BASIC MULTIPLICATION

The first item on the agenda is a new way to do basic multiplication: we shall multiply without using any memorized multiplication tables. Does this sound impossible? It is not only possible, it is easy.

A word of explanation, though: we are not saying that we disapprove of using tables. Most people know the tables pretty well;; in fact, perfectly, except for a few doubtful spots. Eight times seven, or six times nine are a little uncertain to many of us, but the smaller numbers like four times five are at the command of everyone> We approve of using this hard – won knowledge. What we intend to do now is consolidate it. Later in this chapter we shall come back to this point. Now we wish to do some multiplying with out using the multiplication tables.

Let us look at the case of multiplying by eleven. For the sake of convenience in explaining it, we first state the method in the form of rules:

MULTIPLICATION BY ELEVEN:

a)The last number of the multiplicand ( number multiplied) is put down as the right-hand figure of the answer.

b) Each successive number of the multiplicand is added to its neighbor at the right.

c) The first number of the multiplicand becomes the left-hand number of the answer. This is the last step.

In the Trachtenberg system you put down the answer one figure at a time, right to left, just as you do in the system you now use. Take an easy example, 633 times 11:

6 3 3 x 1 1 = The answer will appear under the 633,

one figure at a time, from right to left, as we apply the rules. This will be our form for setting up the work from now on. The asterisks above the multiplicand of our example will quickly identify the numbers being used in the each step of our calculation. Let us apply the rules:

First Rule : Put down the last figure of 633 as the right-hand figure of the answer: 6 3 3 x 1 1 = _ _ _ 3

Second Rule: Each successive figure of 633 is added to its right-hand neighbor.3 plus 3 is 6: 6 3 3 x 1 1 = _ _ _ 63

Apply the rule again, 6 plus 3 is 9: : 6 3 3 x 1 1 = _ _ _ 963

Third Rule: The first figure of 633, the 6, becomes the left-hand figure of the answer : 6 3 3 x 1 1 = _ __ 6963

The answer is : 6,963.

Multiplication Of Eleven With Longer Numbers

 

Longer numbers are handled in the same way. The second rule, “ each successive number of the multiplicand is added to its neighbor at the right,” was used twice in the example above; in longer numbers it may be used many times. Take the case of 721,324 times 11:     7 2 1 3 2 4   x   1 1

First Rule: The last figure of 721,324 is put down as the right-hand figure of the answer:

7 2 1 3 2 4  x  1 1= _ _ _ _ _ 4

Second Rule: Each successive figure of 721,324 is added to its right hand neighbor: 7 2 1 3 2 4  x  1 1 =_ _ _ _ _ 64

                                                                                                                            7 2 1 3 2 4  x  1 1 = _ _ _ _ _564

                                                                                                                            7 2 1 3 2 4  x  1 1 = _ _ _ _4564

                                                                                                                            7 2 1 3 2 4  x  1 1 =  _ _ _34564

                                                                                                                            7 2 1 3 2 4  x  1 1 = _ _ _934564

Third Rule: The first figure of 721,324 becomes the left-hand figure of the answer:  7 2 1 3 2 4  x  1 1=_ _ _7834564

The answer is:7,934,564.

           Try one yourself: 441,362 times 11.

When is ∏ day celebrated and why?

∏ day is celebrated on 14th March every year. In the American format, when the date is written, the month is written first followed by the date. For example 10th March will be written as 3/10. So in the American format, 14th March is 3/14 which is the value of ∏ corrected to two decimal places. Also 22nd July is celebrated as ∏ - approximation day as 22/7 is an approximate value of pi which we use in our calculations.

Value of ∏ then?

In the earlier days, the approximate value was used. The Indian text “Shatapatha Brahmana” gives the value of ∏ as 339/108 = 3.139. It was Archimedes who worked rigorously in estimating the value of pi. He made an estimate that ∏ = 3.1419. Later Liu Hui developed a quicker method to estimate the value of ∏ and gave the estimate as 3.1416. Many researchers are working on estimating the value of ∏. The current estimate of ∏ runs to 1,351,100,000,000 decimal places. This work was done by a famous Japanese mathematician, Yasumasa Kanada and his team. It is important to mention that Srinivasa Ramanujan in the year 1910, f found a method to compute the value of ∏, which could give its value up to 8 decimal places. This method was used as the base by Yasumasa Kanada to develop the quickest algorithm that computes the value of ∏. The value of ∏ is 3.14159265 correct to 8 decimal places.

Get to know Mathematics (Pi)

MEANING OF THE WORD Pi?

The word pi is derived from the Greek word for perimeter. It was coined by William Jones in 1707 and was popularized by Leonhard Euler in 1737.It is also known as circular constant, Archimedes constant or Ludolph’s number.

Techniques To Boost Your Brain Power

1. Practice pranayama and meditation

2. Develop positive mental attitude

3. Be with happy frame of mind

4. Feed your brain with negative ions spent most of your time in parka and open space

5. Eat a high protein and low calorie diet

6. Alcohol is an enemy of your brain

7. Drink more than your usual amount of water

8. Learn to alternate left and right brain dominance through nostril breathing

9. Silence saves your energy and increases brainpower

10. Brain gets stimulated in deep concentration

Principles Of Effective Learning

1. Concentration sustained attention-effective learning is by bringing our mind back every time it wanders over things.

2. Resolution learning takes place only when a person makes up his mind very firmly to learn.

3. Habit-concentration is a habit and habits are perfected by practice.

4. Interest-to create interest affirmation techniques will help.

5. Relaxation-concentration occurs most naturally when body and mind are relaxed.

6. Repetition learning takes place very effectively when it is repeated over many times.

7. The law of Spaced Learning – the materials to be learnt should be spaced over several days. This will be better remembered than materials learnt by practicing on one day. Daily practice should be a rule, either learning or acquiring a skill.

8. The law of over learning – read the material over and again to yourself silently and aloud you can repeat it several times without making a mistake.

9. The law of Whole learning – material should be studied as a whole rather than bit-by-bit.

10. The law of confidence – repeat the statement to yourself, Day by Day in every way I remember better and better

Main Aim To Develop memory And Concentration

1. I strongly believe that I have the potential for creative genius.

2. I firmly believe that the only competition worthy of me is with myself, no one is superior to me, no one is inferior to me, I am what I am.

3. My time is the precious currency of my life, which I utilize most productively and creatively.

4. I shall seal the dead past not to worry about the unborn future but live and enjoy the realistic present.

5. I strongly endorse the view that success is not just money or position in essence it is the total fulfillment of our innate potential.

6. I shall become so engrossed in a project that I simply cannot allow myself to become ill or indisposed.

7. I shall reach and maintain alpha waves of mental state and thereby generate creative ideas most of the time.

8. I shall cherish an ideal-and devote myself for its realization.

9. I shall enjoy whatever I do not finish any project within the stipulated time frame.

10. I am the maker of my own destiny and always try to be happy and cheerful.

About Basic Maths

Learn simple easy methods to perform complicated multiplications and divisions with our easy tips taught in here.The best method for high-speed multiplication,division,addition,subtraction and square root-without a calculator. Keep checking us daily as new content is being added.