Integers – Properties of addition and subtraction of Integers.

CBSE CLASS 7 MATHEMATICS
INTEGERS – Chapter 1
Properties of Addition and Subtraction of Integers:

I. Closure property:
Closure under addition:

For any two integers a and b, a+ b is an integer.
For example take two integers (-10) and 3, their sum = (-10) + 3 = -7, which is also an integer. So we can say that integers are closed under addition.
Closure under subtraction:

For any two integers a and b, a-b is an integer.
For example take two integers (-10) and 3,
their difference = (-10) – (3) = (-10)+ (-3) = (-13), which is also an integer.
So we can say that integers are closed under subtraction.
II. Commutative Property:

Under addition:
For any two integers a and b, we can say a + b = b + a.
For example take two integers (-10) and 3, then (-10) +3 = -7
and 3 + (-10) = -7.Both are equal therefore, addition is commutative for integers.
Under subtraction:
Subtraction is not commutative for integers.
Take any two integers (-10) and 3, then (-10) – (3) = (-10) + (-3) = -13
and 3- (-10) = 3+ (+10) = 13.Both are not equal. So subtraction is not commutative for integers.

III. Associative Property:
For any integers a, b, c we can say a + (b + c) = (a + b) + c.
Take any three integers -3, 1 and -7.
Then a + (b + c) = (-3) + [1 + (-7)] = (-3) + (-6) = -9.
(a + b) + c= [(-3) +1] + (-7) = (-2) + (-7) = -9.
Both are equal therefore addition is associative for integers.

IV. Additive Identity:
For any integer a, a + 0 = a = 0 + a.
Thus zero is an additive identity for integers.
Examples:
(-8) + 0 = -8
0 + (-8) = -8.