Fun Numbers Part 1

A number is a mathematical object used to count and measure. A notational symbol that represents a number is called a numeral but in common use, the word number can mean the abstract object, the symbol, or the word for the number. There are certain numbers, when used for some operations gives interesting results. It is fun exploring such numbers. If these interesting numbers are kept in our memory it makes calculation easy for many problems

Let us first put in all the numerals ; 0 1 2 3 4 5 6 7 8 9

Let us take the case of 9 this is a wonder number. multiply any number with 9 and then take the sum of the digits of the result to one number, it will be a 9

2 x 9 = 18 : 1 + 8 = 9
7 x 9 = 63 : 6 + 3 =9
43 x 9 =387 : 3 + 8 + 7 =18 : 1 + 8 = 9
123 x 9 =1107 : 1 + 1 + 0 + 7 = 9

Take the case of this number 12345679  x 9 = 1111111111

Easy multiplication with nine

Example 1 : 785 x 9
Step 1 : Subtract the one's digit from 10 and it becomes the one's digit of the product here
10 - 5 = 5  : : 5
Step 2 : Subtract the ten's digit from 9 and add the one's digit to it to give the next digit
1 + 5 = 6: : 6
Step 3 : Subtract the next upper digit from 9 and then add the previous position digit of the number
9 - 7 = 2:  2 + 8 = 10 : :  0  {1} - carried forward
Step 4 : Here 1 is carried forward so 1 (065). Now Subtract 1 from the first digit , i.e 7 and add the carried forward 1
7 - 1 = 6 : 6 + 1 = 7 ::  72 + 8 = 10 : : 0 so 1 (5156)

Step 5 : 1 -1 = 0 :
Hence 1684 x 9 = 151560 +1 = 1:  1
9 - 8 = 1 : 

SO the product 785 x 9 = 7065

Example 2 : 1684 x 9

Step 1 : 10 - 4 = 6 :: 6

Step 2 : 9 - 8 = 1 : 1 + 4 = 5 :: 5

Step 3 : 9-6 = 3 : 3 + 8 = 11 : : 1     {1}- carry forward

Step 4 : 9 -1 =8 : 8 + 6 =14 : 14 + 1 = 15 :: 5