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    E:\Working\Orange_Education\TouchPad_Maths_4\Open_Files\Chap_03\Chap_03
                 \ 10-Nov-2025  Bharat Arora   Proof-8                                     Reader’s Sign _______________________ Date __________

                MulTiPliCATion By 3-DiGiT nuMBErS

                Multiplying by a 3-Digit number Ending with Two 0s

                Let us learn how to multiply a number by a 3-digit number ending with two 0s (100,
                200, 300, ...). Observe the results of the following examples.

                  a.  57 × 100 = 5700                                   b.  438 × 100 = 43800
                  c.  48 × 200 = (48 × 2) × 100 = 9600                  d.  164 × 300 = (164 × 3) × 100 = 49200

                  e.  205 × 400 = (205 × 4) × 100 = 82000  f.  105 × 800 = (105 × 8) × 100 = 84000

                To multiply a number by a 3-digit number ending with two 0s, we write two 0s (00)
                at the end and multiply the number by the digit in the hundreds place.

                Multiplying by any 3-Digit number

                Example 1. Find 276 × 234.

                Solution.

                Step 1.  Multiply by the ones digit.
                           276 × 4 = 1104                                            TTh  Th  H T O

                Step 2.  Multiply by the tens digit.                                         2 7 6
                                                                                  ×          2 3 4         200 + 30 + 4
                           276 × 30 = 8280
                Step 3.  Multiply by the hundreds digit.                                 1   1 0 4         276 × 4
                                                                                         8   2 8 0         276 × 30
                           276 × 200 = 55200
                                                                                  +   5  5   2 0 0         276 × 200
                Step 4.  Add the products.
                                                                                      6  4   5 8 4         276 × 234
                           1104 + 8280 + 55200 = 64584

                Therefore, 276 × 234 = 64584.

                Example 2. Find 137 × 506.

                Solution.        TTh  Th  H T O                                      TTh  Th  H T O
                                          1 3 7                                               1 3 7

                               ×         5 0 6         500 + 0 + 6                 ×          5 0 6        500 + 0 + 6

                                         8 2 2         137 × 6            Or                  8 2 2        137 × 6
                                         0 0 0         137 × 0                     +  6   8   5 0 0        137 × 500
                               +  6   8  5 0 0         137 × 500                      6   9   3 2 2

                                  6   9  3 2 2

                Therefore, 137 × 506 = 69322.

                       50        Mathematics 4

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