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Arithmetic Videos - Real Player Format
Four Groups of Videos follow.
For quicker results, Start with fraction videos first and cover the
others as needed.
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Primes, How to Recognize Them.
Extras include statement and justification of rules for division by
2, 3, 5, 9 and 11, and the calculation of remainders for division by
2, 3, 5, 9 and 11.
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Fractions, Operations
With. Addition, Multiplication and Reduction (Simplification)
using primes, LCM, GCD. Euclid's Algorithm for
computing the GCD of a pair of whole numbers provides a method for
simplifying fractions, quickly without using prime decomposition of
numerators and denominators.
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Greatest Common Divisors,
Calculation using Primes or Euclid Algorithm.
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Least Common Multiples,
Calculation using Primes or Greatest Common Divisor
Pen and pencil arithmetic skills is a must for algebra and a plus for the
use of arithmetic in daily life.
Primes may be used in simplifying expressions involving fractions and
square roots. See the calculation of GCDs and LCMs below.
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[Play
Video] 5 minutes - A Times Table (10 x 10) and how a
number is not prime (composite) if it is in the interior of
the table, that is if it is a product of smaller natural
numbers. Some where in here is a Definition for Primes. A
Natural number is composite if it is not prime.
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[Play
Video] 9½ minutes - Digit- Based Rules for
recognizing divisibility by the divisors 2, 3, 5, 9, 10 and
11 or calculating the remainders on division by
these divisors. These rules follow from 10 = 0 mod
2 or 5, and 10 = 1 mod 3 or 9, and 10 = -1
mod 11. Exercise: (1) Use 100 = 2
mod 49 to develop a digit-based rule for division by 49 or
7. (2) Give digit-based rules for division by 2,
3,5, 7, 11 and 13 that apply to the hexadecimal
representation of whole numbers.
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Square Root Rule: A number N is prime if it is not
divisible by all primes p whose square p2 is
less than or equal to N. On the other hand if a
number N is not prime, it will be divisible by a prime p
with p2 less than N+1. With a calculator, the
best bet is check where all primes p < sqrt(N)
starting with the smallest. Here if N = Mq where all
primes < p are not divisor of the prime N then all
primes < p will not be divisors of M. With the aid of a
calculators and rules for divisibility by 2,3, 5, and 11,
you can quickly get the prime decomposition of a whole
number N.
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[Play
Video] 10 minutes - Recognizing Primes in the interval
to 100 by eliminating all numbers that are multiples of
primes < 11 = the first prime with square 112
= 121 > 100. (The Sieve of Erasothenes)
If a first number N is a product of two
factors, the square of the larger factor will be
greater than or equal to the first number, and the
square of the smaller will be less than or equal the first
number N. So if the first number N can be factored, there
will be a divisor, the smallest factor in a product with
square < the first number N. That in turn implies
there will be a prime < the smallest factor
which divides N and whose square is <
N. From the study of logic (the contrapositive of an
implication rule), if all primes with square < N
do not divide N, N cannot be written as a product of
factors - natural numbers smaller than N.
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[Play Video] 2½ minutes - Prime
Factorizations (also called decomposition) for numbers in
the interval 2 to 15.
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[Play Video] 3 minutes - Prime
Factorizations for numbers in the interval 16 to
30.
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[Play Video] 4½ minutes - Prime Factorizations
for numbers in the interval 31 to 49.
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[Play Video] 4 minutes - Prime
Factorizations for numbers in the interval 50 to
66. Note: 51 = 3 x 17 is not prime as stated in video.
Oops.
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[Play Video] 5½ minutes - Prime Factorizations
for numbers in the interval 67 to 82.
Note: 76 = 2 x 38 = 2 x 2 x 19. Video shows 17 instead
of 19. Oops
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[Play Video] 5½ minutes - Prime
Factorizations for numbers in the interval 83 to
100.
Note: 90 = 6 x 15 = 2 x 3 x 3 x 5 = 2 32 5
Video write 4 x 15 instead of 6 x 15. Oops
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Start here if you wish and refer to methods for obtaining Prime
Factorization, GCDs, LCDs as needed.
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[Play
Video] 3-4 minutes. Equivalent fractions -
Lowering and raising terms (the values of numerators and
denominators) to obtain equivalent fractions.
Simplification involves lowering terms - cancelling common
factors or divisors on top and bottom. Addition &
subtraction of fractions may involve raising terms to
obtain a common denominators. See below.
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[Play
Video] 2-3 minutes A few examples of Simplifying
Fractions - lowering terms by canceling common factors
until there are no more common factors, so that the
numerator and denominator are relatively prime, that is
there prime decompositions have no primes in common.
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[Play
Video] 2-3 minutes. Multiplying Fractions
with cancellation of common factors done first
(recommended) or not, with more simplification to be done
later.
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[Play
Video] 5 minutes. How to add fractions using common
denominators. Here the common dominators is the lowest
or least common denominator (LCD) and its given by the
least common multiple (LCM) of the denominators in the
fractions added together. Here the listing
multiples method is used to compute the LCM. The
alternative of not using the LCD for the fractions is
explored to show what happens when the LCD is not used.
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[Play
Video] 3 minutes Another example of how to add
fractions with and without the least common
denominators with an explanation that not using the LCD
(least common denominator) leads to ratios that can
be simplified. So use of LCDs is promoted.
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[Play
Video] 3 minutes - Comparison of Fractions Size or
Magnitude, and more examples of the use of common
denominators in addition and subtraction.
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[Play
Video] 3 minutes - Another example of the listing
multiples method to find the LCM and thus the LCD for
the sum of two fractions.
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[Play
Video] 4 minutes - Factorization method to
obtain a common denominator, here the LCM and thus
the LCD for the sum of two fractions. See if you can
recognize the GCD of the denominators here. It is not
mentioned here. In this example, the LCD is given by
a product that does not have to be evaluated explicity due
to cancellation of common terms after addition of
fractions.
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[Play
Video] 2 minutes - Fraction Simplification using
Prime Decomposition (factorization) to identify common
factors for cancellations.
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[Play Video] 5 minutes - Product Simplification
using Prime Decomposition by Canceling Common Primes,
thus avoiding some denominator and numerator
multiplication. An alternative common factors as they
appear, more opportunistic, is given and is to be
recommended.
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[Play Video] 5 minutes - How to use Prime
Factorization or Decomposition for LCM and LCD for a
pair of denominators, an example.
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The simplification, multiplication and addition of Fractions may depend
on recognition and cancellation of common factors, prime or not. See how
GCDs and LCMs (or LCDs) may be used in the addition and multiplication of
fractions.
See how to compute greatest common divisors with and without the use of
prime factorizations.
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[Play
Video] 7 minutes. Finding All Divisors of a Natural
number from its Prime Factorization/Decomposition
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[Play
Video] 6 minutes. Computing GCD for pairs of Natural
Numbers from their Prime Factorizations
/Decompositions)
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[Play
Video] 2½ minutes Computing GCD from
Prime Factorizations /Decompositions, another
example.
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[Play
Video] 3 minutes. Computing GCDs using Primes,
yet another example.
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[Play
Video] 6½ minutes. Euclid Algorithm computes GCDs
not using Prime Factorization.
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[Play
Video] 3 minutes. Another Euclid Algorithm
GCD example with result confirmed using Prime
Decomposition.
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[Play
Video] 1½ minutes. Two numbers are relatively
prime when and only when they have GCD =1 when
and only when the numbers have no prime divisors in common.
Euclid algorithm leads to a quick identification of
relatively prime whole numbers in the numerators and
denominators of fractions by themselves or products.
.
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[Play
Video] 4 minutes. Two Ways to Find the GCD of a pair
of numbers. Both lead to the same result.
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Euclid's algorithm provides a means to compute the GCD without mentioning
prime factorization. The latter is best for computations with large
numbers - numbers for which the prime factorization is not immediately
obvious. Euclid algorithm can be implemented on calculator.
For a pair of denominators, the greatest common dominator is given by
their least common multiple.
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[Play
Video] 2¼ minutes. Common Multiples and
Least Common Multiples for a par of natural
numbers, finding by listing mutliples of first and
second number - the list method.
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[Play
Video]2¼ minutes. Least Common
Multiple for a pair of Natural numbers from Prime
factorizations of each, and then by list method.
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[Play
Video]1 minute. Least Common Multiple for a pair
of Natural numbers by computing the GCD divisor with the
aid of Prime Factorization of each.
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[Play
Video] 4 minutes. Least Common Multiple for a
pair of Natural numbers by computing the GCD divisor
with the aid of Euclid's Algorithm, 1st
Example.
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[Play
Video] 3 minutes. Least Common Multiple for a
pair of Natural numbers by computing the GCD divisor
with the aid of Euclid's Algorithm, 2nd Example.
Note use of calculator.
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Secondary
Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges
with local curriculum control. Study how to include site content - its skill development how-TOs and innovations
into present or future lesson plans - some reading required.
Road
Safety Messages and Questions: When and why should you face
traffic when walking along a road or cycle path? Is it a good
idea to hang limbs outside of cars etc? What gives more
protection in a crash: a car, motorbike or bicycle?
See too, the BBC-Belgium story Texting and
Driving - texting & the impossible test - the article links to a gruesome utube video on the subject
The Logic of Injustice:
How Texas sent
an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for
justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning
first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon
due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions
by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate
is not compensation for years or decade
of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern
Based Reason may slowly lead to greater precision in reading, applying and
writing laws.
May 2012, Composition Starting:
Pre-School and Primary Mathematics - Quantitative Skills, An
Intellectual View, Feedback Welcome:
The 8 Most Popular Site Inlinks
Parent Center: Help your child or teen
learn:
Parent-friendly
Work Booklets for ages 3+ to 13 Use these or others to check
or build skills. Other booklets are available but these booklets
allow parents unsure of themselves in mathematics to help their
children. The selection acquired in Canada is published in the
USA. So it has a US orientation. In retrospect, the selection
shows parents what to check with the booklets or by other ways,
the choice is theirs. But in retrospect, the selection does not
cover integral and fractions liquid weights and measures - ask
the publishers to correct that! For ages 9 to 12 say, parents may
compensate by showing boys and girls how to use weights or mass,
and further measures in food preparation. Beyond that children
may be shown how to measure and calculate angles, lengths and
areas [proportional amounts too] directly or by using maps and
plans drawns to scale. Learning how to gather and measure all the
ingredients, pots and pans for a dish or a meal, along with
cleaning up sets the stage for like activities or experiments in
science courses, and in developing organizational skills,
gives boys and girls a head start. Good luck. At the other
extreme, more comprehensive than light, if your motto is
McCainian: drill, drill, drill then Toronto
mathematician and actor John Mighton's jump math organization has jump math
workbooks for at least grades 3 to 8 for at-home and in-school
use - training sessions for teachers available. Jump math has
been expanding to cover older students. Jump Math Samples: plus
Fractions for
Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8
[unread - likely to be good]. and
Mathematics
Skills For Ages 3 to 14 - technical!
Skills with take
home value - A few ideas
Basic skills include
time-date-calendar Matters; money matters; map, plan and
scale diagram matters;counting, measuring and figuring;
decision making with logic and likelyhood; being careful and
being aware of the domino effect of mistakes; reading and
writing with precision.
Is your child able to add, subtract and multiply amounts
of money, work with fractions, work with clocks and calendars,
work with maps and plans, and measure length, weight-mass and
volume? Schools may promote your son or daughter without
providing basic skills in reading, writing and
arithmetic.
Arithmetic
and Number Theory Skills
Algebra
Starter Lessons
Geometry
- maps plans trigonometry vectors
More
Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
-
How to Ace Calculus: Street Wise Guide - Mostly
Text.
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Flash
Video for Calculus Phobics
They cover basic topics in ways likely to complement your
notes, your textbooks and site material. When Goldilocks
trespassed in the house of the three bears, she found three bowls
of porridge, two not to her liking, and one just right. Different
bears have different tastes. As invited guest here and elsewhere,
if one or more explanations is not to liking, try another. It may
be better or just right.
Unsolicited Advice
Learning to do and high marks if it comes to easy is often
deceptive - light rather than deep. For that reason, students
with learning difficulties determined not to let it get in their
way may go deeper and farther than those with none. High marks,
if the come easy, may be deceptive - provide a too light and not
a deep mastery. That could have been your problem in secondary
school, one that leads to comprehension shock or difficulties in
calculus and more generally in the first year of college. Bon
Appetite.
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