Page 18 - WCS - Electrical
P. 18

WORKSHOP CALCULATION & SCIENCE  - CITS



           Assignment
           1  Convert the following into improper fractions.
                      2 2
                    2
                                                          3 3
                     = __________
                                                          3
                                                       7
              a       1 1   2 =  __________              7 7  + + 3 =  _________
                       __________
                  12
                     =
                                                            = _________
                                                       7
                    12
                       __________
                   7 7 2 =
                                                        + 3
                                                              _________
                       __________
                                                          4 4 3 =
                                                              _________
                   1 1 7 2 7 = = __________            7  7 8 8  7 + 3  = _________
                  1   2 =
                       __________
                                                       7
                  1
                   7 =  __________                     8 + 3 =+ + 4 3 4 = = _________
                                                              _________
                                                       8  7
                       __________
                  17
                   3 3 7 =
                                                              _________
                                                      8 +
                                                          4 =

                   3   2
                     = __________
              b      4   3 7 2  = = __________    2      8 8+ 4 4 = 3 3 _________   7  3
                  4 4   3 7 2

                       __________
                                                      3 38  7 7
                                                         4 44 3 3
                     =
                   43 2 1
                     = __________
                       __________
                  1
                                                         4 4 3
                                                       7
                  1
                       __________
                                                             3
                     =
                 4   3 = = 2
                       __________
                   5 = __________
                  4 1 5 5 3 = __________  1 7  =  __________ 3 = _________       +  =  _________
                                                              = _________
                                                      3 8  7 +
                                                              = _________
                                                       + + 4 =+
                                                                _________
                                                           + + 3_________
                                                      3
                     = __________
                  4 5 3 7   2 7
                                                        +
                       __________
                                                            =
                                                                _________
                                                       + 4 + 37
                                                              = _________
                                                           +3 =
                  4 7 1
                                                         5 5 4 + 3
                   5 = __________
                                                      3  3
                      =
                                                                _________
                   5 5 7
                       __________
                                                             8 8 3 =
                                                      5 5  3 + 4 48
                                                       8  7
                                                          43
                       __________
                                                             8 _________
                        __________
                   3 3 = 2 =
                                                             =
                                                              =_________
                                                      5 + 448 +
                                                      3 +
                  3 3   3 5 3 1
                                                                _________
              c      4 1  = ___________     3          1 1 55+ 55 5  3 8  7 5 + 4 8 = = _________  8  4
                   37 3
                                                        + 5 4
                                                           + 8 3 _________
                     = _________
                                                         5 + 3 =+ 4 3 =+
                      =
                       __________

                                                                _________
                  3   3 5 3 7
                                                     5 + 8
                       __________
                     =
                                                         +
                                                            7 78 _________

                                                           + 8 =
                                                              =_________
                   33 3   2 =
                     = __________
                  4 4
                   5 5 3 =__________
                       __________
                                                                 7 7
                                                        8_
                 4 7
                     =
                                                        7 4
                                                            78 3 3
                                                       3
                                                         4 3
                       __________

                                                                 7
                   5 = __________
                 3   3 = = _________
                   1
                                                                   = _________ 3
                     = ___________

                  3 4   3 = __________    4  5  =  _________ + + 4 4 4  + + = 3 3 7 =  _________  4  3
                                                       1 55  3 8
                                                          1 1 7 8 3
                  3 5 3 5   3 5
                                                     6 6   1 55   3
                       __________
                   5 = __________
                      =
                                                              + = ___
                                                                   =______
                                                          17 3 _________
                                                        + + =+ +
                                                     6   1 43 +
                  3 5 4

                       __________
                                                               37 _________
                                                      61 +
                                                                    _________ +
                       __________
                                                          1
                                                                     _________
                                                           12 7 + 77 =
                                                                 9 9 7 =_____
                 3 5 5   7
                                                                3 ____
                                                           12 = 3
                        __________
                   4
                   12 5 = 3 =
                                                           12 3+ _________
                                                                    _________
                   12
                                                                 9 =
           2  Convert the following into mixed numbers. 6   1 + 55  3 8 55 4 4 1 + ++   4 1+ ++ 43  + 785 1 8  +3 3 9 7 _________  5 +  8  =  _________
                                                           7 + 3 8
                                                          4 4
                                                                   = _________
                                                     6
                   12 5 3 4 5 3

                        __________
                                                                     _________ 5
                      =
                                                                 7 =

                                            3
                                                          112 =+
                                                     6 4 1 +
                                                     5
                     = __________
                                                     6 5
                   12 5 3
                                                          1 8
                       __________
                     = 5
                                                           12 + 3
                                                                    _________
                                                                9 =
                                                               3 _________
                                                      4 +543 +
                       __________
                   3
                   12 = __________
                                                           12 3+ =+
                  12 3 3 =
                  3
                                                       4 1+ 12
                   12 = 5
                                                     6 4
                  3
                                                       5
                       __________
                                                        + 5
                                                            + 8
                  11 = __________

                  11 = __________
                                                                 _________
                  11 = __________
              a   12 5   3 5 = __________  3  5  =  __________ 4 5 7  = 9 9 =  _________  7  7
                  4
                      __________
                                                                 9 7 7
                                                         4 1 5 1
                  3   3 =
                                                           12 7 8
                                                                               1

                     = __________
                  12 =

                                                                 9 7
                       __________
                                                           2 2 12 7 3
                      =
                                                        4 4 4 1  3
                  11 5 3
                        __________
                                                        4 1 5 6
                                                                   = _________
                   5
                                                                 7 =
                                                           27 8 3+
                                                         − − 2 +
                  11 3 5
                                                                    _________ 6
                                                             = _________
                                                                    _________
                                                               3
                        __________
                                                              _________
                                                     6
                  11 = 3 =
                                                     6
                  11 __________
                                                             = 3+ _________
                                                         −2 1 7 =+
                                                                     _________
                                                        4 1+ 1 +
                                                                  = 7
                                                        +
                                                                   =
                  36 3 5 =  __________     12        6  4  4 4   1 + + + 1 5 1 1 5  = 3+ _________  + 1 12  +  3 9  =  _________
                                                              _________
                        __________
                  11 =
                                                                 97 9
                                                       5 5  4 − 2 12 124
                                                           5 5 2 = 7
                   36  12
                                                               _________
                  12
                                                                     _________ 4
                                                      4 6
                                                                 9 3
                   36 5
                                                                    =
                                                           5 = +
                  12
                                                           12 8
                                                       4 4   5
                  11   3
                                                             = _________
                                                       5 − 2 =− 12 71
                   12

                     = __________
                                                               _________
                                                                      _________
                       __________
                   36 = __________
                     = 5 =
                                                       5 4 6
                                                         − 5 2 1+
                                                                3
                                                                 9 7 =
                       __________
                       __________
                     = __________
                                                       5 −
                                                              _________
                                                       5− 5 1+ 124
                  3
              b  36 = __________             =  __________ 5 = + + 3 9  =  _________
                                                      6
                     36 = =
                    12
                  14 36 = __________
                       __________
                                                              _________
                  11 11
                                                           5 = 12
                                                       5 4
                  14  12
                      __________
                  36 = __________
                  11
                  14 = =
                                                       5 5 5  4 4 4
                                                            7 2
                  36 11 5 = __________    11           6   1    3 3 5 212  + 3 7 9 9 =  _________  4  2
                       __________
                                                          3 5 2
                                                       4
                  14 = __________
                  14  12 =
                       __________
                                                            = _________
                  14 11
                                                           2 1 =
                                                       5 5  4 + −
                                                            = _________
                                                       5 −
                                                            = _________
                                                              _________
                   18 ___________
                   18 = _________
                  14 =

                                                              _________
                   18 11

                                                              _________
                                                         −3 =− 2
                                                         − − 3 =− 4
                  36 36
                                                                  9
                     = __________
                   18
                  14  12
                                                       6 6  5 − 3 124 5
              c    18 11 = = __________    36  =  __________ 4 4 3 = 2 5 = _________  5  −  5  =  _________
                                                              _________
                       __________
                                                       5  5 4
                                                          5
                                                       5
                  14
                  36
                     =
                                                          5
                       __________
                                                       5 5 −
                                                          4 = =
                                                              _________
                                                               _________
                                                            = _________

                   36 =
                       __________
                                                       6 − 3 =− 55  4
                     18 = __________
                  10 18 =__________
                                                              _________
                                                       6 5
                                                         − 4 3 2 =−
                                                               _________
                       __________
                  10=
                       __________
                    36
                  10 = __________
                                                       6− 4 − 55
                                                              _________
                   18 = =
                                                               _________
                  14 14
                       __________
                                                       6
                                                          4 = =
                   10  36
                   18 11 = __________     14          6 − 4 =  _________
                                                            5
                                                        5
                      =
                  10 = __________
                  14
                                                           2
                  14
                                                       6 6 6  5 5 35
                       x x __________
                  11 10 = __________
                  11 10  36 = __________                6  5  4  3 3 4 3 5  1 1  1 1   5  3
                                                          4 3
                       x
                                                                  1
                  11 14

                                                             1 _________
                  10  18
                                                                     = _________
                                                       6  5 − −
                     = = x __________
                   1118 =
                                                            = =
                         __________
                         __________
                                                                      _________ −
                                                               − −_______
                                                                1 1 1
                                                     2 2   6 −
                                                                     =
                                                              __

           3  Place the missing numbers.   18  =  __________ 3 3 =_________         =  _________
                        18
                                                            − − 1 _________
                  11 10
                  13 11 = x11 18 14
                                                        − − 3 =−
                         __________
                     = x
                                                                      _________
                                                               −_____
                                                        −3 =− 3
                                                            − 1__
                                                                     =__
                                                     2   6 5
                                                                1 1

                   36 =
                     = __________
                      91 x __________
                                                             3 3 1 1− 1
                       __________
                                                          8 8 3 − 1
                   14
                                                                  16 1 =
                                                      7 7 6 − 3 55 46
                       91 __________
                                                          43
                                                      26 5
                                                       6
                     =
                                                                  16
                                                                       _________ 46
                    18
                                                                  16 =
                                                                      _________
                       91 __________
                  13 = x11 = __________
                                                       6 −
                      =
                  13 = __________
                                                                  1 =
                                                                     = _________
                                                     2   6 −
                         __________
                         __________
                                                                       _________
                  13  18
                       x
                                                               − 1
                                                                 116
                                                        − 8
                                                          8 − 1 1−− 3 =
                                                            − 3 1 _________
                  10
                 13 = =
              a   11 10 10 = 91 __________  10       2 2 7 36 7 − 3 46  5 − 4 = 3 1− _________
                        __________
                                                     2
                                                      7 −
                                                          8 −
                                                                 16 =
                                                                1
                                                                      _________
                                                             3 −
                      91 __________
                                                       7− 8 − 46
                                                          8− 3 _________
                                                              3 1− 16
                       91 __________
                                                     2 7
                   14
                                                             =
                                                                      _________
                   13 = 9113 10  18 =
                                                                  16 =
                                                           4
                   3 3 10
                      = x
                  13  11
                                                        5
                                                           3
                                                           5 5 3 1 1
                                                        2 87 6 6 36
                      42 91 x__________
                                                        2 2 87 6
                                                          3

                  11  42  __________       11  x          6  3 4  16 1 1       6  3   1    1
                                                                 16 1
                  11
                      42 91 x
                                                           5 3 1
                   3 1310

                                                              8 = ________
                         __________
                    = = 42 x __________
                                                                  ______________
                                                             + =
                   3  11  18=
                                                                    = =
                         __________
                    = 42 __________
                                                             + − 1−
                   10
                                                        −
                     =
                                                                1
                                                                      _________
                                                     2______
                                                                  _____________ −
                         __________
                     =
                                                         −5−
                                                                      ____
                                                                    =
                                                     2
                                                       2
                       x x 42 __________
                        x
                  5 5  3 = 42 __________
                                                                      _________
                                                              8 = 1− 1
                                                      2   2− 36
                                                                   1
                                                       22
                   11 =
                  3  3 = __________          =   ____ 2 2 2   2 36 − −− − − 5 − + 8 = 11_________ ___  2  −  − 1  =  _________
                                                       7 7 2 − 5−−
                                                              8 = 1−
                                                                  ________
                                                                     =
                  13
                      x __________
                                                        6
                                                           4
                        x 91
                                                                  16
                                                           6 8 =+3 13 3
                                                                 161
                  5 = 42 __________
                                                                       _________ 87
                  13 =
                                                      2   2 87 2
                                                                 16
                         ___________
                                                                 1
                                                             −
                                                              8 = ________
                                                                      =
              b   3 = 9113  11 42 91 _________  13  91   2 7   6 7 7 − 5 +− 8 3 −− 8 8 6 6 5 + 3 − ________  3  16
                                                         −
                                                                  ________
                  5 = 10
                                                             +8 = 1631
                                                      2 7 52 7   6
                                                         − 6
                    = x 91 x __________
                  5  3 13  11 =
                      x __________
                                                                        _________
                                                      2 2
                                                                   1 =
                                                       7 −
                       x x x __________
                   9 9 5 = x5 13  = 91 __________     2 7 − 6 + 8 = 1− ________
                                                      2 7

                                                                 1 16
                                                           6 8 =+ − 3
                                                        7− 6 8
                                                                 ________
                                                                       _________
                                                                −
                                                                      =

                      x 42 91
                  5  3 13 423
                                                       7
                                                           8
                                                                   16

                                                           6 5 3 5
                   9 3 11

                                                                   1
                       x x 42x
                                                              3
                         __________
                     = = x 91 __________
                   9 5  3 13 = 42  __________   3  42       7 2 6 2   7 2 7   3 3 6 5 8  1 3     5 5 16    2  5
                     = x __________
                                                        2
                         __________
                                                           5 +
                                                      2 2 2
                                                           3 +− − −

                          __________
                                                                  5 =
                    =
                   9 = = 98 x __________    =    __________ −  8 = 1− ________8 = ______________ −  + 8 =  ________
                                                                       ___
                        __________
                                                                              2
                  14 9 = x9 = 423
                                                                 ________
                                                         −
                         __________
                                                              8 =
                                                      2
                                                         5   3 +− 5
                                                                3   5 ________
                  14  3 5
                      98 __________
                      98 x
                                                           7   2 7
              c    5  = 98 __________     5    x      2   2 5 5   3 +  8 = 3 3   5  7  6

                                                          5 6 +− 8 6
                      x42
                         __________
                                                                  64 5 5 16
                  14 = x9 = x5 = 9113
                         __________
                                                       7 2 7
                                                           4 4 3 3 65 3
                  14 5
                   9
                                                               8
                                                                 3 =
                                                                  64 ________
                       x x
                                                                3
                      98 __________
                          __________
                 14 = 423 =
                                                                  64 5 ________
                                                       2
                                                                3 =
                   45= 984
                  45
                                                         5
                 1
                   45 = x5
                       98__________
                  14
                                                                 3 64
                                                       2 7
                                                         5 4 3 6
                                                                  64 ________
                                                                3 =
                 14
                                                              +
                                                         5−
                                                          4
                      45 9  3  =98 x x x  __________    9  x    2 5   7   2 − 4 3 6 5 + 8 8   5
                     = _________
                   45 5 9
                 14 9
                                                         5 7
                                                                3 64
                                                           4 4 6
                       _________
                                                                  64
                     = 98 x 42

                       _________
                     45 9 5
                                                            5
                                                           7

                  60 45 = = =
                       x x __________
                                                          4 3_ 3
                         __________
                       _________


                         __________
                  60= =
                         __________
                                                       2
                      _________
                                                                  64 5 ________
                  45 9
                        x
                                                          4 3 +
                  60 = =
                                                           3 −
                         __________
                                                                  5
           4  Simplify. _________         14  =  98 _________ 6    8 = 64 5 5      3      5
                                                         5 5
                       _________
                  45 14
                     = = 98
                                                                3 3
                        x
                                                                                         3
                                                                                 5
                 1
                                                         5
                                                                3
                 14
                      = x
                      98 __________
                  60 984   9 5
                       _________
                                                                3   5
                                                        7
                                                         5   3 6
                    60 = 9814   9
                  60
                       _________
                        x __________
                                                          4   3 4
                  60
                    8 8 ==
                                                                  64 5
                    8 14
                                                                  64
                                                                 3
                  60
                                                          4 5

                    8 45
                     = _____________
                                                                  64 5
                                                           4   3
                  45
                       __________
                    45
                                                                  3
                                                          5
                   8 60  = = 98  _______   45             5 4        64            4      64
                     = 98
                      8 45 14
                       __________
                                                                 3 64
                     = x _________
                    9 =
                       __________
                  12 8 = _________
                  12 = 9814
                       _________
                                                                   64
              a    8 = = = = __________   60  =  _________    3 4 4    5
                  12 = _________
                    45
                     = _____________
                          _______
                       __________
                   8 60 60
                  12  45
                                                                   64
                  12 = _________
                  60
                       __________
                   12 12 = = 9814
                  12  45
                        _________
                   12 60
                     60  __________         8             5  4   3  64
                        _________
                   12 8 8

                  12 =
                  12 8
                   12 8 60
                     = __________
                     =
                       __________
                    45 =
                       __________
                     = __________
                   60
              b   12 = __________            =  __________
                     12 =
                       __________
                       __________
                  14 12 = __________
                     8
                  14 = _________
                  14 = =
                      __________
                   12
                  12   8
                     = __________
                  12 = __________         12
                  12 =
                       __________
                  12 12 60
                       __________
                  14 = __________
                  14   8 =
                    2 2 __________
                  14 12
                     14 =

                    2
                  12 12
                   14 12  =  __________    12
                 5 5   14
                      = __________
                      =
                  x x 2 8
                  12
                        __________
                        __________
                  x2
              c    12 12 = __________        =  __________
                      = __________
                 5
                     =
                        __________
                    12 =
                   x5 2 = _________
                    3 3 2 = ___________
                    3 =__________
                 5   5 5   x 14   14 = = __________  14
                       __________
                  x 2 =
                        __________
                   x 3 2 12
                  14 12
                      =
                        __________
                 51
                       __________
                    3 =
                  x4  12
                    3 = __________
                  x 3 =
                 5

                  3 3 14
                        __________


           5  Multiply. 3 2 14 2 = __________     2
                  3 3 2
                  3    12
                   x 2 =
                    2 = __________
                        __________
                 5 5
                      = __________
                  x 14 =
                   x2 x
                       __________
                        __________
                 5
                   x x
                    2 = __________
                        __________
                      = =
                      = 2 __________
                 3  3 x5 4 4  3 2x = __________  5 x  =  __________
                 4 2x = 2 3

                       __________
                  3 3
                   x2 = _________
                       =
                        __________
                  x3 x5 14 2 = ___________  3

                    2 x
                  5
                 4 x = __________
                  4 3 32 =
                        __________
                       __________
              a    4 2x = __________      3
                   x 3
                 4
                       =
                  5

                    53
                  3 53 4  3   3
                    5 2
                  3
                  3
                      = __________
                        __________
                        __________
                     2
                  3 4  3 x =
                        __________
                   x5 2 = __________
                   x 5
                    2 = =
                   x   x
                      = __________
                 4 4  3 x5
                 3  3 x 3 x x 5 3 = __________  x 2 =  __________
                        __________
                    6 6 5 =__________2 =
                 4   4
                        __________
                 3 x 3 3
                 4 x 5 = __________2x =
                 4
                        __________
                 4
              b  3 4  3 x 6 5 6 = = __________  4
                 4 x
                        __________
                    6 = __________2x =
                 1 1 x 644
                        __________
                    6
                 4
                 1 x =
                    3 3 = __________2
                    3

                   ÷ ÷ 3 6 5 5
                 4  3 4 3

                        _________
                 1 4   33
                   ÷3 6 5
                        _________
                 4 4  1 ÷ 3 534
                         =
                      = __________
                   x
                       =
                        _________
                    4 4 3   =__________
                      = __________

                        __________
                 1  1 x 2x =   =   = _________   3  x 5  =  __________
              c 4 ÷ 31 ÷ x 53 x ÷ 4 3 65 6    = =   = _________  4  6
                    4   = __________
                         = _________
                        _________
                  4
                 4 1 4  3 4
                    4 = __________
                4 ÷ 64 x
                        _________
                 4
                         __________
                 4÷ 4 64  3 x
                    4 _________  = 5 =

                    4 31  3 3 4 3 x 6  =  __________   1  3
                 4  1

                   3 4 3 6
                  4  1 4
                6
                        = ________
                       ________
                         = _________
                6 ÷ ÷ 3 31  3 ÷
                      ÷    = 5 = _________  ÷    =  _________
                6 ÷3 ÷ 4
                        = _________  = 6
                       ________
                        _________
                         __________
                       =
           6   Divide 4 4 3   =÷ 3 =÷ 31 x  3 ________  4  4
                 6
                       ________
                   4   = 43 4
                  4  1 4
                          =
                         = ________
                6 ÷ 3   =÷ 44 ÷
                         _________
                 6
                       ________
                   4 = =÷ 6
                6 ÷ 4 344  1 4
                         _________

                6 ÷
                       ________
                6 ÷ 4 ÷ 44
                    2 24
                      4  4 ________  = =   _________     3
                 3 3 4 3 3
                    2 3
                   1
                 3 4 3 44

                      = __________
                        __________
                   ÷ ÷ 2 ________  =
                6 ÷ 6 ÷
                         _________
                6 ÷ ÷
                        __________
                        =   =
              a  3  3 6    3 3  = ________  b  6 ÷    =  ________
                      = ________
                    7 7 2 = ________
                   ÷2   = 3
                        __________
                 4 4  3 ÷ 2=÷

                 4 ÷ 2 =÷ 4 =÷ 44 4
                    7 =
                        __________
                 3 43  = __________         4
                  6
                        ________

                        __________
                 4 3
                 6
                 4 ÷ ÷
                   ÷ 7 2 4 3 =
                 4÷ 7 4
                        __________
                     7 = ________  =
                 4 6 ÷
                   2 2 4  3    3  7 = ________  __________
                     4
                     1 1 7 2 3 2
                 3
              c  2 4  3  1 7 2 4  x_________   3  2
                 2
                   = = 1 2 =÷
                       x_________
                        __________
                   ÷ ÷
                 6
                        __________
                       x_________
                 2  2    = 1 =÷ 2 = ________  = __________  ÷  =  __________
                 3 3  2 = 1 =÷ 3
                        __________
                    12 1 x_________
                    12 2 7
                 4  3 4
                    12 x_________
                 2 = 74 ÷ 4  =  ________  4  7
                    7
                 3 = 1 x___________
                       x_________
                     1 7
                 3  2 4  3
                         __________
                    12 x_________
                3 = = 12 2 =÷ 12x_________
                 3 = 12 =÷ 74
                3
                         __________
                3  2
                   14 12 3 2 4  12 1 1 7 7 1 1 2 1 1 x_________   2  1
                 14 123  2 4
                 14 =
                       x___________
                         ________
                  =÷
                       =
                        x________

                        x________
                    = 1x_________
                      1
                 14 = 2
                        x________
                 14= = = 1 x_________    3  =  12  x_________
                 14
                 24 12 74 3
                     12
                 1 3
                 24 = 14 1212
                     12 1 x________
                     12 x_________
                     12 x________
                3 =
                 1
                        x________
                      1
                 24 = 14 = 123  2 =
                        x_________
                      1
                 14  = 12 x________
                 24
                24 = = 123
                     12 x________
                        x_________
                      12x________
                2
                     12
                 24 = 124 3
                   2
                      1
                   14  1 12 1            14   1             5
                 7 7 24 3  14
                     1 1 12 1 12 1
                 7 24
                  14
                       x_________
                       x_________
                         x________
                 7 14 = =
                        x________
                   =
                       x_________
                 7  7    = = 1 1 x_________  =  x________
                        x________
                   = 1
                   =
                 8 8  7 = 1 114
                        x________
                    12 1 x_________
                 3 24
                    12 x_________
                24  14
                    12 121
                 8 = 1 x__________
                     =
                 7 = 1224  = 12 12  x_______  24  12
                       x_________
                     1
                 8  7 24  14 =
                    12 x_________
 CITS : WCS - Electrical - Exercise 1  8 = = 12 12 1 x________  CITS : WCS - Electrical - Exercise 1
                 8 = 12 = 1224
                8
                         x_______
                    12x__________
                       12
                  24 1
                  7
                  8  7  14  12 1 1  x_______   7  =  1  x_________
                8   724
                    12 1 12
                     1 x_________
                  7 =
                     7 7 x__________
                 3 3 = =
                       x_________

                      1
                  = 7
                 3 =
                     7 x_________
                8
                       =
                       = _________
                  3 1217 24 128
                         _________
                       = x_________
                8
                   + 7 12
                    =
                 3  3 8    + + 7 12  _________  8  12
                         _________
                    12 7 =
                    12 = x_________
                 4 4  3 + 7 12 17 =
                    12
                         _________
                 3 4 3  + 12 12 = _________
                 4 + 7 =+ = 128

                        x_________
                         _________
                     7
                 4 + 8

                         _________
                    12 =
                 4 7
                      1
                         _________
                     12 =

                    12 7 x_________
                 4  3 = 73
                 3 4+ 12 128 + 12 = _________   3  +  7  =  _________
                    12 7
                 4  3 +
                     7 =
                         _________
                 8

                      7
                         _________
                 4  3 124 + + 3  127 = = _________  4  12
                          _________
                 4 +
                    12 =
                          _________
                 4  3 +
                    12 7 =
                          _________
                        =
                      12
                  4
                  3 4 + + 12 =  _________
                      7
                  4
                     12
                  4  12
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