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28+
          WORKSHOP CALCULATION & SCIENCE  - CITS
                                           =
                                              7
                                             +
                                         28+ + 4  =  + 7
                                       + + 56
                                         4
                                       + - 56  =  − 14
                                         4
                                       - - 72  =  − 14
                                         4
                                       - + 72  = −8
                                         9
                                           =
                                             −8
                                       − 96 9
                                       +
                                       − 96  =  +16
                                        − 6
                                             +16
                                           =
                                       5y − 6  20
                                       5y  =  20
                                            5
                                        5
                                          =
                                       x 5  5
                                       x
              When  an expression contains addition,  subtraction,  multiplication  and  division,  perform the
                                       4
                                            25
                                       5x
              multiplication and division operations first and then do the addition and subtraction.
                                       4
                                       5x  =  25
                                            5
                                        5
                                          =
                                        5
           Example                     10a  5
                                       10a
                                        2a
               12 x 8 – 6 + 4 x 12 = 96 – 6 + 48 = 138
                                         8ac
                                        2a
                                       −  8ac
                                         2bc
               102 x 6 – 6 x 2 + 3 = 17 – 12 + 3 = 8
                                       −
                                         5m −×
                                       − 2bc  6n − 7p
           Parentheses and grouping symbols 6n5m −×−  − 28mn − 7p
                                       5a + − 20 28mn
               (    ) Brackets         5a + 20
                                           28
                                       7a +
                                        m
               {    } Braces           a 7a + = 28 m− n
                                        m
                                            a
                                        n
               7 + (6–2) = 7 + 4 = 11  a a 3 n  = a m− n
                                                    1
                                             3
               6 x (8–5) = 6 x 3 = 18  2 a 3  = 2 − 2 =  2 =  2
                                       2
                                             3
                                                    1
                                        2
                                          =
           Parentheses                 2 2  2× 2 − 2 = = 2 =  2
                                                8
                                             2
                                       2×
                                       2
                                                    2
                                              =
                                       2×
                                          2×
                                                8
                                             2
                                           2
                                                4
                                        2×
           These are symbols that indicate that certain addition and subtraction operations should precede multiplication
                                                    2
                                              =
                                                  =
                                                4
                                           2
                                               n
                                        n 2×
                                       a
                                            
                                             a 
           and division.  They indicate that the operations within them should be carried out completely before the remaining
                                          =
                                              
                                               n
                                            
                                        n
                                       a
                                             a 
                                            
           operations are performed.  After completing the grouping, the symbols may be removed.
                                             b  
                                       b =
                                             
                                        n
                                            
                                               2
                                             b 
                                        n
                                        3
                                       b
           In an expression where grouping symbols immediately preceded or followed by a number but with the signs of
                                                         4
                                                      2
                                       2
                                            
                                                   2×
                                             2 
                                               2
                                        3
                                          =
                                                 =
                                                        =
                                            
                                               
                                                      2
                                       2
                                                         4
                                                   2×
                                             2 
                                            
           operation omitted, it is understood, that multiplication should be performed.
                                                         9
                                        2
                                                      3
                                                   3×
                                             3  =
                                       3  =          =
                                        2
                                                         9
                                                      3
                                                   3×
                                         n 
                                             1 3 
                                       3
                                        −
           Grouping symbols are used when subtraction and multiplication of negative number is done.
                                       a
                                           =
                                             1
                                         n
                                        −
                                              n
                                       a
                                           =
                                             a
           To remove grouping symbols which are preceded by negative signs, the signs of all terms inside the grouping
                                              n
                                              1 a
                                        −
                                         2
                                       2
                                           =
           symbols must be changed (from plus to minus and minus to plus).
                                              1
                                        −
                                              2
                                         2
                                       2   =  2
                                           2 2
                                                  2
           Parentheses which are preceded by a plus sign may be removed without changing the signs of the terms within
                                             2
                                               
                                       
                                         3 
                                                7 
                                        1 
           the parentheses.               1  2  =     7   2
                                         3 
                                         4  =
                                                4  
                                       7 4
                                          7 
                                       
                                              49 4 
                                               
           When one set of grouping symbols is included within another set, remove the innermost set first.
                                            =
                                         ×
                                       7  7   49
                                              16
                                       4
                                          4
                                         ×
                                            =
           When several terms connected by + or – signs contain a common quantity, this common quantity may be placed
                                          4
                                       4
                                              16
           in front of a parentheses.
               8 + 6(4–1) = 8 + 6 x 3 = 26
               (6+2) (9–5) = 8 x 4 = 32
           Plus 4 less negative 7 is written as 4 – (–7).
           Plus 4 times negative 7 is written as 4(–7).
               4 – (–7) = 4 + 7  = 11
               8 – (7–4) = 8 – 3 = 5
               3 + (–8) = 3 – 8  = –5
               7 + (4 – 19) = 7 + (–15) = 7 – 15 = – 8
               3 {40 + (7 + 5) (8–2)}
                       = 3 {40 + 12 x 6}
                       = 3 x 112 = 336.
               8x + 12  -  quantity 4 may be factored out giving the expression 8x + 12 as 4 (2x + 3).
                                                           22
                                            CITS : WCS - Electrical - Exercise 4
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