Readings for Session 8 – (Continued)  

Introduction to Subtraction of Whole Numbers

        Subtraction is often considered to be the inverse operation of addition, that is,

a – b = c  only when  b + c = a.

We may use this inverse relationship to check the answers to subtraction problems.  In this session, we also learn how to use this inverse relationship to solve addition and subtraction equations. But, first, we consider how subtraction relates to sets and use this relationship to motivate subtraction as an inverse operation for addition.  

How does the operation of subtraction used in the following problem relate to sets? 

Sam had $836 in a checking account and wrote a check for $429. How much money did Sam have in the checking account after the check was written? 

        The checking account is a set of dollars where the whole number 836 represents the cardinality of the set and the check represents a subset of the checking account with a cardinality of 429 where 429 dollars are removed from the account. The subtraction, $836 – $429 = $407, gives a new whole number that represents the cardinality of a set for the new checking account balance.

        We develop subtraction of whole numbers through the set concept of removing the elements in a subset of a set from the set. On the next page, we defined these concepts as the complement of a set and the set difference between two sets.

  

      

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