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The Magic of Maths Tables

Maths is a beautiful subject!!


Let us start from tables 1 to 10
Divide them as even and odd number tables and explore the magic in each of them.
1,3,5,7,9
2,4,6,8,10
Let us examine the pattern of each of the even tables 2,4,6,8 first.

2's Table
2*1= 2
2*2= 4
2*3= 6
2*4= 8
2*5= 10
2*6= 12
2*7= 14
2*8= 16
2*9= 18
2*10= 20
Observe the one's place of mul products -- they follow the pattern 2,4,6,8,0 ..2,4,6,8,0 throughout!!

4's Table
4*1= 4
4*2= 8
4*3= 12
4*4= 16
4*5= 20
4*6= 24
4*7= 28
4*8= 32
4*9= 36
4*10= 40
Observe the one's place of mul products -- they follow the pattern 4,8,2,6,0 ..4,8,2,6,0 throughout!!

6's Table
6*1= 6 (6)
6*2= 12 (3)
6*3= 18 (9)
6*4= 24 (6)
6*5= 30 (3)
6*6= 36 (9)
6*7= 42 (6)
6*8= 48 (3)
6*9= 54 (9)
6*10= 60 (6)
6*11= 66 (3)
6*12= 72 (9)
Pattern one Observe the one's place of mul products -- they follow the pattern 6,2,8,4,0 ..6,2,8,4,0 throughout!!
Pattern two The sum of the digits of the mul products follow a pattern of 6,3,9..6,3,9 - marked in parenthesis - throughout the table!!


8's Table
8*1= 8 (8)
8*2= 16 (7)
8*3= 24 (6)
8*4= 32 (5)
8*5= 40 (4)
8*6= 48 (3)
8*7= 56 (2)
8*8= 64 (1)
8*9= 72 (9)
8*10= 80 (8)
8*11= 88 (7)
8*12= 96 (6)
8*13= 104 (5)
8*14= 112 (4)
8*15= 120 (3)
8*16= 128 (2)
8*17= 136 (1)
8*18= 144 (9)
Pattern one Observe the one's place of mul products -- they follow the pattern 8,6,4,2,0 ..8,6,4,2,0 throughout!!
Pattern two The sum of the digits of the mul products follow a decreasing pattern of 8,7,6,5,4,3,2,1..9,8,7,6,5,4,3,2,1 .. - marked in parenthesis - throughout the table!!


Beautiful isn't it??

Now , let's move on to odd number tables - starting from 3 to 9.
3's Table
3*1= 3 (3)
3*2= 6 (6)
3*3= 9 (9)
3*4= 12 (3)
3*5= 15 (6)
3*6= 18 (9)
3*7= 21 (3)
3*8= 24 (6)
3*9= 27 (9)
3*10= 30 (3)
3*11= 33 (6)
3*12= 36 (9)
If you sum up the digits of each mul product (marked within parenthesis) you can observe the pattern 3,6,9..3,6,9 repeating throughout!!!

5's Table
5*1= 5
5*2= 10
5*3= 15
5*4= 20
5*5= 25
5*6= 30
5*7= 35
5*8= 40
5*9= 45
5*10= 50
Observe the one's place of mul products -- they follow the pattern 5,0 ..5,0 throughout!!

7's Table
7*1= 7 (7)
7*2= 14 (5)
7*3= 21 (3)
7*4= 28 (1)
7*5= 35 (8)
7*6= 42 (6)
7*7= 49 (4)
7*8= 56 (2)
7*9= 63 (9)
7*10= 70 (7)
7*11= 77 (5)
7*12= 84 (3)
7*13= 91 (1)
7*14= 98 (8)
7*15= 105 (6)
7*16= 112 (4)
7*17= 119 (2)
7*18= 126 (9)
7*19= 133 (7)
7*20= 140 (5)
7*21= 147 (3)
7*22= 154 (1)
As you can observe the pattern marked in parenthesis, this is the only table that is really odd!!! Odd numbers are odd though :) We can see an alternating cos curve pattern (because it is in decreasing pattern - Cos 0 =1 and Cos 90=0 as you may know!) that dips from odd to even to odd and so on when we add the digits of the mul products.

The next is the 9 table which brings with it many patterns!!

9's Table
9*1= 9 (9)
9*2= 18 (9)
9*3= 27 (9)
9*4= 36 (9)
9*5= 45 (9)
9*6= 54 (9)
9*7= 63 (9)
9*8= 72 (9)
9*9= 81 (9)
9*10= 90 (9)
9*11= 99 (9)
9*12= 108 (9)
9*13= 117 (9)
9*14= 126 (9)
9*15= 135 (9)
9*16= 144 (9)
9*17= 153 (9)
9*18= 162 (9)
9*19= 171 (9)
9*20= 180 (9)
9*21= 189 (9)
9*22= 198 (9)
9*23= 207 (9)
9*24= 216 (9)
9*25= 225 (9)
9*26= 234 (9)
9*27= 243 (9)
9*28= 252 (9)
9*29= 261 (9)
9*30= 270 (9)
Pattern one - If you sum up all digits of the mul product they all tell you they are 9's table:)) This is throughout the table.

Pattern two - The one's place of the mul product decreases from 9 to 0 and ten's place increase from 0 to 9 as you traverse the table down from 1 to 10.
Of course this pattern slightly modifies from 11 onwards as you have to treat the hundreds and ten's place together as a single changing entity.
Did you think I multiplied hard to get until 9*30.... not at all. I diligently followed the pattern to fill up the mul product.
Isn't it really simple and beautiful??

Pattern three - Observe the mul product from 1 to 5 - and that from 6 to 10. The numbers from 6 onwards is the reverse of the mul product above it. Look for it below:
9*1=9 9*10=90
9*2=18 9*9=81
9*3=27 9*8=72
9*4=36 9*7=63
9*5=45 9*6=54
This pattern is only observable from 1 to 10 and not further down :)


Knowledge is bounty and each subject has it's own beauty. The magic in each number table demystifies the fact that you don't have to really mug up tables to remember them!! Please enjoy table reading by observing these patterns and you will start loving Maths tables:) They are no longer nightmarish!!! For more information continue to watch my ebook on "The Math Magic" coming up shortly.