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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.
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Place Value
whole number counting with decimals
Digit by Digit Decimal Place Value
First Example
Decimal place value says
3452 = 2 ones + 5 tens + 4 hundreds + 3 thousands
where the plus sign + may be read as the word and. The
recognition of place value from right to left means the place value of the
leading digit is found last rather than first. We might read
3452 aloud as 3 thousands, 4 hundreds, 5 tens and
2 ones
So the right to left direction in which place value is found
<<<<<<<<<<<<<<<<
3452
>>>>>>>>>>>>>>>>
is opposite to the left to right direction in which the number is read aloud
in word form.
Second Example
The significance or value of the the digits in the larger whole number
represented by the decimal
23,456,778
<<<<<<<<<
is given from right to left by 8 ones, 7 tens, 7 hundreds, 6
thousands, 5 ten thousands, 4 one hundred thousands, 3 millions, 2 ten millions,
and read from left to right as
2 ten millions, 3 millions, 4 one hundred thousands, 5 ten thousands,
6 hundred thousands, 7 hundreds, 7 tens and 8 ones
Each column in a decimal representation of a whole number, except for the
last, has a place value ten times greater than the following column
Groups of Three Place Value
Second Example Revisited
Reading Aloud in Groups of Three
We may also read 23,456,778 backward as
778 ones, 456 thousands and 23 millions,
and forward as
23 millions, 456 thousands and 778 ones
Third Example
For longer numbers, we find place value from right to left
96 456 899
138 443 704 789 123
<<<<<
123 ones
789 thousands
704 millions
443 billions (a US billion is a thousand million)
138 trillions
899 quadrillions
456 quintillions
96 sextillions
Hence from left to right, 96 456 899 138 443
704 789 123 is
96 sextillions, 456 quintillions, 899 quadrillions,
138 trillions, 443 billions,
704 millions, 789 thousands and 123 ones
Each group of three (or less) in a decimal representation of
a whole number, except for the last group of three, has a place value a
thousand times greater than the following column
Reading numbers aloud from right to left and then left to right
in groups of three could provide two to four hilarious exercises in
primary or secondary school mathematics class.
Fourth Example:
Avogrado's Number
N = 6.02 * 1023 = 602 000 000 000 000 000
000 000
= 602 sextrillions or 0.602 septrillions.
| sextrillions |
quintillions |
quadrillions |
trillions |
billions |
millions |
thousands |
ones |
| 000 |
000 |
000 |
000 |
000 |
000 |
000 |
000 |
| 21 |
18 |
15 |
12 |
9 |
|
6 |
3 |
To come: UK version of above exercise
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www.whyslopes.com
Number Theory
Start 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..
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