Play with numbers

Think of a two digit number, say 42, then subtract the reverse of its digits, 24, from 42

42-24 =18

hence 18 is product of 9 

also 1+8=9

Choose any two digits number and for each one reverse the digits and subtract the smaller number from the larger.  Look at all the answers you get.  Do they all have a common divisor?  What do the digits sum to each time?  

Some Examples:

92-29 =63

hence 63 is product of 9 

also 6+3=9

41-14 =27

hence 27 is product of 9

also 2+7 =9

83-38 =45

hence 45 is product of 9

also 4+5 =9

You see how fascinating and enjoying it is. In each case the difference is divisible by 9 (i.e. the common factor is 9) and the sum of the digits of the difference is always 9.

Vedic Maths Squaring - Fast Version

 

Vedic Maths Squares - Numbers NOT close to 100 

 

 

 

 

 

Square of Number

How to know if the number is prime or not?

Fastest way to square three digit numbers

Quickest method to find square root.

All from nine and the last from ten

All from nine and the last from ten

 Nikhilam Navatashcaramam Dashatah or "All from nine and the last from ten"

1000-357               =            (9-3)(9-5)(10-7)                                 =            643

1000-64                =            1000-064 = (9-0)(9-6)(10-4)             =            936

1000 -908             =             (9-9)(9-0)(10-8)                                 =            092

1000 -343             =             (9-3)(9-4)(10-3)                                 =             657

10000- 435           =             10000-0435 =(9-0)(9-4)(9-3)(9-5)=            9564      

Magic of Nine

Magic of Nine

Multiply any number with 9, 99, 999,………….…

 999×384=383616

(second number -1)(subtract 9 from each of these new digits)
ie.( 384 -1) and (9-3)(9-8)(9-3)

999 x 454  = 453546

999 x 657 = 656343

9999 x  878 = 8779122

9999 x 658 =6579342

99999 x 548 = 54799452

999 x  999 = 998001

9999 x 1001 = 10008999

Multiplication of two digit numbers

Multiplication of two digit numbers

When tens digit are same and the sum of unit digits is 10

 

57x53    = 5 x 6 (100) + 21     = 3021

44 x 46  =  2024

62 x 68  =  4216

31 x 39  =  1209

84 x 86  =  7224

How it works

ab  x  cd
where
c=a
b+d=10

(a x10 + b)(c x 10 + d)
(a x 10 + b)( a x 10 + 10 - b)
100 a² + 100a – 10 ab + 10 ab+ 10b –b ²
100 a² + 100 a + 10b - b²
100 (a) ( a + 1 ) + b(10 - b)

100( a )(a+1)+bd

Simple Math Trick :Easy way to learn Table of 19

Easy way to learn Table of  19

19  x  n =                    2n-1      and        10 - n  

19 x 1  =  19                     2x1 =2 -1=1                      10-1  = 9

19 x 2  =  38                     2x2 =4 -1=3                      10-2   = 8
19 x 3  =  57                     2x3 =6 -1=5                      10-3   = 7
19 x 4  =  76                     2x4 =8 -1=7                      10-4   = 6
19 x 5  =  95                     2x5 =10 -1=9                    10-5   = 5
19 x 6  =  114                   2x6 =12 -1=11                 10-6  =  4
19 x 7  =  133                   2x7 =14 -1=13                 10-7  = 3
19 x 8  =  152                  2x8 =16 -1=15                  10-8   = 2
19 x 9  =  171                   2x9 =18 -1=17                 10-9   = 1
19 x 10  =  190                2x10 =20 -1=19                10-10 = 0

From 11  to  20

19  x  n =                   2n-2         and       10 - n  

19 x 11  =  209                2x11 =22 -2=20                10-1    = 9

19 x1 2  =  228                2x12 =24 -2=22                10-2    = 8
19 x1 3  =  247                2x13 =26 -2=24                10-3    = 7
19 x1 4  = 266                 2x14 =28 -2=26                10-4    = 6
19 x 15  =  285                2x15 =30 -2=28                10-5    = 5
19 x1 6  =  304                2x16 =32 -2=30                10-6    = 4
19 x 17  =  323                2x17 =34 -2=32                10-7    = 3
19 x 18  =  342                2x18 =36 -2=34                10-8    = 2
19 x1 9  = 361                 2x19 =38 -2=36                10-9    = 1
19 x 20  =  380                2x20 =40 -2=38                10-10    = 0

Double and Half Method

Double and Half Method

        The double and half method is used to make two numbers easier to multiply. The idea is you can double one number and half the other before multiplying.

         1)  35 x 24 =    35 x 2  x  24 ÷ 2   =   70 x 12 = 840.

Here 24 is divided by 2 and multiple that 2 with 35  to  make the figures easy to multiple orally

                The answer is 840.

         2)  57 x 22 =   57 x 2  x  22 ÷ 2  = 114 x 11 = 1254.

                The answer is 1254.

Here  22 is divided by 2 and  multiple that 2 with 57  to  make the figures easy to multiple orally

       3)   6 ¹/₄ x 96 =

         Multiply and Divide by 4.

          6 ¹/₄ x 4 x  96 ÷ 4  =  25 x 24 = 600.

        The answer is 600.

         4)   66 x 21 =

       Multiply and Divide by 6.

        66 ÷ 6  x  21 x 6 =  126 x 11 = 1386.

      The answer is 1386.

 

Divisibility Test of Numbers

Divisibility Test of Numbers 

Dividing By 2:      A number is divisible by 2 if the last digit is even.

Dividing By 3:     A number is divisible by 3 if the sum of all the digits is divisible by 3.

Ex [1]                 34,164 is divisible by 3 because 3+4+1+6+4 = 18 which is divisible by 3.

  To find the remainder of a number divided by 3, add the digits and find that remainder. So if the

digits added together equal 13 then the number has a remainder of 1 since 13 divided by 3 has a

remainder of 1.

Dividing By 4:     A number is divisible by 4 if the last 2-digits are divisible by 4.

Ex [1]                 34,164 is divisible by 4 because 64 is divisible by 4.

  To find the remainder of a number divided by 4 take the remainder of the last 2 digits. So if the

last 2-digits are 13 then the number has a remainder of 1 since 13 divided by 4 has a remainder

of 1.

Dividing By 5:   A number is divisible by 5 if the last digit is a 5 or a 0.

To find the remainder of a number divided by 5 simply use the last digit. If it is greater than 5,

subtract 5 for the remainder.

Dividing By 6:   A number is divisible by 6 if it is divisible by 2 and by 3.

Ex [1]               34,164 is divisible by 6 because it is divisible by 2 and 3.

Dividing By 7:   A number is divisible by 7 if the following is true:

1. Multiply the ones digit by 2.

2. Subtract this value from the rest of the number.

3. Continue this pattern until you find a number you know is or is not divisible by 7.

Ex [1]               7203 is divisible by 7 because

a) 2x3= 6.

b) 720 – 6 = 714 which is divisible by 7.

Ex [2]               14443 is not divisible by 7 because

a) 3x2= 6.

b) 1444 – 6 = 1438.

c) 8x2= 16.

d) 143 – 16 = 127 which is not divisible by 7.

Dividing By 8:   A number is divisible by 8 if the last 3-digits are divisible by 8.

Ex [1]               34,168 is divisible by 8 because 168 is divisible by 8.

Dividing By 9:   A number is divisible by 9 if the sum of the digits is divisible by 9.

Ex [1]               34,164 is divisible by 9 because 3+4+1+6+4 = 18 which is divisible by 9.

Dividing By 10: A number is divisible by 10 if the last digit is a 0.

Dividing By 11: A number is divisible by 11 if this is true:

Step1:               Add all even place digits  of a number

Step2:               Add odd place digits of a number

Step3:               Subtract 1st Step from the 2nd Step

If this value is 0 then the number is divisible by 11. If it is not 0 then this is the remainder after dividing by 11 if it is positive. If the number is negative add 11 to it to get the remainder.

Ex [1]               6613585 is divisible by 11 since (5+5+1+6) – (8+3+6) = 0.

Dividing By 12:   A number is divisible by 12 if it is divisible by 3 and by 4.

Ex [1]               34,164 is divisible by 12 because it is divisible by 3 and 4.

Multiplying And Adding Numbers

Multiplying And Adding Numbers In The Form: ab + bc

A. From algebra we can factor: ab + bc = b(a + c)

B. Using numbers instead of variables we get the following:

1. Take out the number that both sides have in common.

2. Add the remaining numbers.

3. Multiply the number in step 1 with the result in step 2 for the answer.

Ex [1] 15 x 12 + 15 x 8 =_________.

a) Rewrite in the form 15 x (12 + 8).

b) 15 x 20 = 300.

c) The answer is 300.

Ex [2] 16 x 16 + 16 x 17 =_________.

a) Rewrite in the form 16 x (16 + 17).

b) 16 x 33 = 48 x 11. See Double and Half.

c) 48 x 11 = 528. See Multiplying by 11.

C. Ex [2] uses a variety of different methods. This is just how I would do the problem,

but there are many different ways of going about solving this problem. This is up to

you.

 

Adding Squared Numbers Part 4

Adding Squared Numbers In The Form: a² + (10a)²

A. This method is very easy since from algebra we know:

a² + (10a)² = 101a²

B. Therefore, you square the smaller number, then multiply by 101 for the answer.

Ex [1] 14² + 140² =_________.

a) 14² = 196.

b) 196 x 101 = 19796.

c) The answer is 19796.

Ex [2] 31² + 310² =_________.

a) 31² = 961.

b) 961 x 101 = 97061.

c) The answer is 97061.

 

Adding Squared Numbers Part 3

Adding Squared Numbers In The Form: a² + (7a)²

A. This method is very easy since from algebra we know:

a² + (7a)² = 50a²

B. Therefore, you square the smaller number, then multiply by 50 for the answer.

Ex [1] 6² + 42² =_________.

a) 6² = 36.

b) 36 x 50 = 1800.

c) The answer is 1800.

Ex [2] 15² + 105² =_________.

a) 15² = 225. See Squaring a Number Ending in 5.

b) 225 x 50 = 11250.

c) The answer is 11250.

Adding Squared Numbers Part 2

Adding Squared Numbers In The Form: a² + (3a) ²

A. This method is very easy since from algebra we know:

a² + (3a) ² = 10a²

B. Therefore, you square the smaller number, then multiply by 10 for the answer.

Ex [1] 32² + 96² =_________.

a) 32² = 1024.

b) 1024 x 10 = 10240.

c) The answer is 10240.

Ex [2] 49² + 147² =_________.

a) 49² = 2401

b) 2401 x 10 = 24010.

c) The answer is 24010.

Adding Squared Numbers Part 1

Adding Squared Numbers In The Form: a² + (2a)²

A. This method is very easy since from algebra we know:

a² + (2a)² = 5a²

B. Therefore, you square the smaller number, then multiply by 5 for the answer

Ex [1] 11² + 22² =_________.

a) 11² = 121.

b) 121 x 5 = 605.

c) The answer is 605.

Ex [2] 25² + 50² =_________.

a) 25² = 625.

b) 625 x 5 = 3125.

c) The answer is 3125.

 

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