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WALKTHROUGH                                                                                     Course Guide

                 B. SUBTRACTION

                        Subtraction is the operation of taking one number or amount away from another. It is
                 the inverse operation of addition.

                        In a subtraction equation, the subtrahend is taken away from the minuend to give a
                 difference.                                                                                            M1_L1
                                              Minuend                                             
                                                ⏞    −      ⏞     =      ⏞
                                                              
                                                                           
                                                   
                        Subtraction is neither Commutative nor Associative.
                     •  Consider the integers 7 and 4.
                        We see that:                 7 - 4 = 3                                                          M1_L2

                                                     4 - 7 = - 3

                        Therefore,                   7 - 4 ≠ 4 - 7
                        In general, for any two integers a and b
                                                     a - b ≠ b - a

                        Therefore, we conclude that subtraction is not commutative for integers.

                     •  Consider the integers 7, 4 and 2
                                                    7 - (4 - 2) = 7 - 2 = 5
                                                    (7 - 4) - 2 = 3 - 2 = 1

                                Therefore, 7 - (4 - 2) ≠ (7 - 4) - 2
                                In general, for any three integers a, b and c

                                                    a - (b - c) ≠ (a - b) - c.
                                Therefore, the subtraction of integers is not associative.

                        Subtraction is the addition of sign numbers and there is a rule to follow. To subtract

                 integers (number), change the sign of the integer (number) that is to be subtracted (subtrahend)
                 and proceed to addition. Then follow the rules of adding sign numbers:

                            a.  If both signs are positive, the answer will be positive.

                                                     (+)    + (+)    = (+)  

                            b.  If both signs are negative, the answer will be negative.
                                                      (-)    + (-)    = (-)  
                            c.  If the signs are different subtract  the smaller absolute value from  the larger

                                absolute value and the answer will follow the sign of the larger absolute value.
                                                       (+)    + (-)    = (+)       if    >   

                                                       (+)    + (-)    = (-)       if    <   
                 LESSON 2: FUNDAMENTAL OPERATIONS                                              2.5 | P a g e
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