Problem (Page 88). In a group of nine coins, eight weigh the same ...

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3.1. ADDITION AND SUBTRACTION 29Name the three coins in the chosen group a, b, c.(3) Balance a against b.a = b =) counterfeit coin is c.a 6= b and chosen group heavier =) counterfeit coin is heavier of a and b.a 6= b and chosen group lighter =) counterfeit coin is lighter of a and b.Two models of addition:3.1. Addition and Subtraction(1) The set model – uses the union of disjoint sets.Definition (Addition of Whole Numbers). Let A and B be any two wholenumbers. If A and B are disjoint sets with a = n(A) and b = n(B), thena + b = n(A [ B).“a” and “b” are called addends or summands.Addition is called a binary operation since two numbers are combined to producea unique number.
30 3. WHOLE NUMBERS: OPERATIONS AND PROPERTIES(2) The measurement model – uses directed arrows on a number line.Properties of whole number addition:Closure propertyThe sum of any two whole numbers is a whole number.Example. The even whole numbers are closed under addition.The odd whole numbers are not closed under addition. Why?Commutative propertyLet a and b be any whole numbers. Then a + b = b + a.Associative propertyLet a, b, and c be any whole numbers. Then(a + b) + c = a + (b + c).
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Problem (Page 88). In a group of nine coins, eight weigh the same ...

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