Basic Calculation-01

1. SQUARES OF THE NO HAVING 5 AT THE UNIT PLACE

25²  =  (2×3) × 100 + 25 = 625

35²  =  (3×4) × 100 + 25 = 1225

45²  =  (4×5) × 100 + 25 = 2025

55²  =  (5×6) × 100 + 25 = 3025

65²  =  (6×7) × 100 + 25 = 4225

75²  =  (7×8) × 100 + 25 = 5625

85²  =  (8×9) × 100 + 25 = 7225

95²  =  (9×10) × 100 + 25 = 9025

105²  =  (10×11) × 100 + 25 = 11025

115²  =  (11×12) × 100 + 25 = 13225

125²  =  (12×13) × 100 + 25 = 15625

2. MULTIPLICATION OF TWO NOS. HAVING 5 AT THEIR UNIT PLACES

(i) 35 ´ 45  =  [(3×5) ×100 + 25 ] + 1×50  = 1575  

     ↓     ↓                                         ↑

      3       5                                    ( 4  ̶  3)

(ii) 45 ´ 65  =  [(4×7) ×100 + 25 ] + 2×50 = 2925

     ↓     ↓                                         ↑

      4       7                                      ( 6  ̶  4)

(iii) 55 ´ 85  =  [(5×9) ×100 + 25 ] + 3×50 = 4675

      ↓     ↓                                          ↑

      5       9                                        ( 8  ̶  5)

(iv) 65 ´ 95  =  [(6×10) ×100 + 25 ] + 3×50 = 6175

       ↓    ↓                                            ↑

        6     10                                       ( 9  ̶  6)

(v) 45 ´ 85  =  [(4×9) ×100 + 25 ] + 4×50 = 3825

      ↓     ↓                                         ↑

       4       9                                      ( 8  ̶  4)

(vi) 75 ´ 105  =  [(7×11) ×100 + 25 ] +3×50 = 7875

       ↓      ↓                                            ↑

        7       11                                      ( 10  ̶  7)

(vii) 85 ´ 125  =  [(8×13) ×100 + 25 ] + 4×50 = 10625

        ↓     ↓                                             ↑

         8      13                                        ( 12  ̶  8)

(viii) 35 ´ 65  =  [(3×7) ×100 + 25 ] + 3×50 = 2275

         ↓     ↓                                         ↑

         3       7                                      ( 6  ̶  3)

(ix) 65 ´ 115  =  [(6×12) ×100 + 25 ] + 5×50 = 7475

      ↓      ↓                                             ↑

      6       12                                        ( 11  ̶  6)