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2Aug/094

Divisibility Rules including 7 and 13

Divisibility by 2: If its unit’s digit is any of 0,2,4,6,8.
Ex : 100 is divisible by 2 while 101 is not.

Divisibility by 3: If the sum of its digits is divisible by 3.
Ex: 309 is divisible by 3, since sum of its digits = (3+0+9) = 12 , which is divisible by 3.

Divisibility by 4: If the number formed by the last two digits is divisible by 4

Ex: 2648 is divisible by 4, since the number formed by the last two digits is 48 which is divisible by 4.

Divisibility by 5: If its units digit is either 0 or 5.
Ex: 20825 and 50545 are divisible by 5.

Divisibility by 6: If it is divisible by both 2 & 3.
Ex: 53256 is divisible by 6 because it is divisible by 2 as well as 3.

Divisibility by 7: If after subtraction of a number consisting of the last three digits from a number consisting of the rest of its digits the result is a number that can be divided by 7 evenly

Ex.: 414141 is divisible 7 as 414-141= 273 is divisible by 7

Many different ways to test divisibility by seven have been devised. Some are long and complex, a few involve rewriting the digits, and one even consists of a grid-like box. We have chosen one of the more simplistic versions even though in almost every case it is quicker to merely perform long division.

Divisibility by 8: If the last three digits of the number are divisible by 8.
Ex: 3652736 is divisible by 8 because last three digits (736) is divisible by 8.

Divisibility by 9: If the sum of its digit is divisible by 9.
Ex: 672381 is divisible by 9, since sum of digits = (6+7+2+3+8+1) = 27 is divisible by 9.

Divisibility by 10: If the digit at unit’s place is 0 it is divisible by10.
Ex: 69410, 10840 is divisible by 10.

Divisibility by 11: If the difference of the sum of its digits at odd places and sum of its digits at even places, is either 0 or a number divisible by 11.
Ex: 4832718 is divisible by 11, since:
(Sum of digits at odd places) – (sum of digits at even places)
= (8+7+3+4)-(1+2+8) = 11

Divisibility by 12: A number is divisible by 12 if it is divisible by both 4 and 3.
Ex: 34632
(i) The number formed by last two digits is 32, which is divisible by 4
(ii) Sum of digits = (3+4+6+2) = 18, which is divisible by 3.

Divisibility by 13:  Remove the last digit of a number. Multiply it by 4 and add it to the remaining truncated number.  Continue doing these steps until you reach a 2 digit number. If the result is divisible by 13, then so was the first number.

Example: 113945-->11394+20=11414-->1141+16=1157-->115+28=143 (since this number is divisible by 13, you can say 113945 is also divisible by 13)

You can go a step forward

14 + 12 = 26 is 2*13, so 113945 is divisible by 13.

Divisibility by 14: If a number is divisible by 2 as well as 7.

Divisibility by 15: If a number is divisible by both 3 & 5.

Divisibility by 16: If the number formed by the last 4 digits is divisible by 16.
Ex: 7957536 is divisible by 16, since the number formed by the last four digits is 7536, which is divisible by 16.

Divisibility by 24: If a number is divisible by both 3 & 8.

Divisibility by 40: If it is divisible by both 5 & 8.

Divisibility by 80: If a number is divisible by both 5 & 16.

Next in this series, based on your responses, we will share the divisibility rules of 17, 19, 23, 29, 31, 37, 41, 43, 47

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22Jul/090

Speed Multiplication by 111 : Vedic Maths

Multiplication of a number consisting of only ones with another number becomes very easy using Vedic Maths techniques.

MULTIPLYING A NUMBER BY 111
To multiply a two-digit number by 111, add the two digits and if the sum is a single digit, write this digit TWO TIMES in between the original digits of the number. Some examples:

36x111= 3996
54x111= 5994

The same idea works if the sum of the two digits is not a single digit, but you should write down the last digit of the sum twice, but remember to carry if needed. So

57x111= 6327
because 5+7=12, but then you have to carry the one twice.

For 3 digit numbers
Carry if any of these sums is more than one digit.
Thus 123x111 = 1 | 3 (=1+2) | 6 (=1+2+3) | 5 (=2+3) | 3

Similarly,
241x111 = 26751

For an example where carrying is needed

Say, 352x111=3 | 8 (=3+5) | 10 (=3+5+2)| 7 (=5+2)| 2
= 3 | 8 | 10 | 7 | 2 = 3 | 9 | 0 | 7 | 2
= 39072

(Because of the carries, it may be easier to do the sums and write the answer down from right to left.)

If you like this Vedic Maths Trick, please let us know.

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22Jul/090

Origin of Vedic Mathematics

Origin of Vedic Math or Vedic Ganit

At the beginning of the twentieth century, when there was a great interest in the Sanskrit texts in Europe, Bharati Krsna Swamiji tells us some scholars ridiculed certain texts which were headed 'Ganita Sutras'- which means mathematics. They could find no mathematics in the translation and dismissed the texts as rubbish. Bharati Krsna Swamiji, who was himself a scholar of Sanskrit, Mathematics, History and Philosophy, studied these texts and after lengthy and careful investigation was able to reconstruct the mathematics of the Vedas. According to his research all of mathematics is based on sixteen Sutras, or word-formulae.

-

Bharati Krsna wrote sixteen volumes expounding the Vedic system but these were unaccountably lost and when the loss was confirmed in his final years he wrote a single book: Vedic Mathematics, currently available. It was published in 1965, five years after his death. The term Vedic Mathematics now refers to a set of sixteen mathematical formulae or sutras and their corollaries derived from the Vedas.

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15Jul/090

Vedic Multiplication by 11

Speed Vedic Multiplication Trick

Vedic Multiplication by 11

Step 1.

Assume that there are two invisible 0 (zeroes), one in front and one behind the number to be multiplied with 11

say if the number is 234, assume it to be  0 2 3 4 0

Step 2.

Start from the right, add the two adjacent digits and keep on moving left

02340

Add the last zero to the digit in the ones column (4), and write the answer below the ones column. Then add 4 with digit on the left i.e. 3. Next add 3 with 2. Next 2 with 0.

0+4 = 4

4+3 = 7

3+2 = 5

2+0 = 2

So answer is 2574

Similarly,

36 x 11 = 0+3   |   3+6   | 6+0  = 396

74 x 11 =0+ 7 |  7+4 |  4+0 =  7  | 11 |  4 = 814   (1 of 11 is carried over and added to next digit, so 7+1 = 8 )
6349 x 11 = (0+6)  |  (6+3)   |   (3+4)   |   (4+9)  |   9+0 =  69839

This method works for all the number, no matter how long or short, times 11. Just try it yourself and get amazed at the simplicity of the concept.

In the next post will learn Vedic Multilplication by 111, 1111, 11111, and so on.

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13Jul/090

Vedic Maths Workshop

We are very pleased to announce that Quickermaths.com is conducting a workshop on VEDIC MATHEMATICS on this Sunday and Monday, 19th and 20th July, 2009

The workshop will be on VEDIC MATHEMATICS [quicker calculation techniques that would help you to increase your calculation speed tremedously sharpen your intellect. The seminar will be conducted by Prof. Vineet Patawari (B.COM (H), ACA, PGDM), a passout of the esteemed Indian Institute of Management, Indore. He has conducted various seminars and workshop in city schools and colleges. He is spreading the popularity of Vedic Mathematics worldwide through www.QuickerMaths.com

Seminar Details
Days & Dates - Sunday and Monday, 19th and 20th July, 2009
Time – 10.30 am to 1.30 pm on both days
Venue – BG-109, Sector - II, Salt Lake, Kolkata -700091
Fees – INR. 750 / Student (inclusive of charges for study material)
You can pay by Cash, Cheque or Demand Draft, payable at Kolkata (in favour of "Preksha Consultancy Private Limited")
The fee needs to be deposited on or before 17th July, 2009 (Friday) at BG-109, Sector - II, Salt Lake, Kolkata -700091.

The feedback from students from eminent colleges, specially students preparing for competitive examinations like CAT, GMAT, GRE, MAT, etc. is very encouraging and we are happy to see such acceptance of Vedic Maths: a great gift from the sages of India

For any clarification or further information, please feel free to call us at 033-40046740, or mail back.

Team Quickermaths.com
033-4004-6740
+91-98302-64971

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12Jul/093

Vedic Maths Subtraction

Learn Amazingly Fast Vedic Mathematics Subtraction

Very often we have to deduct a number from numbers like 1000, 10000, 100000 and so on.

This Vedic Maths Subtraction method found as sutra in ancient vedas, is given below is very useful for such subtractions.

Memory Trick: ALL FROM 9 AND THE LAST FROM 10

Use the formula all from 9 and the last from 10, to perform instant subtractions.

For example 1000 - 357 = ?      (subtraction from 1000)

We simply take each figure in 357 from 9 and the last figure from 10.
Step 1. 9-3 = 6
Step 2. 9-5 = 4
Step 3. 10-7 = 3

So the answer is 1000 - 357 = 643
And that's 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      (subtraction from 10000)

9-1 = 8
9-0 = 9
9-4 = 5
10-9 = 1

So answer is 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

Corollary: If last term is 0, keep that last term as 0 and subtract the last non Zero term from 10 .

Illustration: 10000 - 920 = 10000 - 0920 = (9-0) (9-9) (10-2) 0 =9080

Illustration: 100000 - 78010 = (9-7) (9 - 8 ) (9- 0) (10 - 1) 0 = 21990

If you like this vedic maths subtraction, please leave a comment.

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11Jul/090

Multiply 2 numbers, sum of whose unit places is 10

Vedic Multiplication: This method of multiplication which is from Vedic Maths will make it very easy to multiply two numbers when sum of the last digits is 10 and previous parts are the same

44 x 46 = (4 x (4+1))  | (4 x 6) = (4 x 5)  | (4 x 6) = 2024

*| is just a separator. Left hand side denotes tens place, right hand side denotes units place

37 x 33 = (3 x (3+1)) |  (7 x 3) = (3 x 4) | (7 x 3) = 1221

11 x 19 = (1 x (1+1)) |  (1 x 9) = (1 x 2)  | (1 x 9) = 209

As you can see this method is corollary of  "Squaring number ending in 5"

Also it can be extended such as

E.g. 1: 292 x 208.

Here 92 + 08 = 100, L.H.S portion is same i.e. 2

292 x 208 = (2 x 3) x 10 | 92 x 8  (Note: if 3 digit numbers are multiplied, L.H.S has to be multiplied by 10)

60 | 736 (for 100 raise the L.H.S. product by 0) = 60736.

E.g. 2: 848 X 852

Here 48 + 52 = 100,

L.H.S portion is 8 and its next number is 9.

848 x 852 = 8 x 9 x 10 | 48 x 52 (Note: For 48 x 52, use methods shown above)

720 | 2496

= 722496.

[L.H.S product is to be multiplied by 10 and 2 to be carried over because the base is 100].

Eg. 3: 693 x 607

693 x 607 = 6 x 7 x 10 | 93 x 7 = 420 / 651 = 420651.

Note: This Vedic Maths method can also be used to multiply any two different numbers, but it requires several more steps and is sometimes no faster then multiplying by hand. Thus try to use it where it is most effective

How do you like this Vedic Maths technique, please let us know. You can also share this with your friends.

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10Jul/090

Squaring number ending in five : Vedic Maths Trick

This is the most common, yet very interesting trick of Vedic Maths.  Using this technique you can find the square of any number ending in 5 very easily.  Given below is the step by step explanation of this Vedic Maths Method

Let us take a 2 digit number,

Say the number is a5 (=10a+5), where is the digit in ten's place

Square of a5= a x (a+1) | 25

For example,

452 = (40 + 5) 2, It is of the form (10a+b) 2 for a = 4

Giving the answer a (a+1) | 25 ( |     stands for concatenation}

i.e. 4  x  (4+1) | 25 = 4 x 5 | 25 = 2025

Similarly we can proceed for 3 digit numbers ending in 5

Few more examples:

952= 9 x 10 | 25 = 9025

1252 = 12 x 13 | 25 = 15625

5052 = 50 x 51 | 25 = 255025

Test yourself

Find out the square of 85, 245, 145, 35, 15, and 95?

Answer: 7225, 60025, 21025, 1225, 225, 9025

Please let us know if you like this Vedic Maths trick

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8Jul/090

Vedic Mathematics Course Outline

VEDIC MATHS COURSE

  1. Vedic Addition
  2. Vedic Subtraction
    1. "All from 9 and the last from 10"
    2. Various other methods
  3. Multiplication (inclusive of mental multiplication)
    1. "By one more than the previous one"
    2. Multiplication by 9, 99,  ( and so on), 11, 111, (and son on..)
    3. Base method of multiplication and many more
    4. "Vertically and crosswise (multiplications)"- criss cross method
  4. Part of Division (you will be amazed)
    1. "Transpose and apply"
    2. Special division cases
  5. Squaring (it's so simple) :
    1. More than 10 different methods will be discussed for different cases
  6. Square root of perfect squares and imperfect squares
  7. Cubing(using things differently)
  8. Cube Roots (by seeing only & not by working on it). Different methods for perfect cube and non-perfect cube
  9. Dates and calendar
  10. Magic Square
  11. Special mathematical tricks and techniques
  12. Application of vedic mathematics in trigonometry, geometry, algebra and calculus
  13. Value (finding and remembering) of fractions
  14. Checking the accuracy of different mathematical operations
  15. Differential calculus
  16. Solving an algebraic equation of one variable
    1. "Transpose and adjust (the coefficient)"
  17. Solving simultaneous equation and quadratic equation
    1. "If the Samuccaya is the same (on both sides of the equation, then) that Samuccaya is (equal to) zero"
    2. By the Paravartya rule
    3. "If one is in ratio, the other one is zero."
  18. Solving cubic equation
  19. Solving fractional equation
    1. "The ultimate (binomial) and twice the penultimate (binomial) (equals zero),"

The above course is just an outline. Lot of other topics, techniques, shortcuts will be part of  Vedic Maths. Mathematical games, puzzles, riddles, etc. are also included to make every kid sharp.

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8Jul/090

Benefits of Vedic Mathematics

Some interesting facts about Vedic Mathematics:

Helps students to get rid of math phobia and improve grades
Helps students solve mathematical problems about 15 times faster.
Helps in intelligent interpolation.
Reduces burden on the student as he/she has to know tables up to nine only.
Improves mental calculation.
Improves concentration as well as confidence.

Very simple, direct, totally unconventional, original and consummate

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