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Commutative Integers hold the commutative Integers do not hold the commutative
Property property for addition, as the sum property for subtraction, as the
of two integers in any order is the difference of two integers in any order
same. is not the same. If a and b are any two
If a and b are any two integers, then integers, then a – b ≠ b – a.
a + b = b + a. E.g., 7 – 3 = 4 and 3 – 7 = –4. So 4 ≠ –4
E.g., 2 + 3 = 5 = 3 + 2

Associative Integers hold the associative Integers do not hold the associative
Property property for addition, as the sum property for subtraction, as the
of any three integers grouped in difference of any three integers grouped
any order is the same. in any order is not always the same.

If a, b, and c are any three integers, E.g., 3 – (7 – 2) = 3 – 5 = – 2 and
then a + (b + c) = (a + b) + c (3 – 7) –2 = –4 – 2 = –6
E.g., 2 + (3 + 4) = 2 + 7 = 9 and \ 3 – (7 – 2) ≠ (3 – 7) –2
(2 + 3) + 4 = 5 + 4 = 9
\ 2 + (3 + 4) = (2 + 3) + 4

Existence of When an integer is added to its
Additive Inverse opposite number, we get zero as the
result.
If a is an integer, then (–a) is its
opposite, i.e., a + (– a) = 0 = (– a) + a.
Thus, (–a) is called the additive
inverse of a.
E.g., 4 + (–4) = 0 = (–4) + 4
Property of zero When zero is added to an integer, When zero is subtracted from an
we get the same integer. If a is an integer, we get the same integer. Thus,
integer, then a + 0 = a = 0 + a. if a is an integer, then a – 0 = a.
Here, 0 is also called the additive E.g., 5 – 0 = 5
identity. But if we subtract any integer from 0,
E.g., 6 + 0 = 6 = 0 + 6. we will get the additive inverse or the
opposite of the integer. E.g., 0 – (+2) = –2
Property of 1 Addition of 1 to any integer gives its Subtraction of 1 from any integer gives
successor. its predecessor.
If a is an integer, then a + 1 is the If a is an integer, then a – 1 is the
successor of a. predecessor of a.
E.g., 5 is the successor of integer 4 E.g., 8 is the predecessor of integer 9
which is obtained by adding 1 to 4, which is obtained by subtracting 1 from
i.e., 4 + 1 = 5. 9, i.e., 9 – 1 = 8.

Life Skills
Ruhi and Roma participated in an interschool quiz competition on Environment Day, where positive marks
were awarded for every correct answer and negative marks for every incorrect answer. If Ruhi’s scores in 6
successive rounds were: 85, –7, 40, 68, –12 and 50, and Roma's scores in 6 consecutive rounds were: 70, 24,
–17, 46, 58, and 48, then who scored more and how much? How do you contribute to a healthy environment?

Mathematics-7 10