Page 15 - classs 6 a_Neat
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EXAMPLE 3: Simplify: 16 -[11-{8 ÷ (17 + 3 × 2 -19)})  EXAMPLE: 6.   Simplify,    1   1  1   1  1  1     
                                          3 ÷   1 −  2     2 −−  6       
                                                        2
                                                4
                                          4
                                                            4
 SOLUTION:  The given expression  SOLUTION      We have:          
          = 16 - [11 - {8 ÷ (17 + 3 × 2 -19)
          = 16 - [11 - {8 ÷ (17 + 6 -19)
                                                    1
                                        1
                                  1 
                                                1
          = 16 - [11 - {8 ÷ 4] = 16 - [11  - 2]       3 ÷   1 −  1     2 −− 1           
          = 16 - 9 = 7.       =   4    4  2   2  4  6     
 EXAMPLE 4:  Simplify: 14 - [12 - {9  - (7 - 6 - 2)})    13   5  1 5  1  1     
                                            
                              =   ÷   −     −−         
                                            
 SOLTIONS:   The given expression    4    4  2 2  4  6     
          = 14 - [12 -{9-(7 -6-2)}]    13   5  1 5  3 2    −  
                                            
          = 14 - [12-{9-(7 - 4)} ]      [removing vinculum]  =   4  ÷    4  −  2 2 −             [removing bar]
                                            
 = 14 - [12-{9-3}]         [removing parentheses]       12     
                                            
 = 14 - [12-6]  [removing braces]    13   ÷  5  −  1 5  −  1     
                                            
 = 14 - 6  [removing square brackets]  =     4    4  2 2 12           
                                            
 = 8.
                              =     13   ÷    5  −  1 30 1    −         
                                            
 1    2  3   1  5              4   4   2    12     
 EXAMPLE 5. Simplify: 5 of    −    +÷
 2    3  5   2 11           =   13   ÷  5  −×                [removing parentheses]
                                          1 29 
 SOLUTION:  The given expression      4      4  2 12       
 11    2  3   1  5
 =  of    −    +÷              13   5  29      13   30 29    −    [removing braces]
 2    3  5   2 11           =  4  ÷        4  −  24       =    4  ÷        24        
 11    10 9   −  1  5
 =  of      +÷              =    13  ÷  1 
 2    15   2 11                  4  24   
 11  1  1  5
 =  of  +÷  [removing parentheses]
 2  15  2 11                  =      13 23  ÷    =  78                  [removing square brackets]
 11  1  5                        4   1 
 =  +÷  [removing ‘of’]
 30  2 11
 11  1  5
 =  + ×  [removing’+’]
 30  2 11
 11  5
 =  +  [removing ‘x’]
 30 11
 11 33 =  44
 +
 =   [performing addition]
 30  30
 22  7
 =  = 1  ⋅
 15  15
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