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E:\Working\Focus_Learning\Math_Genius_3_(11-09-2024)\Open_Files\CHAP_03
             \ 12-Sep-2024  Surender Prajapati   Proof-5                                  Reader’s Sign _______________________ Date __________





              regrouping both Hundreds and tens
              If there are not enough ones and tens in minuend, we regroup both hundreds and tens.
              Example 3: Subtract 267 from 421.

              Solution:  Write the numbers in columns and follow the given steps:
                             Step 1: Subtract the ones. Step 2: Subtract the tens.                Step 3: Subtract
                             Since 1 < 7, regroup tens  Since 1 < 6. So, regroup  the hundreds.
                             and ones.                       hundreds and tens.                   3 hundreds –
                             2 tens 1 one = 1 ten 11  4 hundreds 1 ten                            2 hundreds
                             ones.                               = 3 hundreds 11 tens                 = 1 hundred
                             Now, 11 ones – 7 ones           Now, 11 tens – 6 tens

                                 = 4 ones                        = 5 tens

                                        H   t    O                       H    t   O                    H    t   O
                                            1   11                           11                            11
                                        4   2    1                       3    1   11                   3    1   11

                                    – 2     6    7                       4    2   1                    4    2   1
                                                                      – 2     6   7                 – 2     6   7
                                                 4
                                                                              5   4                    1    5   4
                             Thus, 421 – 267 = 154

              Subtraction with Zeros

              Example 4: Subtract 268 from 500.
              Solution:   Write the numbers in columns and follow the given steps:
                             Step 1: Subtract the ones.
                                       Since, 8 cannot be subtracted from 0. So, regroup                  H    t   O

                                      tens and ones. But there are no tens. So, first regroup                  9
                                      hundreds and tens and then tens and ones.                            4   10  10
                                      5 hundreds 0 tens = 4 hundreds 10 tens                               5   0    0
                                      Again, 10 tens = 9 tens 10 ones                                  – 2     6    8

                                      Now, 10 ones – 8 ones = 2 ones                                                2
                            Step 2: Subtract the tens.               Step 3: Subtract the hundreds.
                                      9 tens – 6 tens = 3 tens                 4 hundreds – 2 hundreds = 2 hundreds

                                            H   t    O                   H    t   O
                                                9                             9               Knowledge Desk

                                            4   10  10                   4   10   10            Aryabhatta, an
                                            5   0    0                   5    0   0             astronomer and
                                                                                                mathematician of
                                        – 2     6    8                – 2     6   8        India who introduced
                                                3    2                   2    3   2        'zero' in the 5th century.
                                       Thus, 500 – 268 = 232




              Mathematics-3                                                                                          53
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