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YOU are better than YOU think. Show
yourself how:
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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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Chapter 18
Rules for Algebra
Sum Grouping and Ordering
By applying chains of reason based on mathematical induction and starting
with the associative and commutative properties for multiplication, it possible
to show that the order in which a sum is computed should not affect the result.
Here numbers in the sum can be added and grouped together in any order. This
justifies sums being written without parentheses to indicate the order of
addition in them.7
7A
physical analogy for this is as follows: imagine umpteen bags of marbles, all
of which are to be placed in a larger container. The total number of marbles
put the larger container does not depend on the order in which the smaller
bags are put in, and it does not depend on how the smallers bags are grouped
together before they are put in. Discussing about this physical analogy
departs from the pure development of mathematical concepts from the long
chains of reasoning starting with rules or assumptions that involve no
physics.
Chapter sections: [ 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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