Integers include whole numbers and their negative counterparts. Addition and subtraction of integers follow several rules: the sum or difference of two integers with the same sign is the sum or difference of their numerical values with that sign, while the sum or difference of two integers with opposite signs is the difference or sum of their numerical values with the sign of the integer with the greater numerical value. Multiplication and division of integers also follow specific rules where the product or quotient of integers with the same sign is positive and with different signs is negative.

1. INTEGERS
Integers form a bigger collection of
numbers which contains whole
numbers and negative numbers.

2. Properties of addition and
subtraction
• Integers are closed under addition and
subtraction both. That is, a + b and a – b are
again integers, where a and b are any integers.
• Addition is commutative for integers, i.e. a +b =
b + a for all integers a and b.
• Addition is associative for integers, i.e. (a+b)+c =
a+(b+c) for all integers a, b and c.
• Integer 0 is the identity under addition. That is,
a+0= 0 + a = a for every integer a.

3. Addition of Integers
• Rule 1 : The sum of two negative
integers is obtained by taking sum of the
numerical value of the addends.
• Example:
• i) (+4)+(+6)=+(4+6)=(+10)
• ii) (+123)+(+97)=+(123+97)=(220)

4. integers
Rule2: The sum of two negative
integers is obtained by giving the
negative integer sign to the sum of
their numerical values.
Example:
i) (-6)+(-2)= -(6+2)= -8
ii) (-70)+(-3 3)= -(70+33)= -103

5. integers
• Rule3:
• To add a positive and a negative integer,
we find the difference between their
numerical values and give the sign of
the integer with more numerical value.
• (-54) + (+39) = -(54-39) = -15

6. Subtraction of Integers
• Rule: For any two integers a and b
• a – b = a+(-b) = a+ (additive inverse of b)
• Example:
• (i) (+5)-(+8)=(+5)+(additive inverse of +8)
• = (+5) + (-8) = -3
• (ii) (-7) + (additive inverse of +6)
• = (-7)+(-6) = -(7+6) = -13

7. Multiplication of integers
• Product of a positive and a negative integer is
a negative integer, whereas the product of
two negative integers is a positive integer.
E.G., -2 x 7 = 14 and -3 x -8 = 24
• Product of even number of negative integers is
positive, whereas the product of odd number
of negative integers is negative.
• E.G., -2 x -3 x -4 x -5 = 120, -2 x -3 x -4 = -24

8. Properties of Multiplication
• Integers are closed under multiplication.
• Multiplication is commutative for integers.
• The integer 1 is the identity under
multiplication, i.e. 1xa = ax1 = a for any integer
a.
• Multiplication is associative for integers, i.e.
(axb)xc = ax(bxc) for any three integers, a, b
and c.

9. Division of Integers
• Rule 1 : The quotient of two integers
with the same sign is positive integer
obtained by dividing the numerical
value of the dividend with the
numerical value of the divisor.
• E.G.,
• (i) (-25) ÷(-5) = +5,
• (ii) (+12) ÷(+3) = +4

10. integers
• Rule 2: The quotient of two integers with
different signs is the negative integer
obtained by dividing the numerical value of
the dividend with the numerical value of the
divisor.
• E.G.
• (i) (+36) ÷(-6) = -6
• (ii) (-32) ÷ (+4) = -8

11. integers
•THE
• END