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Tutors - All Subjects
(use at your own risk)
AU:
tutorfinder.com.au
CDN :
findatutor.ca
CDN: .i-tutor.ca
CDN:
Montreal Tutors
NZ: findatutor.co.nz
UK:
tutorhunt.com
USA: wiziq.com
USA: ziizoo.com
YOU are better than YOU think. Show
yourself how:
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Read logic
chapters 1 to 5 in online volume Three
Skills for Algebra for greater skills & confidence
in work
and study.
Learn to read notes and textbooks like a lawyer, so that no nuance, no
subtlety and no clause escapes your attention. |
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Logic
chapters 1 to 5 re- appear not in sequence, as is or longer,
in Volume 1A, Pattern Based
Reason, Bon Appetite.
Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
Logic
mastery makes the hard, easier. Logic
mastery leads to better, stronger and richer comprehension. Logic
mastery improves reading and writing. Logic
mastery ease learning difficulties. Logic
mastery gives a headstart. In sum, logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
liinear Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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Caution: Site advice is approximately
correct, for some circumstances, not all. That leaves room for thought |
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What may be learnt and when depends on how skills
and concepts are developed. Making the hard easier and clearer will allow
earlier & richer development of skills and concepts.
Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice.
For online automated help in senior high school maths & calculus,
visit quickmath.com For Automatic
Calculus and Algebra Help with derivatives, integrals, graphs, linear equations,
matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range of
services, some free, some not, all based on webmathematica. Good luck.
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Previous: Chapter Entrance
2 Working with Formulas
Changing Calculations
Changing a formula for a number (or quantity) can reduce or lessen the amount
of arithmetic needed to calculate it.12
2Computers
can be told (programmed) to calculate results for us. One method to compute a
result may require ten times more additions and multiplications than a second
way. So if the second way takes a computer 15 minutes to do, the first way may
take the computer, 150 minutes = 2[1/2] hours. Rules for arithmetic say how to
change calculations without changing their results.
Changing the way a number or quantity is computed can also lead to formulas
for other numbers or quantities. Examples of this have been given. Recall from
the formula A = L·W for the area A of a rectangle,
we obtained formulas for its length L and its width W. From the
compound interest formula A = P(1+i)n we
obtained formulas for P and i. (Aside: note the two roles of the
letter A. It is an actor in both the area formula and in the compound
interest formula. The letter A has one role or meaning when we look at
the area formula and another role when we look at the compound interest
formula.)
In this chapter, we will describe a large set of arithmetic rules and
properties which say when two calculations or formulas give the same result.
This knowledge allows us to replace one formula by another in a larger
expression without changing whatever is being computed by the larger expression.
Chapter Sections: [ Up ] [ 18 Changing Formulas ] [ 18. Proper Use of Equal Sign ] [ 18. Replacement & Substitution ] [ 18 Real Numbers & Quantities ] [ 18 Rules for Algebra ] [ 18 Sums as Factors I ] [ 18 Sums as Factors II ] [ 18 Addition Properties ] [ 18 Sum Associative Property ] [ 18 Sums and Number 0 ] [ 18 Replacing Subtraction by Addition ] [ 18 Times Properties ] [ 18 Sum Grouping and Ordering ] [ 18 Product Associative Property ] [ 18 Products with the Number 1 ] [ 18 Product Grouping and Ordering ] [ 18 Power Rules ] [ 18 To Divide, Multiply ] [ PS: Rules for Fractions and Division ] [ 18 Inconsistent Nttn ]
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www.whyslopes.com
2. Three Skills for Algebra
Foreword, Chapters
& Appendices
Foreword
1. Introduction
2. Implication Rules
3. Chains of Reason
4. Romeo and Juliet
4. Induction Mathematical
5 Knowledge Islands
6 Old Language
7 Arith Skill Check
7. The Next Chapters
8 The Three Skills
8 VNR-Concise-Encyclopedia
PS. What is a Variable
9. Algebra Talk
10 Two More Skills
11 Why Shorthand
12 Shorthand Usage
13 What's Next
14 Compound Interest
15 Linear Equations
PS I. Distributive Law
PS II. Polynomials
16 Painless Proofs
17 Pythagoras
18 Rules of Algebra
19 Functions & Sets
20 Degrees & Radians
21 What's Next
22. Arith & Geometric Sums
23 Summation Notation
24 Your Money
25 Induction & Recursion
26 What's Next
27 Pronouns in Logic
28 Occurrence Tables
29 Contrapositive
30 Truth Tables
31 Indirect Reason
A. Advice For Learning
Words Before Symbols:
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
Complex number: starter lesson
Solving Linear Equations:
A. Letters and Lengths
B. & C. Solving Linear Eq'ns
with stick diagrams.
(i) x + 20 = 29
(ii) 2x + 5 = 20
(iii) 3x + 10 = 32
(iv) 5a + 16 = 3a+ 24
(v) (½)x + 8 = 24½
(vI) (¾)a + 16 = (¼)a+ 24
(vii) (¾)q + 17 = 32
(viii) 13 =[2/3]x +7 twice
(x) Animated Examples
(i) Integral Coefficients (A)
(ii) Integral Coefficients (B)
(iii) Fractional Coefficients
(iv) With
Parameters
Problem Solving with Linear
Equations in one or many
unknowns, and in essentially
one unknown - Symbols before
words.
C. Solving Linear Eq'ns
without
Stick Diagrams
D.
Problems in
essentially one unknown
E: 2D Systems - Sub Methods.
F. Larger Systems
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