# 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.