills
For
Algebra
Volume 2
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Chapters and Appendices
Book Entrance
9 Numbers & Quantities
9 Everyday Words
9 Words Math Usage
9 Precision or Not
9 Numbers & Quantities
9 Changing Units
9 Further Readings
Foreword
1. Introduction
2. Implication Rules [4]
3. Chains of Reason [3]
4. Induction Mathematical
4. Romeo and Juliet
6 Old Language
5 Knowledge Islands [2]
7 Arith Skill Check [4 X 2]
Arith Webvideos
7. The Next Chapters
8 The Three Skills
8 VNR-Concise-Encyclopedia
PS. What is a Variable [8]
9. Algebra Talk [7]
10 Two More Skills[5]
11 Why Shorthand
12 Shorthand Usage [10]
13 What's Next
PS: The 4-th Skill For Algebra
14 Compound Interest [6]
15 Linear Equations [5]
16 Painless Proofs
17 Pythagoras
PS I. Distributive Law
PS II. Polynomials
18 Rules of Algebra [20]
19 Functions & Sets
20 Degrees & Radians
21 What's Next
22. Arith & Geometric Sums [2]
23 Summation Notation
24 Your Money [3]
25 Induction & Recursion [4]
26 What's Next
27 Pronouns in Logic
28 Occurrence Tables
29 Contrapositive
30 Truth Tables
31 Indirect Reason
Pathways for Learning
Would you like to show yourself or others how to be algebra
power users?
What is a Variable?
Introduction
Variation between Examples
Variation of Letters
A letter denotes a variable
Cases of Double Variation
Three Notions of a Variable
Constants, Parameters
& Variables
Talking about numbers
Dependent
or Independent
Variable, a Matter of Choice
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Chapter 9
Talking about Numbers or Quantities
Chapter Sections: [ Up ] [ 9 Numbers & Quantities ] [ 9 Everyday Words ] [ 9 Words Math Usage ] [ 9 Precision or Not ] [ 9 Numbers & Quantities ] [ 9 Changing Units ] [ 9 Further Readings ]
5.1 Changing Units
In responding to questions how much, we have a choice in the units of
measurement used. Quantities come with units. Numbers come without. A quantity
says how much. A number counts or says how many. You may measure weight or mass
with kilograms or with pounds. You may measure length in centimeters (cm),
meters (m), kilometers (km) inches, feet or miles. You may measure your savings
or investments in dollars and cents, or in your favorite currency. You may also
count items (objects, things, people). This gives or yields a number. For
instance, the number of meters in a kilometer is 1000. The number of people in
this room could be 5.
In reporting quantities or measurements, the choice of units affects the
number of units. Changing the unit of measurement will change the number. For
example, the amount of time 2 hours is the same as the amount of time 120
minutes, but the numbers 2 and 120 are different. We can say we have two
units of time when the time is measured in hours. We can say we have 120 units
of time when time is measured in minutes. But we cannot say the amount of time
is 2 or 120 without saying or somewhere saying what unit of measurement is used.
The following example shows how to change the unit of measurement.
To express the quantity 10.5 hours in terms of minutes, we replace 1 hour by
60 minutes = 60 × 1 minute This gives
Chapter Sections: [ Up ] [ 9 Numbers & Quantities ] [ 9 Everyday Words ] [ 9 Words Math Usage ] [ 9 Precision or Not ] [ 9 Numbers & Quantities ] [ 9 Changing Units ] [ 9 Further Readings ]
Next Section: 9-Further Readings.
Next Topic: What is a Variable:
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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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