learning table of 9 in seconds.

This post is really interesting to write as we all must have struggled in our childhood while learning tables or youngs student must be ....as its tedious task to learn so many tables....so here we have some techniques or ways to solve tables in less time.

The First case.

The annexed table of products produced by the single digit multiplier 9 gives us the necessary clue to an understanding of the sutra:

The meaning of the sub corollary thus fits in smoothly I.e, that the multiplicand has to be decreased by 1 and as for the right hand side , that is mechanically available by the subtraction of the left hand side from 9 which is practically a direct application of the Nikhilam Sutra.

● 9 x 2

(2-1)/(9-(2-1))

1/9-1

1/8

18 answer.

● 9 x 3

(3-1)/9-(3-1)

2/7

27 answer.

The second case::

● 11 x 99

(11 - 1)/99-(11-1) = 1089

● 12 X 99

( 12-1)/99-(12-1)=1188

And so on.....

Keep learning keep smiling 😊😊

Multiples and Sub - Multiples

This is the continued part of previous post I.e, Multiplication. 

How to solve numbers with minimal calculations or mentally .Here we will discuss some more cases , where numbers are just half the base(10)

Or we can say near 5,50,500,5000,50000 etc.

Case 1.

41 x 41

Here we will take base as 50 (100÷2)

41-9

41-9

---------

41-9/9×9

32/81

But as we have assumed base as 50 because numbers are closer to 50. Base 50 is half of 100, so we will divide the answer by 2.

32÷2/81

16/81

= 1681 is answer.

       Or

Another way to solve the same problem .

41x41

Assume base as 10 

10 x 5=50

41-9

41-9

---------

32/81

X 5/

---------

160/81

As we have taken base 10 . So 8 will be carried over.

168/1

1681 answer. 

Why we have multiplied the above with 5. So if u are wondering then the answer is because we have taken the base as 10 and the number are closer to 50 base and to make it 50 we have multiplied it by 5.  Thus we have to multiply the answer  by 5.

 Or

Another way if you want to assume base as 40 because numbers are 41 x 41

Then 10 x 4= 40

So,

41 + 1

41 + 1

----------

41+1/1×1

42/1

×4

--------

168/1

1681 answer. 

EXAMPLE::

1. 49 x 49

Working  base 100/2

49-1

49-1

--------

48/01

÷ 2

----------

24/01=2401

  Or

Working base 10x5

49-1

49-1

-----------

48/1

×5

-----------

240/1

2401 answer.

Example 2

23 x 21

Working base 10 x 3= 30

23 - 7

21 - 9

-------------

23-9/ 7x9

14/63

×3

-------------

42/63

6 will be carried over because of base 10 

48/3

483

Or

Working base 10x2

Then

23+3

21+1

---------

24/3

×2

--------

48/3

483 answer.

● Direct short cut for square. Using the first corollary which is arising out of the 'Nikhilam ' Sutra means : whatever the extent of its deficiency, lessen it still further to that very extent and also set up  the square of that deficiency. 

 A. 9x9 

9-1

9-1

-------

9-1/1×1

8/1

81

B. 7 x 7

 (7-3)/3^2

4/9=49

C. 11^2 = (11+1)/1^2=121

D. 12^2=(12+2)/2^2= 144

E. 13^2 =(13+3)/3^2=169

F. 14^2 =(14+4)/4^2= 18/16=196

G . 15^2 =(15+5)/5^2= 20/25=225

And so on.....

In the next post we will learn how to write table quickly ... by using simple techniques  of the same sutra....rather than memorizing it....

Keep learning. Keep smiling 😊😊😊

 

Multiplication ( Traditional versus Vedic mathematics approach )

 MULTIPLICATION (  Short - cut )

The first impression we all have when we have to do multiplication of long numbers or many digits like  88 x 88 ...91 x 57 .....75 x 75....1243 x 987 etc...is where is paper and pen or calculator. 

But by using sutras from vedic mathematics we will learn to do such calculations in few minutes that to be orally or minimal calculations and the plus point is we don't have to learn tables...we just need to know basic tables till 9.

1. To find the squares ending with 5

     a.  25 x 25 = 625

     Process is first number multiply first number         plus 1 and multiplication of last two 5.

       2 × (2+1) / 5×5

       2 × 3/ 25

        625

      

    b.   35 x 35 = 1225 

           3 x ( 3 + 1) / 5×5 = 1225

    C. 45 x 45 = 2025

         4 x ( 4+1) / 5 x 5 = 2025

         And so on.............

2. To Multiple ( using  vedic sutra Nikhilam Navatascaramam means all from 9 and last from 10)

Single digit numbers    

   a.  9 × 7

  ● Suppose we have to multiply 9 by 7.

    We should take as base for our calculations,          that power of 10 which is nearest to the                    numbers 

      (10) 

      9 - 1

      7 - 3

    Now subtract the base 10 from the sum of given number I.e ( 9 + 7)

  So 16 - 10 = 6

    Or  

 Subtract the sum of two deficiencies ( 1+ 3) from base 10

     10 - 4 = 6

     Or

 Cross subtract deficiency 3 on the second row from the original  no. 9

   9 - 3 =6

   Or 

Cross subtract in the converse way 

   7 - 1 = 6

Result will be same

● Now , Vertically multiply the two deficit figures ( 1 and 3 ) . The product is 3. And this is the right hand side portion of the answer .

     Thus 9 × 7 = 63

     (10) 

      9 - 1

      7 - 3

     -----------

   9+7 - 10 / 1× 3

   16 - 10 / 3

     63 Answer.

   

b.    8 × 6

      Assuming base 10

        8 - 2

        6 - 4

     -------------

    8+ 6 -10/ 2×4

    = 48 answer

      Or

    8-4 /2×4

   = 48

This proves the correctness of the formula .The algebraic explanation for this is very simple:

 ( x - a) (x - b )= x ( x - a - b) + ab

 C.  7× 6

     (10)

     7 - 3

     6 - 4

  ------------

   3/ 12(4×3)

 As you can see product is of double digit and we have taken the base of 10 . So in this case we will only keep unit digit  I.e 2 and 1 will be carried over to the left 

 Thus 

(10)

     7 - 3

     6 - 4

  ------------

   3/ 12(4×3)

   3+1/ 2

 =    42 answer

Double  digit numbers.

 

a. 91 × 91

Here we will take 100 as base.

 91× 91

91 - 9

91 - 9

------------

91-9/9×9

82/81

= 8281 answer

b. 88 x 98

88 - 12

98 - 2

------------

88-2 / 12 ×2

86/24

= 8624 

c.  56 × 98

56 - 44

98 - 2

-------------

56 - 2 / 44x2

54/88

=5488 answer.

d. 25× 99

25 - 75

99 - 1

-----------

25 -1 / 75x1

2475 

= 2475 answer.

e.  88 x 91

88 - 12

91 - 9

--------------

88-9/ 12 x 9

79 / 108

 As we have taken 100 as base . So we will keep two place values on right side and carry the surplus digit over to the left.

 88 - 12

  91 - 9

--------------

88-9/ 12 x 9

79 / 108

79 +1 /08

80/08

 = 8008 answer.

Three digit numbers we will take base as 1000 and four digit numbers we will take base as 10000. And so on....

 Now if we have to multiply 

Special cases:::

a. 12 x 11

In this case we will take base as 10 as it is nearest to 10 but no. Is more so.

(10)

12 + 2

11 +1

-----------

12+1/2×1

132

= 132 answer

b. 17×12

17 + 7

12 + 2

------------

17+2/7×2

19/14

So again carry forward

19+1/4

=204 answer.

c. 12 x 8

12 +2

8 - 2

----------

12-2/2×(-2)

10/-4

= 96    (10/0 - 4)=96

 d. 108 x 97

108 + 8

97 -3

-------------

108-3/ 8 x ( -3)

105/ -24

105 /00

-        24

---------------

104/76

10476 answer

e.  1033 × 997

Take base as 1000

1033+33

997 - 3

-----------------

1033 -3 / 33x(-3)

1030/ -099

We have taken 0 because base is 1000 . So instead of 33 x 3 = 99 ...we have written 099

1030/000

-         099

------------------

1029/901

= 1029901 answer.

 

    

   

     

 

Vedic Mathematics

My first impression while writing about this topic was Vedic mathematics must be maths used during vedic period ....I think many will have such impression when u just read the topic...

But...........

VEDIC MATHEMATICS  is a book written by Indian monk Jagadguru Swami Sri Bharati Krishna Tirtha Sankaracarya of Govardhan Matha, Puri.

● His vast and versatile learning, his spiritual and educational attainments, his wonderful research achievements in the field of Vedic mathematics and his consecration of all these qualifications to the service of humanity as such. 

● His Holiness, better known among his disciples by the beloved name 'Jagadguru ' or ' Gurudev' , was born of highly learned and pious parent in March, 1884.

● Jagadguru, named as Venkatraman in his early days, was an exceptionally brilliant student and invariably won the first place in all the subjects throughout his educational career. He was awarded the title of ' SARASWATI' by the Madras sanskrit association in July, 1899.

● His public life under the guidance of late Hon'ble Sri Gopal krishna Gokhale , C.I.E in 1905 in connection with the National education Movement and the South African Indian issue. 

● His inclination towards Vedas was very much and the definition of Veda given by Sri Swami ji is.

" The very word 'VEDA' has this derivational meaning I.e. the FOUNTAINHEAD and ILLIMITABLE store house of all the knowledge "

VEDAS:

The vedas are wellknown as four in number 

1. Rigveda 

2. Samaveda 

3. Yajurveda 

4. Atharvaveda 

And have four Upavedas and the Six Vedangas.

● Swami ji naturally regarded mathematics or the science of calculations and computation to fall under this category. The Sixteen sutras on which the vedic mathematics is based form part of a Parisista of the Atharvaveda. 

1. Ekadhikena purvena 

     Meaning::  By one more than the previous 

 Very useful in finding the products of number .

2. Nikhilam Navatashcaramam Dashatah

     Meaning:: All from 9 and last from 10

3. Urdhav-Tribhagyam

    Meaning:: Vertically and crosswise

4. Paravartya Yojayet

    Meaning:: Transpose and adjust 

5. Sunyam Samyasamuccaye

    Meaning:: When the sum is same .That the                              sum is zero.

6. Anurupye Sunyamanyat

     Meaning:: If one is in the ratio the other is               equal to zero. This also used to                                 solve algebraic equations. 

 7. Sankalana vyavakalanabhyam

     Meaning:: By addition and subtraction. Mainly                          used for algebraic equations. 

 8. Puranapuranabhyam

     Meaning:: By completion and non completion. 

 9. Chalana kalanabhyam

     Meaning:: Difference and similarity. Mainly                                used in calculus to find square                                  roots of quadratic equations. 

10. Yavadunam

      Meaning:: Whatever is the extent of its                                       deficiency .

11. Vyastisamastih

      Meaning:: Part and whole. 

12. Sesanyankena Caramena

      Meaning :: The remainder by last digit.

13. Sopantyadvayamantyam

       Meaning:: The ultimate and twice the                                          penultimate. 

14. Ekanyunena Purvena 

       Meaning:: By one less than the previous. 

15. Gunitasamuccayah

        Meaning:: The product of the sum is equal                                 to the sum of product 

16. Gunakasamuccayah 

        Meaning:: The factor of the sum is equal to                               the factors.

Swami ji wants " Mathematics without tears " and using these sutras your mental calculations will definitely increase and u don't have to learn squares or use long traditional methods of multiplication and division and much more......

 

 Keep smiling and keep learning..😊😊😊

IMPORTANCE OF NUMERACY

In my last post we have discussed the basic definition/meaning of Numeracy .

Now we will definitely talk about its importance and   WHY IS IT IMPORTANT TO LEARN THIS SKILL....and if not then how it will affect our life or we can say our daily life without this skill....

WHY is the problem of numeracy so hard to tackle?

Numeracy has been a problem for quite sometimes , the question we must ask ourselves ...are we stuck with the problem or there are ways to solve it...

Research shows that :::

● Fear of maths

● Lack of confidence 

● Dislike of classroom based teaching .

plays  a major role in preventing adults with poor numeracy skills.

There are evidence of low numeracy skills 

which are impacting economy; individuals earning/wages; employment; personal finances.

All economic studies shows numeracy is very important, when it comes to jobs

According to the SKILLS OF LIFE survey( National strategy in England) shows how low numeracy have been a long term problem for the U.K

Numeracy percentage in 2003 was 26% and 2011 was 22 % which is getting worse not better.

They have definitely comeup with practical approaches and targeting 95% skill level by 2020.

 OECD  (Organisation for economic co-operation and development) is an international organisation that works to build better policies for better lives and promote world trade and improve global economy has a survey regarding numeracy  and literacy skills .

POOR  NUMERACY  IS  A  PROBLEM  WE  MUST TACKLE  NOW . 

As High Numeracy skills are better for ::

😊😊😊😊

 

NUMERACY

What is NUMERACY......

Why INDIA aims to achieve universal fundamental numeracy by 2025......

These are question which will definitely strike in ur mind with new education policy which has changed the whole prospective of Indian education.

So here we present Numeracy which is integral part of our life.....

NUMERACY is the skill / ability to use numbers and mathematical approaches in all aspects of life not just doing simple addition and subtraction but is very important for individuals to develop logical thinking and reasoning strategies  in their every day life(from new born to professional).

Basic Skills::

Addition, Subtraction,counting ,sorting ,recognising shapes , using comparative ( short and tall), or superlative(shortest and tallest).etc..

Interpret data, charts, graphs...

Make sense of numbers , time, patterns , reading receipts , paying Bills etc...

HOW TO IMPROVE OUR BASIC SKILLS

-Ask open ended question.

-Use manipulatives

-Use hands on 

-Think about thinking 

-Personalise your child 's learning experiences.

-Make your child involve in day to day household or anything u do.

    For example

Give me two tomatoes. 

Change ur tone while using big or small, empty or full etc.

I hope now we can understand our National Mission of Numeracy according to new education policy and its importance. 

 Keep smiling...

Keep using your numeracy skills and educating our future generations......😊😊

WE REVOLVING AROUND MATHS....

We revolving around maths and maths revolving around us.

If we just look around us we will see how we are surrounded with the magic of numbers. 

From the tooth brush to needle everywhere . 

Rather than considering Maths as subject which really stops our heart beat and seeing numbers ,fraction ,geometry gives us heart attack or numb our hand.

Just feel it once.....

While making ur favourite dish.

Cleaning your floor.

Walking around your house.

In the park 

While dressing up  .

your favourite ice cream.

Girls  ur make up box

Boys ur cricket kit or any sports.

How everything is associated with the magic of numbers.....which we call maths.....

We are surrounded with shapes, area , Perimeter, Ratio and Proportion etc.

Even while sharing pizza we are using fractions.

Cooking food you are using ratio and Proportion without knowing....

Just want to concluded with my first ever post rather than considering it as a subject which you always want to escape.Feel it once,visually it...

These skills are very important for your career.

Whether you want to be a doctor, enginner ,chef, painter, artist anything and everything. 

See you..

Keep smiling..