Page 64 - Start Up Mathematics_3
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Observe the pattern in the table of 11.

            1 × 11 = 11 (the product is 11, i.e., 1 written 2 times)

            2 × 11 = 22 (the product is 22, i.e., 2 written 2 times)
            3 × 11 = 33 (the product is 33, i.e., 3 written 2 times)



            9 × 11 = 99 (the product is 99, i.e., 9 written 2 times)
            10 × 11 = 110 (???)



                  10 written 2 times
                  10 10 = 1(0 + 1)0 = 110




                   add                                                                     1 1

              11 × 11 = 11 11 = 1(1 + 1)1 = 121                                        × 1 1
                                                                                           1 1
                                                                                   + 1 1 0
                          add                                                          1 2 1

            Similarly, 12 × 11 = 12 12 = 1(2 + 1)2 = 132 and so on.




                                     add

            What do you observe?
            To multiply a 2-digit number by 11 we follow the given steps.

              1.  Write the 2-digit number two times.

              2.  Add the middle two digits and keep the other digits as it is.  This gives the
                   product. If the sum of the middle two digits is 10 or greater than 10, then carry
                   1 to the digit to the right.

            Example 1:       Find 57 × 11.

            Solution:        1.  5 7 5 7                      (Write 57 two times)


                                    add
                             2.  5 (7 + 5) 7                  (Add the middle two digits)

                                    = 5 (12) 7                (12 is a 2-digit number)
                                       1

                                    = 5 (2) 7                 (Keep 2 and carry over 1)



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