Grade 7 Chapter1
Intergers
Notes 1.3
Properties of Addition of Integers
Closure property under Addition
For every integer a and b, a+b is also an integer.
Adding two positive integers results in positive integers, whereas adding two negative integers will
results in the sum with a negative sign. But, the addition of two different signed integers, will result in
subtraction only. See few examples below:
• 2+2 = 4
• 2 + (-2) = 0
• -2 + (-2) = -4
• -2 – (-2) = 0
Commutativity Property for addition
for every integer a and b, a+b=b+a
Associativity Property for addition
for every integer a,b and c, (a+b)+c=a+(b+c)
Additive Identity
For every integer a, a+0=0+a=a here 0 is Additive Identity, since adding 0 to a number leaves it
unchanged.
Example : For an integer 2, 2+0 = 0+2 = 2.
Additive inverse
For every integer a, a+(−a)=0 Here, −a is additive inverse of a and a is the additive inverse of-a.
Example : For an integer 2, (– 2) is additive inverse and for (– 2), additive inverse is 2.
[Since + 2 – 2 = 0]
Intergers
Notes 1.3
Properties of Addition of Integers
Closure property under Addition
For every integer a and b, a+b is also an integer.
Adding two positive integers results in positive integers, whereas adding two negative integers will
results in the sum with a negative sign. But, the addition of two different signed integers, will result in
subtraction only. See few examples below:
• 2+2 = 4
• 2 + (-2) = 0
• -2 + (-2) = -4
• -2 – (-2) = 0
Commutativity Property for addition
for every integer a and b, a+b=b+a
Associativity Property for addition
for every integer a,b and c, (a+b)+c=a+(b+c)
Additive Identity
For every integer a, a+0=0+a=a here 0 is Additive Identity, since adding 0 to a number leaves it
unchanged.
Example : For an integer 2, 2+0 = 0+2 = 2.
Additive inverse
For every integer a, a+(−a)=0 Here, −a is additive inverse of a and a is the additive inverse of-a.
Example : For an integer 2, (– 2) is additive inverse and for (– 2), additive inverse is 2.
[Since + 2 – 2 = 0]
