Integers include whole numbers and their negatives. Positive integers are numbers greater than zero, negative integers are less than zero. Zero is neither positive nor negative. The sum, difference, product, and quotient of integers are also integers. Integers follow properties like commutativity, associativity, distributivity, additive and multiplicative identities, and additive inverses. Integers are closed under addition, subtraction and multiplication. Division by zero is undefined, and an integer divided by itself is equal to itself.

2. INTEGERS
Integers form a bigger collection of numbers
which contains whole numbers and
negative numbers. For example-…-4, -3, -2,
-1, 0, 1, 2, 3….

3. TYPES OF INTEGERS
POSITIVE
INTEGERS- 1, 2, 3,
4…i.e. the natural numbers
are called positive integers.
NEGATIVE
INTEGERS- -1, -2, -3,
-4… are called negative
integers.
On a number line points to
the right of zero are
positive integers and the
points to the left of zero
are negative.

4. ZERO
Zero is neither
negative nor
positive. It is
greater than
every negative
integer and
smaller than
every positive
integer.

5. MATHEMATICAL APPLICATIONS
OF INTEGERS
The sum of two integers is also an integer.
Example: -5 +7=+2
The difference of two integers is also an integer.
Example: +8-(-4)=8+4=12
The product of two positive integers is always
positive. Example:+8 x +4 =32
The product of two negative integer is always
positive. Example: -3 x -4 =+12
The product of a positive integer with a negative
integer is negative. example: +3 x -2=-6.
The product of zero and an integer is always
zero. Example: 0x 2=0

6. ADDITION AND SUBTRACTION

7. MATHEMATICAL APPLICATIONS
OF INTEGERS (contd.)
If the dividend and divisor
are of the same sign then
the quotient is a positive
integer. Example: -4/-
2=+2
If dividend and divisor are
integers of opposite sign
then the quotient is a
negative integer.
Example:4/-2=-2
Any integer divided by 1
gives the same integer.
Zero divided by any
integer is equal to zero.
Division by zero is not
possible.

8. MULTIPLICATION AND DIVISION

9. COMMUTATIVE PROPERTY
The whole number can be added in
any order. example: 5+(-6)=(-6)+5.
Addition and multiplication is
commutative for integers.
Whole numbers cannot be subtracted
in any order. Example:5-6 is not
equal to 6-5. Subtraction and
division is not commutative for
integers.

10. ASSOCIATIVE PROPERTY
For all integers a, b and c,
(a+b)+c=a+(b+c) i.e. addition is
associative for integers.
For any three integers a, b and c,
(a*b)*c=a*(b*c) i.e. for integers the
multiplication is associative.

11. DISTRIBUTIVE PROPERTY
For any three integers a, b and c,
a*(b+c)=a*b+a*c i.e. integers show
distributive property under addition
and multiplication.

12. ADDITIVE IDENTITY
When we add zero to any whole
number, we get the same whole
number.
Zero is an additive identity for whole
numbers.

13. MULTIPLICATIVE IDENTITY
One is the
multiplicative
identity for
whole numbers
as well as for
integers.
Thus
a*1=1*a=a.

14. ADDITIVE INVERSE
The additive inverse of any integer a is –a
and the additive inverse of –a is a.
The number zero is its own additive
inverse.
INTEGERS ADDITIVE
INVERSE
10 -10
-10 10

15. IMPORTANT POINTS
Integers are closed for addition and subtraction
both i.e. if a and b are integers then a+b and a-b are
also integers.
For any two integers a and b, a*b is an integer i.e.
integers are closed under multiplication.
For any integer a, we have:
i. a/0 is not defined
ii. a/1 is equal to a
Absolute value of an integer is its numerical value
regardless of its sign.

16. THANK YOU
By:-
Shivika
And
Aarushi
7th - b