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
