Division by 9

                                       Division by 9 is also very easy and you can do it very fast mentally

• 24 / 9 = 2 remainder 6

  The first figure of 23 is 2, and this is the answer.
  The remainder is just 2 and 3 added up!

• 42 / 9 = 4 remainder 6

  The first figure 4 is the answer
  and 4 + 3 = 7 is the remainder - could it be easier?

• 133 / 9 = 14 remainder 7

  The answer consists of 1,4 and 7.
  1 is just the first figure of 133.
  4 is the total of the first two figures 1+ 3 = 4,
  and 7 is the total of all three figures 1+ 3 + 3 = 7.

  See one more example

  1232 / 9 = 136 remainder 8

• 842 / 9 = 8₁2 remainder 14 = 92 remainder 14

  Actually a remainder of 9 or more is not usually
  permitted because we are trying to find how
  many 9's there are in 842.

  Since the remainder, 14 has one more 9 with 5
  left over the final answer will be 93 remainder 5

            See one more example

• 123456 / 9 = 136₁16₁ remainder 3 = 13717 remainder 3

       Answer in decimal

       Take  above example 123456 / 9 = 13717 remainder 3

       It is very very easy put decimal after 13717  write remainder 3 and repeat it again and again .

       13717 .3333333333333..   It is our required answer .

      With the help of this concept we can solve some other problems
      Take few examples
      1234/81     =  ????   It is  just   1234   we divide 1234  by 9 two times  and get required answer
                                                       9x9

                         =  136 ₁   remainder 1       =   137.1111111      =1 4₁.23456  =15.23456
                                 9                                     9                                

       362/63  =??????    362    =    3₁  0 remainder 2   =   4 0.222222  =   5.7460
                                     9x7                     7                         7

       489/45  = ?????   Apply little presence of mind here   ,Multiply  489 and 45  to 2
                       489x2    =  978  =    108remainder 6  =  108.66666   =   10.866666
                        45x2          90                  90                        10                            

                                                                                                  

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