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

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3.2. MULTIPLICATION AND DIVISION 45This is based on another four-fact family:Division Property of zeroIf a 6= 0, then 0 ÷ a = 0.What about dividing by 0?(1) If a 6= 0 and a ÷ 0 = c, then a = 0 · c = 0, a contradiction.(2) If 0 ÷ 0 = c, then 0 = 0 · c for any whole number c, so there is no uniquequotient. Thus division by 0 is undefined.Division with Remainder – having some objects left over.Theorem – a statement that can be proved based on other results.Theorem (Division Algorithm). If a and b are any whole numbers withb 6= 0, then their exist unique whole numbers q and r such thata = bq + r where 0 apple r < b.a is the dividend, b the divisor, q the quotient, and r the remainder.
46 3. WHOLE NUMBERS: OPERATIONS AND PROPERTIESAlternative ways of viewing the repeated-subtraction approach.Problem (Page 118 # 11b).i) 61 8 ÷ 7 8 = 7 8ii) 17 8 ÷ 3 8 = 5 8iii) 30 8 ÷ 6 8 = 4 8iv) 16 8 ÷ 2 8 = 7 8v) 44 8 ÷ 6 8 = 6 8vi) 25 8 ÷ 7 8 = 3 83.3. Ordering and ExponentsOrdering and Whole Number OperationsDefinition (“Less Than” for Whole Numbers).For any two whole numbers a and b, a a) if and only if there is anonzero whole number n such that a + n = b.apple means less than or equal to.means greater than or equal to.
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Problem (Page 88). In a group of nine coins, eight weigh the same ...

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