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.
