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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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