In just FIVE minutes you should learn to quickly multiply up to 20×20 in your head. With this trick, you will be able to multiply any two numbers from 11 to 19 in your head quickly, without the use of a calculator.

I will assume that you know your multiplication table reasonably well up to 10×10.

Try this:

• Take 15 x 13 for an example.
• Always place the larger number of the two on top in your mind.
• Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.
• First add 15 + 3 = 18
• Add a zero behind it (multiply by 10) to get 180.
• Multiply the covered lower 3 x the single digit above it the “5″ (3×5= 15)
• Add 180 + 15 = 195.

That is It! Wasn’t that easy? Practice it on paper first!

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Want to Learn More?

The one book I recommend

“Super Math-E-Magics”
by V.A. Stephen Lenaghan

It may be available from Amazon.com or one of the other online sellers of used books

The 11 Rule

You likely all know the 10 rule (to multiply by 10, just add a 0 behind the number) but do you know the 11 rule? It is as easy! You should be able to do this one in you head for any two digit number. Practice it on paper first!

To multiply any two digit number by 11:

• For this example we will use 54.
• Separate the two digits in you mind (5__4).
• Notice the hole between them!
• Add the 5 and the 4 together (5+4=9)
• Put the resulting 9 in the hole 594. That’s it! 11 x 54=594

The only thing tricky to remember is that if the result of the addition is greater than 9, you only put the “ones” digit in the hole and carry the “tens” digit from the addition. For example 11 x 57 … 5__7 … 5+7=12 … put the 2 in the hole and add the 1 from the 12 to the 5 in to get 6 for a result of 627 … 11 x 57 = 627
Practice it on paper first!

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Finger Math: 9X Rule

To multiply by 9,try this:
(1) Spread your two hands out and place them on a desk or table in front of you.
(2) To multiply by 3, fold down the 3rd finger from the left. To multiply by 4, it would be the 4th finger and so on.
(3) the answer is 27 … READ it from the two fingers on the left of the folded down finger and the 7 fingers on the right of it.

This works for anything up to 9×10!

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Square a 2 Digit Number Ending in 5

For this example we will use 25

• Take the “tens” part of the number (the 2 and add 1)=3
• Multiply the original “tens” part of the number by the new number (2×3)
• Take the result (2×3=6) and put 25 behind it. Result the answer 625.

Try a few more 75 squared … = 7×8=56 … put 25 behind it is 5625.
55 squared = 5×6=30 … put 25 behind it … is 3025. Another easy one! Practice it on paper first!

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Square 2 Digit Number: UP-DOWN Method

Square a 2 Digit Number, for this example 37:

• Look for the nearest 10 boundary
• In this case up 3 from 37 to 40.
• Since you went UP 3 to 40 go DOWN 3 from 37 to 34.
• Now mentally multiply 34×40
• The way I do it is 34×10=340;
• Double it mentally to 680
• Double it again mentally to 1360
• This 1360 is the FIRST interim answer.
• 37 is “3″ away from the 10 boundary 40.
• Square this “3″ distance from 10 boundary.
• 3×3=9 which is the SECOND interim answer.
• Add the two interim answers to get the final answer.
• Answer: 1360 + 9 = 1369

With practice this can easily be done in your head.

Thanks To Ryan

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Multiply By 4

To quickly multiply by four, double the number and then double it again.
Often this can be done in your head.

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Multiply By 5

To quickly multiply by 5, divide the number in two and then multiply it by 10.  Often this can be done quickly in your head.

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The 11 Rule Expanded

You can directly write down the answer to any number multiplied by 11.

• Take for example the number 51236 X 11.
• First, write down the number with a zero in front of it. 051236

  The zero is necessary so that the rules are simpler.

• Draw a line under the number.
• Bear with me on this one. It is simple if you work through it slowly. To do this, all you have to do this is “Add the neighbor”. Look at the 6 in the “units” position of the number. Since there is no number to the right of it, you can’t add to its “neighbor” so just write down 6 below the 6 in the units col.
• For the “tens” place, add the 3 to the its “neighbor” (the 6). Write the answer: 9 below the 3.
• For the “hundreds” place, add the 2 to the its “neighbor” (the 3). Write the answer: 5 below the 2.
• For the “thousands” place, add the 1 to the its “neighbor” (the 2). Write the answer: 3 below the 1.
• For the “ten-thousands” place, add the 5 to the its “neighbor” (the 1). Write the answer: 6 below the 5.
• For the “hundred-thousands” place, add the 0 to the its “neighbor” (the 5). Write the answer: 5 below the 0.
  That’s it … 11 X 051236 = 563596

Practice it on paper first!

toxicology – The study of the nature, effects, and detection of poisons and the treatment of poisoning.

- The study of the adverse effects of chemical and physical agents on living organisms. Toxicology has also been referred to as the science of poisons.

related words : domain of poisoning, poisoning domain,

Information : from sci-tech encyclopedia

• The most important factor that influences the toxic effect of a specific chemical is the dose. All chemicals, including essential substances such as oxygen and water, produce toxic effects when administered in large enough doses. Another significant factor is the route of exposure.
• A third factor is the fate of the chemical after the organism is exposed. The chemical may not be absorbed at all, limiting its possible adverse effects to the site of exposure. If it is absorbed, then it may travel throughout the body and has the potential to cause toxic effects at one or more sites remote from the site of entry. The remote sites where these adverse effects occur are called target organs.
•  Another significant variable is the time course of the exposure. A quantity of chemical administered at one time may have an effect even though the same quantity administered in small doses over time has no effect.
• Acute toxicity refers to effects that occur shortly after a single exposure or small number of closely spaced exposures. Chronic toxicity refers to delayed effects that occur after long-term repeated exposures.

realm -  scope, range,purview

sub- prefix..

trying to come up with a pattern based on that data…

– weeks ago –

UI, jclips interfacing, poisoning types-symptoms data, updated architecture, started the database schema for the KB, algorithm…

– to do –

algorithm for automatic code generation

The other major problems that are being faced by a human expert are the limitation of his memory and processing inability of all the essential knowledge and information required in the process of decision-making. As a result of researches and developments, day by day, new knowledge in enormous amount is being added in every discipline and thus more relevant and accurate advice can be taken from a human expert if his/her own knowledge is accordingly updated which is not an easy task. Human experts are bounded by some humane limitations and it is quite impossible for a human expert to consider all the essential factors while taking decision. Something is always escaped and remained unconsidered. Thus some computer based tools or assistances like Decision support system, Decision making.Map

Expert systems of today support many problem solving activities such as decision making, knowledge fusing, designing, and planning, forecasting, regulating, controlling, monitoring, identifying, diagnosing, prescribing, interpreting, explaining, training etc. using different techniques and it is expected that future expert systems will support even more activities. In the beginning, expert systems were developed in the chemical and scientific domains and by the end of 1970s expert systems were operating in the medicine, chemical, education, natural resources and science domains. Expert system started to gain popularity in the early 1980s[2]. 

Expert systems are domain dependent computer programme that use knowledge and inference procedure of domain specific human expert to mimic his/her problem solving capability and way in which they solve. In the beginning,

source 

http://programming.ccp14.ac.uk/

XSLT-based infrastructure for sharing knowledge between three knowledge modeling and acquisition tools that use different conceptual models for knowledge representation.

A solution based on a programmed extension of a knowledge-modeling tool (using e.g. Java, C++, etc.) can be rather difficult and time consuming. Since XML is now widely accepted as knowledge representation syntax, we believe that a more suitable solution would be to use XSLT. A special advantage of this approach is that even though an XSLT is written independently of any programming language, it can be executed by almost every up-to-date programming language.