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                  Š When a number is multiplied by 100, we put two zeros to the right side of the number.
                  Examples: (a) 643 × 100 = 64300  (b) 8572 × 100 = 857200

                  Š When a number is multiplied by 200, 300, 400, ..., 900, we multiply the number by 2, 3,
                  4, ..., 9 respectively and then put two zeros to the right side of the product so obtained.

                  Examples: (a) 78 × 400 = 31200  (b) 273 × 800 = 218400
                  Š When a number is multiplied by 1000, we put three zeros to the right side of the number.

                  Examples: (a) 15 × 1000 = 15000  (b) 198 × 1000 = 198000
                  Š When a number is multiplied by 2000, 3000, 4000, ..., 9000, we multiply the number

                  by 2, 3,  4, ...,  9 respectively and  put  three zeros to  the  right side  of the  product  so
                  obtained.

                  Examples: (a) 24 × 3000 = 72000  (b) 571 × 7000 = 3997000
              Multiplication of Large Numbers


              Larger numbers are multiplied  in  the same way as smaller  numbers. To  multiply  large
              numbers, we follow the following steps.
              Step 1: Write the numbers in column.                           The number that is to be multiplied

              Step 2: Start multiplication from the ones place.              is called the multiplicand.
                                                                             The number by which we multiply
              Step 3: Move to the tens place,                                is called the multiplier.
                       hundreds place and so on.                             The result  of the  multiplication  is
              Step 4: Add the carry over if any.                             called their product.

              Example 1: Multiply the following.

                    (a)  6172 by 435                                 (b)  4567 by 2315
              Solution:

                    (a) Step 1: Expand the multiplier.
                                  435 = 400 + 30 + 5

                         Step 2:  Multiply by the ones.
                                                                       TL L TTh Th H T O
                                  6172 × 5 = 30860                                  6   1   7   2

                         Step 3:  Multiply by the tens.             ×                   4   3   5        400 + 30 + 5
                                                                                3   0   8   6   0        6172 × 5
                                  6172 × 30 = 185160                       1    8   5   1   6   0        6172 × 30

                         Step 4:  Multiply by the hundreds.         + 2    4    6   8   8   0   0        6172 × 400
                                                                       2   6    8   4   8   2   0
                                  6172 × 400 = 2468800

                         Step 5:  Add all the partial products.

                                  30860 + 185160 + 2468800 = 2684820

                         Thus, 6172 × 435 = 2684820


              Mathematics-5                                                                                          37
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