a very good presentaion on integers in which you can learn addition.subtraction, multiplication and division of integers as well as their properties

1. INTEGERS

2. UNDERSTANDING INTEGERS
• Integers form a bigger collection of numbers which
contains whole numbers and negative numbers.
• The numbers _ _ _, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 _ _
_ etc are integers.
• 1, 2, 3, 4, 5 _ _ _ are Positive integers.
• _ _ _-5, -4 , -3, -2, -1 are Negative integers.
• Integer ‘0’ is neither a positive nor negative integer.
• Integer ‘0’ is less than a positive integer and greater
than negative integer.

3. NUMBER LINE

4. ADDING INTEGERS ON NUMBER LINE
• On a number line when we
• add a positive integer, we move to the right.
• E.g.: -4+2=-2
• add a negative integer, we move to left.
• E.g.: 6+(-4)=2

5. SUBTRACTING INTEGERS ON NUMBER LINE
• On a number line when we
• Subtract a positive integer, We move to the left
• E.g.: (-4)-2=-6
• Subtract a negative integer, We move to the right
• E.g.: 1-(-2)=3

6. SIGNS
SIGN
E.g.: 6+3=9
E.g.: -9-2= -11
greater value
E.g.: +2-4= -2
-2+4=+2

7. ADDITIVE INVERSE
INTEGER ADDITIVE INVERSE
10 -10
-10 10
76 -76
-76 76
0 0

9. CLOSURE PROPERTY
• ADDITION:
Integers are closed under addition. In general
for any two integers a and b, a+b is an integer.
E.g.: -2+4=2
• SUBTRACTION:
Integers are closed under subtraction. If a and
b are two integers then a-b is also an integer.
E.g.: -6-2=-8

10. COMMUTATIVE PROPERTY
• ADDITION:
This property tells us that the sum of two
integers remains the same even if the order of
integers is changed. If a and b are two
integers, then a+b = b+a
E.g.: -2+3 =3+(-2)
• SUBTRACTION:
The subtraction of two integers is not
commutative. If a and b are two integers ,then
a-b = b-a
E.g.: 4-(-6) = -6-4

11. ASSOCIATIVE PROPERTY
• ADDITION:
This property tells us that that we can group
integers in a sum in any way we want and still get
the same answer. Addition is associative for
integers. In general, a+(b+c) = (a+b)+c
E.g.: 2+(3+4) = (2+3)+4 =9
• SUBTRACTION:
The subtraction of integers is not associative. In
general, a-(b-c) = (a-b)-c
E.g.: 3-(5-7) = (3-5)-7
5 = -9

12. MULTIPLICATION OF INTEGERS
• Multiplication of two positive integers:
If a and b are two positive integers then their product is
also a positive integer
i.e.: a x b = ab
• Multiplication of a Positive and a Negative Integer:
While multiplying a positive integer and a negative
integer, we multiply them as whole numbers and put a
minus sign(-) before the product. We thus get a negative
integer. In general, a x (-b) = -(a x b)
• Multiplication of two negative integers:
Product of two negative integers is a positive integers. We
multiply two negative integers as whole numbers and put
the positive sign before the product. In general,
-a x -b = a x b

14. PROPERTIES OF MULTIPLICATION OF
INTEGERS
• Closure under Multiplication:
The product of two integers is an integer. Integers
are closed under multiplication. In general, a x b
is an integer.
e.g.: -2 x 2 = -4
• Commutativity of Multiplication:
The product of two integers remain the same
even if the order is changed. Multiplication is
commutative for integers. In general, a x b =b x a
e.g.: 2 x (-3) = -3 x 2

15. • Associativity of multiplication:
The product of three integers remains the
same, irrespective of their arrangements.
In general, if a, b and c are three integers, then a x (b x c)
= (a x b) x c
e.g.: -2 x (3 x 4) = (-2 x 3) x 4 = -24
• Multiplication by zero:
The product of any integer and zero is always.
In general, a x 0 = 0 x a =0
e.g.: -2 x 0 =0
• Multiplicative identity:
The product of any integer and 1 is the integer itself. In
general, a x 1 = 1 x a = a
e.g.: -5 x 1= -5

16. DISTRIBUTIVE PROPERTY
• Distributivity of multiplication over addition:
If a, b and c are three integers, then
a x (b+c) = a x b + a x c
e.g.: -2 x (4+5) = -2 x 4 + -2 x 5
• Distributivity of multiplication over subtraction:
If a, b and c are three integers, then
a x (b-c) = a x b - a x c
e.g.: -9 x (3-2) = -9 x 3 – (-9) x 2

17. DIVISION OF INTEGERS
• Division of two Positive Integers:
If a and b are two positive integers then their quotient is
also a positive integer.
e.g.: 4 ÷ 2 = 2
• Division of a positive and a negative integer:
When we divide a positive integer and a negative
integer, we divide them as whole numbers and then put
a minus sign (-) before the quotient. We, thus, get a
negative integer. In general, a÷ (-b) = (-a) ÷ b where b =
0
• Division of two negative integers:
When we divide two negative integers, we first divide
them as two whole numbers and then put a positive sign
(+). We, thus, get a positive integer. In general,

18. PROPERTIES OF DIVISION OF INTEGERS
• Integers are not closed under division. In other words if
a and b are two integers, then a ÷ b may or may not be
an integer.
• Division of integers is not commutative. In other
words, if a and b are two integers, then a ÷ b = b ÷ a.
• Division by 0 is meaningless operation. In other words
for any integer a, a ÷ 0 is not defined whereas 0 ÷ a = 0
for a = 0.
• Any integer divided by 1 give the same integer. If a is an
integer, then a ÷ 1 = a.
• For any integer a, division by -1 does not give the same
integer. In general, a ÷(-1) = -a but -a ÷ (-1) = a

19. Made by : Samyak Jain
Class: VII D