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 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.
1 A Definition of Real Numbers
Unsigned Real Numbers
Unsigned real numbers are defined with the aid of fractions and infinite decimal expansions. Finite decimal expansions are decimal fractions.
We assume each finite and infinite decimal expansion gives the length p of a line segment with one end at the origin of a half-line where the segment is a multiple p of a unit length. If p is an unsigned real number, it may be identified with a point on a half-line:
Here finite decimal expansions give decimal fractions; repeating decimal expansions give or correspond to whole numbers or simple fractions; and non-repeating decimal expansions correspond to all other points, numbers or line segment lengths.
Real Numbers with Signs
If p is an unsigned real number, we put +p = p. It may be identified with a point on a half-line as above. Now on infinite line where 0 is identified with a point, a point to be called the origin, the line is divided into two parts. The selection of unit length, and a positive direction allows the use of unsigned real numbers p and positive real number +p = p (by definition) as coordinates on one side of the origin.
The use of negative real number -p = as coordinates on the other side of the origin - the negative side. A negative number n = -p is given by the negative sign prefix - before an unsigned number p.
Remark: The unit lengths in the above two diagrams should be the same.
www.whyslopes.com
Number TheoryStart of Number Theory
Origins of Counting or Tallying
Adding Wholes
Multipling Wholes
Distributive Law Preamble
Distributive Law for Wholes
Consequences
More Consequences
What is a Fraction
Compound Fractions Number Theory
Continued
Decimal Place Value Place Value Reinforcement Comparison Method Addition Method Subtraction Methods Multiplication Methods Division Methods Remainder Arithmetic I Primes & Composites Primes Factorization Theorem Primes & Composites Prime Factorization Aids Prime Factorization Examples Counting Whole No. Factors Arithmetic Videos Square Roots & Primes Long Division Continued Fractions & Decimals Fractions as Decimals 1 = 0.999 Recurring Infinite Decimals Expansion Arithmetic Ratio of Simple Fractions Ratio of Decimal Fractions Unsigned Reals Numbers Signed Coordinates Plane Vectors Horizontal Vectors Adding Vector Multiplies Adding Signed Numbers Multiplying Signed Numbers Distributive Law for Reals Real Numbers Axioms Remainder Arithmetic II
Related Site Pages:
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
Food for thought: 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..