- Closure property
Let a and b be any two real numbers. Then, if a + b is also a real number then we
say that a and b satisfy the closure property with respect to addition. As this idea
is a simple rule, it may be explained to the child orally.
- Commutative property
The property in which the result is unchanged by altering the order of the quantities
is said to be commutative.
Eg. : 3+5 = 5+3
n n n + n n n n n = n n n n n n n n
n n n n n + n n n = n n n n n n n n
Arrange two groups of beads containing 3 and 5 respectively. Ask the child to add the
second group numbering 5 with the first one of 3. The result is 8.
Now, form another two groups wherein the first contains 5 beads and the second 3.
Ask the child to add both. Here again the sum is 8. Observe that the result is
unchanged by altering the order of quantities.
Note : In general,
a + b = b + a
a ×^ b = b ×^ a
Note that commutative property holds good only for addition and multiplication and
is not true in the cases of subtraction and division.
i.e., a-b and b-a, and ba and ab are not equal.
- Associative property
Let a, b, c be any three real numbers. If, (a + b) + c = a + (b + c), then we say that
the three elements a, b and c satisfy the associative property of addition.
