Question

Work out the following multiplication.

12345679
         ×   9
                  

Use the result to answer the following question.

What will be 12345679 × 45?

Answer 1

                12345679
We have,          ×   9
                111111111 

Here, we observe that in the product all the digits are same i.e. 1, which is actually the unit digit of the product 9 × 9. Also, total of digits in the multiplier is 90°.

                                    12345679
We have to compute,           × 45
                                                    

Here, multiplier is 45 whose sum of digits is 9.

Thus, by conjecture we conclude that the product consists of digits 5 only as unit’s digit of 9 × 5 is 5

    12345679
∴           × 45
   555555555