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### Grade 6 - Mathematics1.16 Properties of Whole Numbers (Division)

 1. Closure Property: Consider the following examples: 15/3 = 5 14/5 = 0.8 6/13 = 0.461538462 For any two whole numbers a and b (not equal to zero), their quotient a/b need not be a whole number. Hence, the closure property is not true for division in the set of all whole numbers. 2. Commutative Property: For example: 15/3 = 5 and 3/15 = 0.2 Hence, for any two whole numbers a and b, a/b is not equal to b/a where a is not equal to b. That is, the commutative property is not true for division in whole numbers. 3. Associative Property: Observe the examples, (12/3)/2 = 4/2 = 2 12/(3/2) = 12/(1.5) = 8 Therefore, 12/(3/2) is not equal to (12/3)/2. That is for any three whole numbers a, b(not equal to zero), and c (not equal to zero), (a/b)/c is not equal to a/(b/c). Hence, the associative property is not true for division in whole numbers. 4. Division by 1: Consider the examples, 6/1 = 6; 50/1 = 50;................. If any whole number is divided by 1 the quotient is the same number. For any whole number "a", a/1 = a Directions: Choose the correct answers for the following questions. Also write at least 5 examples of your own for each property and show that the property is not true under division.
 Q 1: Any whole number is divided by the quotient is _________.the same numbera different number Q 2: 50/6 = ?Not a whole numberWhole number Q 3: 8/(4/2) is not equal to (8/4)/2, is this statement correct?NoYes Q 4: 8/4 = 2 means 4*2 = 8, is this correct?YesNo Q 5: (15/3)/2 = 15/(3/2), is this statement correct?NoYes Q 6: 60/12 = ?Whole numberNot a whole number Q 7: Division is an inverse operation to____________?additionsubtractionmultiplication Q 8: a/b = b/a, is this statement correct?NoYes Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!