Vedic Mathematics

Overview

2010-05-31T22:37:00.003+08:00

Lean principles come from the Japanese manufacturing industry. The term was first coined by Bob Hartman in a Fall 1988 article, "Triumph of the Lean Production System," published in the Sloan Management Review and based on his master's thesis at the MIT Sloan School of Management. Krafcik had been a quality engineer in the Toyota-GM NUMMI joint venture in California before coming to MIT for MBA studies. Krafcik's research was continued by the International Motor Vehicle Program (IMVP) at MIT, which produced the international best-seller book co-authored by James Womack, Daniel Jones, and Daniel Roos called The Machine That Changed the World. A complete historical account of the IMVP and how the term "lean" was coined is given by Holweg (2007) .

For many, Lean is the set of "tools" that assist in the identification and steady elimination of waste (muda). As waste is eliminated quality improves while production time and cost are reduced. Examples of such "tools" are Value Stream Mapping, Five S, Kanban (pull systems), and poka-yoke (error-proofing).

There is a second approach to Lean Manufacturing, which is promoted by Toyota, in which the focus is upon improving the "flow" or smoothness of work, thereby steadily eliminating mura ("unevenness") through the system and not upon 'waste reduction' per se. Techniques to improve flow include production leveling, "pull" production (by means of kanban) and the Heijunka box. This is a fundamentally different approach from most improvement methodologies, which may partially account for its lack of popularity.

The difference between these two approaches is not the goal itself, but rather the prime approach to achieving it. The implementation of smooth flow exposes quality problems that already existed, and thus waste reduction naturally happens as a consequence. The advantage claimed for this approach is that it naturally takes a system-wide perspective, whereas a waste focus sometimes wrongly assumes this perspective.

Both Lean and TPS can be seen as a loosely connected set of potentially competing principles whose goal is cost reduction by the elimination of waste. These principles include: Pull processing, Perfect first-time quality, Waste minimization, Continuous improvement, Flexibility, Building and maintaining a long term relationship with suppliers, Autonomation, Load leveling and Production flow and Visual control. The disconnected nature of some of these principles perhaps springs from the fact that the TPS has grown pragmatically since 1948 as it responded to the problems it saw within its own production facilities. Thus what one sees today is the result of a 'need' driven learning to improve where each step has built on previous ideas and not something based upon a theoretical framework.

Toyota's view is that the main method of Lean is not the tools, but the reduction of three types of waste: muda ("non-value-adding work"), muri ("overburden"), and mura ("unevenness"), to expose problems systematically and to use the tools where the ideal cannot be achieved. From this perspective, the tools are workarounds adapted to different situations, which explains any apparent incoherence of the principles above.

Lean Manufacturing

2010-05-31T22:26:00.004+08:00

Lean manufacturing or lean production, is a production practice that considers the expenditure of resources for any goal other than the creation of value for the end customer to be wasteful, and thus a target for elimination. Working from the perspective of the customer who consumes a product or service, "value" is defined as any action or process that a customer would be willing to pay for. Basically, lean is centered on preserving value with less work.

Lean manufacturing is a generic process management philosophy derived mostly from the Toyota Production System (TPS) (hence the term Toyotism is also prevalent) and identified as "Lean" only in the 1990s. It is renowned for its focus on reduction of the original Toyota seven wastes to improve overall customer value, but there are varying perspectives on how this is best achieved. The steady growth of Toyota, from a small company to the world's largest automaker, has focused attention on how it has achieved this.

Lean manufacturing is a variation on the theme of efficiency based on optimizing flow; it is a present-day instance of the recurring theme in human history toward increasing efficiency, decreasing waste, and using empirical methods to decide what matters, rather than uncritically accepting pre-existing ideas. As such, it is a chapter in the larger narrative that also includes such ideas as the folk wisdom of thrift, time and motion study, Taylorism, the Efficiency Movement, and Fordism. Lean manufacturing is often seen as a more refined version of earlier efficiency efforts, building upon the work of earlier leaders such as Taylor or Ford, and learning from their mistakes.

Cooking With Math

2009-10-29T05:28:00.002+08:00

Math is in every kitchen, on every recipe card, and at each holiday gathering. The mathematics of cooking often goes unnoticed, but in reality, there is a large quantity of math skills involved in cooking and baking.

Conversions

Most ranges have dials that display the cooking temperature of the oven. In North America, most of these temperatures are written in Fahrenheit and usually are in increments of 25°. In Canada, recipe and oven temperatures are often presented in degrees Celsius. It is important then to understand how to convert a Fahrenheit temperature to an appropriate Celsius temperature. For example, let’s say your oven displays Fahrenheit temperatures with 50° increments. Your recipe tells you to bake your dish at 220°C. What temperature do you turn your oven to? Well, you will need to convert 220°C to a Fahrenheit measurement.

We use this formula to convert Celsius to Fahrenheit:

To make sure you do not over bake the cookies, you will need to set the oven to 428°F. But remember, your oven only displays the temperature in 50° increments, so you must estimate on the dial where 428°F is, somewhere between 400°F and 450°F. The relationship between celsius and fahrenheit is a linear function:

We also use conversions when we bake or cook to convert sizes and amounts. Many recipes are written in imperial units (teaspoon, tablespoons, and cups). Some newer recipes and measuring devices in Canada are labeled in metric units, such as milliliters (mL). If the recipe calls for ½ cup of butter and your measuring equipment is labeled in mL, how will you know which measurement to use? We can apply this conversion formula: 1 cup = 237mL. This means that ½ cup = 118.5mL. Again, this exact measurement is probably not on the measuring cup. It is probably closest to 125mL, so we will again have to estimate.

Making Enough

Most recipes give guidelines as to how much a single batch will produce. But what if you want more? It seems too time consuming to mix up another batch. What if the recipe makes only one dozen cupcakes and you need three dozen? Clearly, three dozen is three times more than 1 dozen, so we can multiply all the ingredients by three to make a larger batch. It is also important to understand how to multiply fractions. If the cupcake recipe calls for ¾ cup of milk and we want to triple it, we need to know that:

So, we will need 2 and 1/4 cups of milk to make three dozen cupcakes.

This knowledge of fractions is also helpful when we need to make our batch smaller. For example, recipe guidelines approximate that each batch will yield 6 dozen cookies. But, my family is small and I only want 2 dozen cookies. First, we need to see the relationship between 2 and 6. We can see that 2 dozen is one third (1/3) of 6 dozen because 2 x 3 = 6. That means that in order to make only 2 dozen cookies, we will need to use one third of each ingredient. So, if the recipe asks for 2 teaspoons of baking powder, we will only need 2/3 of a teaspoon, since

If we do not have a measuring spoon that is equal to 2/3 teaspoon, we may need to use 1/3 twice, or estimate using ¼.

When recipes indicate how much a particular batch will make, they give a general amount of food. If we are cooking for a group, we need to estimate how much each person will eat and make appropriate amounts of the particular item. For example, if a package of spaghetti makes 1L of cooked spaghetti, will we have enough to feed six people with one package? If not, how much of a second package will we have to use? First, we need to estimate how much each person will eat. We can guess that each person will eat 1 cup of spaghetti, which is 237mL. For convenience sake, we can round this to 250mL. That means that six people will eat 1500mL of spaghetti. If 1L=1000mL, we know that we will need to make one whole package, plus half of the second package to ensure that everyone has enough to eat.

Being Creative

Sometimes, we may not have all the ingredients to make a recipe, but we may have something we can fittingly substitute. How does this affect the measurement amounts in the recipe? For example, let’s imagine we are making Rice Krispie cake. The recipe calls for 32 large marshmallows, but we only have miniature marshmallows. We can still use the small marshmallows, but we will need to estimate how many mini marshmallows would make one large marshmallow, and multiply that number by 32.

What if you want to spice up your chocolate chip cookies by adding almonds and coconut? Your recipe calls for 2 cups of chocolate chips, but you want to add 1/3 cup of almonds and 1/6 cup of coconut. How much chocolate chips do you still have to add? Well, we simply need to subtract, using fractions.

We still need to add 1 and ½ cups of chocolate chips. It is important to remember that when adding and subtracting fractions, we need to use a common denominator.

Weight

Weight often affects cooking time. Consider the following hypothetical situation: we are cooking an 8 pound turkey for Christmas dinner. If the turkey needs to thaw in the refrigerator for 24 hours, per 5 pounds, we need to take the turkey out of the freezer in advance. We can use a proportional relation to help us decide how early to thaw the turkey.

The above proportion reads as follows: 5 pounds is to 24 hours as 8 pounds is to x hours. By cross-multiplying and dividing, we can find an answer of 38.4 hours, which is the solution for x.
If we are instructed to cook the turkey for 20 minutes per pound, how long do we need to cook the turkey? Well, 20 minutes per pound for 8 pounds is 20 x 8 = 160 minutes. And, 160 minutes is two hours and 40 minutes. If we only knew the weight of our turkey in kilograms, we would need another conversion formula (kilograms to pounds) to find the weight of the turkey in pounds first, and then apply the recommendations.

Cost

We also use math when cooking and baking to estimate the cost of a certain dish. We can understand that cheesecake is more expensive to make than a batch of cookies, particularly when people buy ingredients such as flour, sugar, and butter in bulk and cream cheese is more expensive. When comparing recipes, it may be beneficial to estimate the cost of each recipe.

Mathematical skills are used quite frequently when baking and cooking. It can be very helpful to understand how math affects the quality of culinary in order to make the most delicious meals and treats.

Try this cooking Web Quest that involves math.

PPSMI: 'Declining scores prompted policy reversal' (Update)

2009-07-10T17:57:00.001+08:00

KAMPAR: The command of Malaysian students in Science and Mathematics subjects have been on a steady decline forcing the Government to revert the teaching of the subjects to Bahasa Malaysia and other vernacular languages.

Deputy Prime Minister Tan Sri Muhyiddin Yassin said the Trends Report showed Malaysian students’ position in Mathematics dropped to 20 from 10 while Science went down from the 20th place to 21.

"Data showed that when English was not used to teach the two subjects 30 years ago, there was an increase in the number of graduates and professionals."

"And when it was changed in 2003, our students could not cope with the change in language," he said Friday.

Speaking to reporters after opening the Fifth Malaysia Festival of the Mind at Universiti Tunku Abdul Rahman (Utar) here, Muhyiddin, who is also the Education Minister, said the ministry's records also showed a decline in the students’ ability in learning the subjects.

"If we continue, we will see double jeopardy and I do not want Malaysians to face problems later," he added.

Muhyiddin had on Wednesday announced that the subjects would be taught in Bahasa Malaysia or in the mother tongue in vernacular schools from 2012, while English would be given prominence by beefing up the teaching of the language.

Asked whether the Government planned to enlist political parties to help explain the rationale, given that some people were unhappy with the decision, Muhyiddin said:

"We will keep on explaining (but) as the Prime Minister had said, we will not be able to please everybody."

He added the reversal could only be carried out in 2012 because the government had to explain its decision.

"If we do it tomorrow, those who are not aware of it may get a shock," he said.

He reiterated that the decision made by the Government had taken into account many things and it was not done in haste.

"It is not selective of one or two schools. We are talking about more than 10,000 schools nationwide," he said.

Meanwhile, a blog poll by former prime minister Tun Dr Mahathir Mohamad showed that the majority of the 26,000 respondents opposed the policy reversal of the teaching of Science and Mathematics in English.

Dr Mahathir said he included the poll in his blog, chedet.com to gauge people particularly parents actual opinions on the policy reversal.

“Out of the 26,000 respondents we received, 80% disagree to the teaching of Science and Mathematics either in the national language, Chinese or Tamil languages.

“Certainly, after getting the poll results, if my opinion cannot be forwarded to the Government in other ways, I will post my opinion. If there are those in the Government who read my blog,” he told reporters after attending closed-door talk on the position of the institutional monarchy and the Malays in the Federal Constitution from the 1 Malaysia perspective at Putra World Trade Centre here Friday.

Asked whether the Government was making a wrong step by making the policy reversal, he said:

”Yes, yes. I’ve said this many times before because this policy was implemented during the last year of me being the Prime Minister.

“I had definite reasons supported by the Umno supreme council as to why we should teach Science and Maths in English.

“It is not about trying to learn English. It is not about trying to learn Malay. It is simply an acknowledgement of the fact that today’s knowledge comes to us in the English language.

He said that in the past, when Arabs became Muslims, they studied Greek in order to acquire the knowledge of the Greeks.

Subsequently, he said the Europeans, in the dark ages studied Arabic in order to acquire the knowledge of the Arabs.

“Today, the knowledge is with the people who write in English. And for that reason we want to learn English to acquire knowledge, not to learn English, but Science has got a special English language for itself. It is important that we use English to study the Science and Maths.

“I speak what I think. I’m not criticising just anything. I’m criticising something that will affect the future of our children,” he said adding that he was briefed by Deputy Prime Minister Tan Sri Muhyiddin Yassin, who is also Education Minister and his officials a day before the announcement of the policy reversal.

“I don’t expect anything but it was nice of him to come and see me and brief me with his officers. I did give my opinion but it was not reflected in the announcement that was made. It was just a briefing session a day before they officially adopted it.

“It’s quite obvious that they are not going to change their minds even if they talk to me,” he added.

The Scraping Of PPSMI

2009-07-09T20:43:00.000+08:00

It was indeed a black day for education yesterday a decision which will bring unnumbered problems for our future generation. Yesterdays's decision proved and projected the selfish and backward mentality of our leaders. It looks like living in denial has became a norm in the Malaysian society.

To be very blunt and truthful the sole problem with PPSMI are the teachers and not the students. Some may tend to differ but as they say the truth is painful. Most of our teachers in SRK are 99 percent Malays so the need to learn and master the international language is just not there. Who cares ?

Employing a further 13,933 new teachers to uplift the teaching of english is not going to help who is the government trying to fool. During my days in school almost 50 percents of all teaching power were non malay teachers the other 50 malays. It was good mixture frankly. Boy were they good ,english was most frequently used in class and all our malay friends could converse so well. Even the weakest student tried . Our Malay teachers could converse in superb english . We lost this and who is to be blamed?

But all this had changed now where have all the non malay teachers gone to especially in SRK schools. Basically there are none and if so can be counted. Our education system is doomed so long as we think learning another language is a weakness and not a strenght.

I teach, my students learnt a lot of new things and terminology through the impementation of PPSMI best part all of them are MALAYS. I am proud of them they love learning in english. They openly confessed that reverting back to BM is not good for the future of MALAYSIA.

PPSMI: Cabinet to decide on use of english tomorrow

2009-07-09T20:29:00.004+08:00

THE cabinet will make the final decision on the teaching and learning of science and mathematics in the English language tomorrow, Deputy Prime Minister Tan Sri Muhyiddin Yassin said.

Muhyiddin, who is also the Education Minister, said the cabinet would make the decision after he presented the outcome of the various detailed and comprehensive studies made on the teaching and learning of the two subjects in English to the cabinet.

"I have already presented the memorandum on the position of PPSMI (teaching and learning of science and mathematics in English), what had been implemented and what is the level of the command of the English language and the position of science and mathematics since we implemented the system," he told reporters after launching the Gerak Bakti Project for the Ujian Penilaian Sekolah Rendah (UPSR) by Amanah Raya Berhad, here today.

Muhyiddin said he would also present several suggestions and recommendations on how the government could empower Bahasa Malaysia and strengthen the usage of English at all levels in the primary and secondary schools.

He said the presentation was being made after the ministry officials had met the various groups with interests in education, as well as numerous organizations that they had contacted and held discussions with. He said the decision to be made by the government on the teaching and learning of science and mathematics in English would not be based on the pressures and demands from any group.

"I believe we have already obtained a clear picture. We are not making this decision in haste, we are not making the decision out of pressure placed by any group.

"We will decide based on the interest of the students and the importance of improving the system of education in our country," he said.

Among the people approached for their views on the teaching and learning of science and mathematics in English were former prime minister Tun Dr Mahathir Mohamad and members of the Umno Supreme Council.

Meanwhile, the Gerak Bakti Project for the UPSR Amanah Raya Berhad will provide newspapers in the Malay and English languages to rural schools every Monday.

The overall project would cost more than RM500,000 and more than 16,000 students of various races would benefit from the programme.

Also present at the function were Johor Menteri Besar Datuk Abdul Ghani Othman, Amanah Raya Berhad Group Chairman Datuk Dusuki Ahmad, and Yayasan Gerak Bakti national chairman Khairy Jamaluddin.

How to Teach Math

2009-06-08T13:58:00.001+08:00

Step 1
Buy a curriculum that uses manipulatives and teaches math using concrete language. There are many available; two good curriculums are Math U See, Mortensen Math. Research these curriculums to determine which fits your budget and your family.

Step 2
Study the math lesson before presenting it to your children. Practice several of the math problems if you need. Make sure you understand the concept being taught and how to present it to your children.

Step 3
Make the lesson fun and interesting. Let them see that studying math is fun. Don’t tell them that math is hard or that certain aspects of math are only for when they are older. You will be surprised at what a child can understand when their brain is not limited.

Step 4
Take the lessons outside the books. Use opportunities to show how math is involved in everyday life. Use setting the table for basic counting. Use baking for fractions. Use trips for algebra

http://www.ehow.com/

How to Teach a Child Math

2009-06-08T13:53:00.002+08:00

Find out what type of learner your child is if you can. For example, if he is a visual learner, he may do well with flashcards, videos, white boards, toys, games and computers. If he is a book learner, then he may do well reading and doing worksheets.

Step 2
Find out what he is learning in school and tie your lesson in with the unit. It will be more meaningful for the child. It often takes several different approaches to find one that works or make it make sense.

Step 3
Have her accompany you on a shopping trip and figure out how much something costs on sale. Then let them pocket the change. Have them help you count out money or change.

Step 4
Life or consumer math is some of the most important math your child will learn. Teach older children about math by having them solve problems about credit card debt, student loans and shopping around for the best interest rate and terms. Have them work up a mock household budget for when they go off to college. You can have them do a mock shopping trip on the Internet. Inform them of the dangers and responsibilities of credit and loans. Have them do salary research for positions they are interested in.

Step 5
Do math on the fly, or in other words, work it into your day. Ask silly math questions to younger children either in the car, during an activity or before bed. See how well they really do know their math facts. It does not have to be a formal session.

Step 6
If you are doing flashcards, set aside the ones that he does not know immediately and run through them again. The next day, emphasize those same ones. At the end of the week, go through the entire group for a refresher. This is also good to do over the summer to help children retain what they have learned.

Step 7
Sometimes all you have to do is look to your computer for help. There are several free and helpful Internet website resources (see Resources). You could also purchase math CDs and DVDs or games if you do not have Internet access or want more reinforcement.

http://www.ehow.com/

Plus Points

2008-07-16T13:34:00.002+08:00

There are obviously many advantages of using a flexible, refined and efficient mental system like Vedic math. Pupils can come out of the confinement of the 'only one correct' way, and make their own methods under the Vedic system.

Thus, it can induce creativity in intelligent pupils, while helping slow-learners grasp the basic concepts of mathematics. A wider use of Vedic math can undoubtedly generate interest in a subject that is generally dreaded by children.

Development of Vedic Math

2008-07-16T13:28:00.004+08:00

Development of Vedic MathVedic math was immediately hailed as a new alternative system of mathematics, when a copy of the book reached London in the late 1960s.

Some British mathematicians, including Kenneth Williams, Andrew Nicholas and Jeremy Pickles took interest in this new system. They extended the introductory material of Bharati Krishna's book, and delivered lectures on it in London. In 1981, this was collated into a book entitled Introductory Lectures on Vedic Mathematics.

A few successive trips to India by Andrew Nicholas between 1981 and 1987, renewed the interest on Vedic math, and scholars and teachers in India started taking it seriously.

People Opinion..

2008-05-29T08:33:00.002+08:00

What is the importance of learning mathematics?

It's life, mate! From start to end. So when you hand over a twenty to pay for something that cost less £10 ($10), how will you be able to check your change correctly if you can't count the change? When you have to drive 300 miles, and you know you can travel 50 mph on average, how do you know how long it will take you if you can't do division?When you need to cook something and triple the amount of people the recipe will feed, how do you do it without multiplication?Fancy a manual job like being a brickie? You can't figure out how many bricks you need for a job without multiplying.Do you fancy having kids one day? Would you like to build your son a go-cart? You'll need to understand geometry and trigonometry, then.And even if you ignore all these daily things, mathematics gives meaning to science and scientific results -- especially the branch called statistics. When you hear some latest scientific research study on the news, you won't be able to understand it for yourself if you can't half-follow the maths and stats.Moreover, engineering doesnt' happen without lots of maths, either. Manufacturing, industry, all those clever electronic toys? They couldn't be built without some pretty good maths understanding. Do you like music? The rules of music follow precise mathematics, too.

People Opinion..

2008-05-29T07:56:00.007+08:00

What is the real use of mathematics in real life?

1st Opinion....

Everyday life would be quite difficult if you had no knowledge of maths whatsoever. On a basic level you need to able to count your money, multiply, subtract and divide. You need a knowledge of maths if you want to do some DIY at home, to work out how much material to buy for a job. More advanced mathematics is essential if you take up any kind of technical career such as engineering. Working on algebra and geometry also helps with reasoning skills and assists later in life with technical problem solving. Living your day to day life without maths would be extremely difficult. Even if you were a nomad in the desert you would want to count your goats wouldn't you?

2nd Opinion

Living a life unknowing 'Maths' would be living in random oblivion. Mathematics is primarily used for the purpose of scientific calculation of figures and objects. In real life the use of Mathematics can be applicable to every aspect, field, profession and subject etc. In IT field, in Statistics, in Accounts, in Algebra, in Geometry, for instance, Mathematics is used for calculating, multiplying, subtracting, division, differentiating, manipulating and managing the data in desired form. In other professions Mathematics can merely be used for the calculation of currency, recording the profits and loss. In ordinary life Mathematics can be used for the calculation of any specific or general sort. Concisely it can be said that Mathematics can be used for the authentic and scientific variation between and calculation of numbers, amounts, quantities etc; measurements of the frequencies of light and sound, of distance.

3rd Opinion

There are lots of real uses of mathematics in our life. All the mathematics terms base on counting.Today our all businesses base on counting. There is no concept of business without mathematics.Before the mathematics rules people use barter system. They give there goods to others and take the goods from other people. But this system can not continue longer when need of humans increased day by day.We cannot deny the importance of mathematics in our daily life. When we got to shop to purchase some thing we need mathematics.When some one comes to our shop to purchase some thing we need calculations.But the most important use of mathematics in our technologies can not be contradicted. Our most of the system base on computers and all the computer technology are stands on mathematical rules. All computers work on binary code, code of zero and one.So we cannot deny the importance of mathematics in real life.

Multiplying by other numbers

2008-05-20T15:11:00.005+08:00

The 'halve' operation has a particular meaning to the Trachtenberg system.

It is intended to mean "half the digit, rounded down" but for speed reasons people following the Trachtenberg system are encouraged to make this halving process instantaneous. So instead of thinking "half of seven is three and a half, so three" it's suggested that one thinks "seven, three". This speeds up calculation considerably.
In the same way the tables for subtracting digits from 10 or 9 are to be memorized.

Multiplying by 5

Rule: to multiply by 5:
Take half of the neighbor
Add 5 if number is odd
Example:42x5=210 4=2,2=1 43x5=2

Multiplying by 6

Rule: to multiply by 6:
Add half of the neighbor to each digit.
If the starting digit is odd, add 5.

Example:6 × 357 = 2142
Working right to left,7 has no neighbor, add 5 (since 7 is odd) = 12.

Write 2, carry the 1.5 + half of 7 (3) + 5 (since the starting digit 5 is odd) + 1 (carried) = 14.

Write 4, carry the 1.3 + half of 5 (2) + 5 (since 3 is odd) + 1 (carried) = 11.

Write 1, carry 1.0 + half of 3 (1) + 1 (carried) = 2. Write 2.

Multiplying by 7

Rule: to multiply by 7:
Double each digit.
Add half of its neighbor.
If the digit is odd, add 5.

Multiplying by 8

Rule: to multiply by 8:
Subtract last digit from 10 and double
Subtract the other digits from 9 and double
Add result to the neighboring digit on the right.
For the last calculation (The leading Zero), subtract 2 from the neighbour.

Multiplying by 9

Rule: to multiply by 9:
Subtract the last digit from 10. (Ex.: 10 - 3 = 7)
Subtract the middle numbers from 9, and add to the number to the right.
Take away 1 from the first number.

Controversy and criticism

2008-04-04T17:09:00.006+08:00

There has been much controversy amongst Indian scholars about Tirthaji’s claims that the mathematics is Vedic and that it encompasses all aspects of mathematics (Kansara, 1961). First, Tirthaji’s description of the mathematics as Vedic is most commonly criticised on the basis that, thus far, none of the sūtras can be found in any extant Vedic literature (Williams, 2000). However, trying to locate Tirthaji’s references in the Vedic literature would be extremely difficult as it is possible that Tirthaji rediscovered and reconstructed the sūtras from stray references scattered throughout the Atharva-veda, making it difficult to trace them (Trivedi, 1965).

In response to criticisms that the sūtras cannot be located within the texts, several people have explained how textual references should not be the basis for evaluating the Vedicity of the mathematics (Agrawala, 1992). Some propose that Vedic mathematics is different than other scientific work because it is not pragmatically worked out, but is based on a direct revelation, or an “intuitional visualisation” of fundamental mathematical truths (Agrawala, 1992; Pratyagatmananda, 1965). Tirthaji has been described as having the same “reverential approach” towards the Vedas as the ancient rishis that formed them. Thus, it seems as though some believe that Tirthaji may not have found the sūtras within the Vedas, but that he received them spiritually as the rishis did, which should validate them as Vedic.

The controversy about the Vedicity of the mathematics is further confused by the double meaning of veda. Since veda can be translated to mean ‘knowledge’, it is also possible that Vedic mathematics simply refers to the fact that the sūtras are supposed to present all knowledge of mathematics. Tirthaji’s definition of veda does not clearly clarify whether he uses it to represent ‘all knowledge’ or the Vedic texts; rather, it seems that he uses it to refer to both:

Considering the lack of references to the sūtras, coupled with the fact that the language style does not seem Vedic, some propose that the sūtras were simply composed by Tirthaji himself (Agrawala, 1992). In that case, one must consider what motivated Tirthaji to attribute the mathematical sūtras to the ancient texts.

Was it because they are from the Vedas, or does claiming so give them more credibility? Other areas of controversy regarding Vedic mathematics focus on the actual mathematics itself. Tirthaji’s assertion that the 16 sutras of Vedic mathematics encompass all branches of mathematics is an extreme one even if true, and so it is not surprising that many mathematicians challenge it (Kansara, 1961).

They point to the inconsistency between the topics addressed by the system (such as decimal fractions) and the known mathematics of early India, the substantial extrapolations from a few words of a sūtra to complex arithmetic strategies, and the restriction of applications to convenient, special cases.

They further say that such arithmetic as is sped up by application of the sūtras can be performed on a computer or calculator anyway, making their knowledge rather irrelevant in the modern world.

They are also worried that it deflects attention from genuine achievements of ancient and modern Indian mathematics and mathematicians.

Multply 11 With Larger No

2008-04-03T13:50:00.003+08:00

Simple Calculation For the number from 11 to 20

2008-04-03T10:20:00.005+08:00

Applications of Vedic mathematics

2008-04-03T09:25:00.003+08:00

The most notable application of Vedic mathematics is in education. Vedic mathematical strategies may prove to be a useful resource for teachers and students, who may find elements of it easier and more accessible to teach and learn than conventional mathematics.

In particular, these strategies may be an invaluable resource to students that already struggle with mathematics, and could benefit from alternative approaches.

One attempt at incorporating Vedic mathematics into education was made by Mark Gaskell, the head of mathematics at the Maharishi School Lancashire, England (Gaskell, 2000). The school has developed a Vedic mathematics curriculum equivalent to the national one with impressive results. According to Gaskell, the alternative curriculum has resulted in livelier classes, greater student enjoyment and understanding, and improved academic performance (2000).

In fact, the first set of students to complete the course were each able to not only pass, but achieve over 80%, on the General Certificate of Secondary Education, a proficiency test taken by all secondary school British students, a year earlier than their peers in the

regular curriculum (2000).

If harnessed appropriately, there seems to be great potential for how Vedic mathematics can be used to teach, learn and understand mathematics.

Perhaps the most important aspect of including Vedic mathematics in an education system will be taking the step towards becoming open to conceptually different mathematical approaches — approaches that could one day free and transform mathematics education.

Refrence:

http://en.wikipedia.org/wiki/Vedic_mathematics

2008-04-03T09:05:00.001+08:00

Multiplying by 11

11×35= 385

The five in the ones place of the answer is taken from the five in 35.

The eight in the answer is the sum of 35 (3+5=8).

The three in the hundreds place of the answer is taken from

the three in 35.

If the sum is greater than 9

However, if in step #2 the sum is greater than 9, the sum's left digit is added the first digit of the number multiplied by 11. For example:

11×59= 649

The nine in the ones place of the answer is taken from the nine in 59.

The four in the answer is the right digit in the sum of 59 (5+9=14)

The six in the hundreds place of the answer is take from the sum of the five in 59 and the digit in the tens place from

the sum of 59 (5+9=14) --> (5+1=6)

Multiplying a threedigit number by 11

The steps for multiplying a threedigit number by 11 are as follows:

11×768= 8448

The 8 in the ones place of the answer is taken from the eight in 768.

The 4 in the tens place of the answer is taken from the sum of 8, in the ones place of 768, and 6, in the tens place of 768 (8+6=14). As 14 is greater than 9, the 1 is carried over to step 3.

The 4 in the hundreds place of the answer is taken from the sum of 6, in the tens place of 768, and 7, in the hundreds place of 768, plus the carried 1 from step 2 (6+7+1=14). As 14 is greater than 9, the 1 is carried over to step 4.

The 8 in the thousandths place of the answer is taken from the sum of 7, in the hundreds place of 768, plus the carried 1 from step 3 (7+1=8).

2008-03-22T09:58:00.001+08:00

Method for multiplying numbers where the first figures are the same

and the last figures add up to 10.

32 x 38 = 1216

Both numbers here start with 3 and the lastfigures (2 and 8) add up to 10.

So we just multiply 3 by 4 (the next number up)to get 12 for the first part of the answer.

And we multiply the last figures: 2 x 8 = 16 toget the last

part of the answer.

Let try another Example:

81 x 89 = 7209

So we just multiply 8 by 9 (the next number up) to get 72

for the first part of the answer.

Mutply Last figures : 1 x 9 = 09. You will get last part of answer.

2007-12-22T13:27:00.001+08:00

Multiplying numbers just over 100.

103 x 104 = 10712

The answer is in two parts: 107 and 12,
107 is just 103 + 4 (or 104 + 3),
and 12 is just 3 x 4.

Similarly 107 x 106 = 11342

107 + 6 = 113 and 7 x 6 = 42

108 x 109 = 108 + 9 / 8 x 9
= 117 / 72
= 11,772

2007-12-11T13:44:00.000+08:00

VERTICALLY AND CROSSWISE for
multiplying numbers close to 100.

Let say, you want to multiply 88 by 98. Not easy,you might think. But with VERTICALLY AND CROSSWISE you can give the answer immediately, using the same method as above.

Both 88 and 98 are close to 100. 88 is 12 below 100 and 98 is 2 below 100. You can imagine the sum set out like this:
As before the 86 comes from subtracting crosswise: 88 - 2 = 86 or 98 - 12 = 86 you can subtract either way,
you will always get the SAME answer. And the 24 in the answer is just 12 x 2: you multiply vertically.

So 88 x 98 = 8624

Observe similar examples:
97 Squared = 97 - 3 / 3 x 3 = 94 / 09

96 Squared = 96 - 4 / 4 x 4 = 92 / 16.

Instant Subtractions

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Use the formula ALL FROM 9 AND THE LAST FROM 10 to perform instant subtractions.

For example 1000 - 357 = 643
We simply take each figure in 357 from 9 and the last figure from 10.

So the answer is 1000 - 357 = 643
And thats all there is to it!

This always works for subtractions from numbers consisting of a 1 followed by noughts: 100; 1000; 10,000 etc.
Similarly 10,000 - 1049 = 8951

For 1000 - 83, in which we have more zeros than figures in the numbers being subtracted, we simply suppose 83 is 083.
So 1000 - 83 becomes 1000 - 083 = 917

Squaring numbers ending in 5....easy as 123

2007-09-04T02:16:00.000+08:00

A faster way to square numbers that end in 5 .

25²= 2 "By" 3 / ........
= 2 x 3 / ........

To this we tag on the last digit "5" squared:

= 2 x 3 / 5 x 5

= 6 / 25

Thus the answer is 625.

75² = 5625

75² means 75 x 75.

The answer is in two parts: 56 and 25.The last part is always 25.
The first part is the first number, 7, multiplied by the number "one more", which is 8:

so 7 x 8 = 56

Similarly 85² = 7225 because 8 x 9 = 72.

15² = 1 x 2 / 5 x 5 = 2 / 25 = 225
35²= 3 x 4 / 5 x 5 = 12 / 25 = 1,225

45² = 4 x 5 / 5 x 5 = 20 / 25 = 2,025
95² = 9 x 10 / 5 x 5 = 90 / 25 = 9, 025

To multiply any 2 - figure number by 11 less than 5 sec..

2007-09-04T00:33:00.000+08:00

Just put the total of the two figures between the 2 figures.

26 x 11 = 286

Notice that the outer figures in 286 are the 26 being multiplied. And the middle figure is just 2 and 6 added up ( 2 + 6 = 8 ) put at the center

Split 7 & 2 like this 7 2

Add up 7 & 2 ( 7 + 2 = 9 )

and put 9 at the center

7 9 2

This involvement of a carry figure will change the front figure
7 + 7 = 14
we get 77 x 11 = 7₁47 = 847.

Multiply any two Digits numbers From 11 To 19 ....

2007-09-04T00:30:00.000+08:00

In just FIVE minutes you should learn to quickly multiply up to 20x20 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 10x10.

Try this:

Take 15 x 13 for an example.

Always place the larger number of the two on top in your mind.
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 x 5 = 15 ) Add 180 + 15 = 195.