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    E:\Working\Focus_Learning\Math_Genius_3_(11-09-2024)\Open_Files\CHAP_04
                 \ 12-Sep-2024               Surender Prajapati   Proof-5                     Reader’s Sign _______________________ Date __________

                  Step 4:  Add the numbers of boxes diagonally to find the                                      1  5  1 6
                           answer. While adding the numbers diagonally.                                          5     8  3

                           If the sum is of two digits, retain the ones and                               1     2     2
                           carryover the tens to next diagonal and add with                                 = 9   0    4 4
                           them.                                                                     2 + 5 + 1 +  1  0  4

                                Thus, 56 × 34 = 1904.                                                    0 + 2 + 8 =  1

                           practice time 4D

                  1.  Multiply the following:
                       (a)      H    t    O    (b)      th H t O         (c)     th H t O        (d)      th H t O
                                     2    1                     4 2                       2 3                     7 3
                             ×       3    4          ×          4 2            ×          5 6          ×          6 4

                             +                       +                         +                       +

                       (e)     th H t O        (f)      th H t O         (g)     th H t O        (h)      th H t O
                                    2 0 4                   3 4 3                     2 1 6                   2 7 3
                             ×          1 2          ×          2 2            ×          4 3          ×          2 7

                             +                       +                         +                       +

                  2.  Write in the columns and find the product.

                       (a)  14 × 22             (b)  31 × 16             (c)  73 × 52            (d)  29 × 64
                       (e)  234 × 12            (f)  264 × 31            (g)  174 × 42           (h)  365 × 22
                  3.  Multiply the following by using Lattice multiplication.

                       (a)  21 × 11 = _____             (b)  24 × 14 = _____             (c)  31 × 16 = _____

                  exploring Multiplication
                  Multiplying by expanding the bigger number

                  Example:  Multiply: (a) 67 × 5                            (b) 143 × 3
                  Solution:  (a)   Step 1: Write 67 as 60 + 7.              (b) Step 1:  Write 143 as 100 + 40 + 3.
                              Step 2:   Multiply each term of                     Step 2:   Multiply each term of

                                              expanded form by 5 and                      expanded form by 3 and
                                                                                          add products obtained.
                                              add products obtained.                     100 × 3 = 300

                               60 × 5 = 300                                                40 × 3 = 120
                                          7 × 5 = + 35                                       3 × 3 = +  9
                                                  335                                                       429
                  Thus, 67 × 5 = 335.                                       Thus, 143 × 3 = 429.

                  Mathematics-3                                                                                          77

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