The document discusses integers and operations on integers. It defines integers as the set of whole numbers and their opposites, including negative numbers. It introduces the concepts of the additive inverse and absolute value of integers. The four basic operations on integers - addition, subtraction, multiplication and division - are then explained through their properties and rules. Addition and subtraction of integers follows rules about keeping or changing signs based on the signs of the integers. Multiplication and division may result in changing the sign of the product or quotient depending on the signs of the integers.

2. • INTRODUCTION THE first numbers -to be
discovered were NATURAL NUMBERS i.e. 1,2,3,4,…If we include
zero to the collection of natural numbers we get a new
collection known as WHOLE NUMBERS i.e. 0,1,2,3,4,... There are
also numbers known as negative numbers .If we put the whole
numbers and the negative numbers together we get a new
collection of numbers which will look like 0,1,2,3,4,…,-1,-2,-3,-4,-
5…In this collection 1,2,3,…said to be positive integers and -1,-2,-
3,…are said to be negative integers but 0 is neither of them.

3. ADDITIVE INVERSE OF
INTEGERS
• For every integer a there exists its opposite –a such
that :-
• a +{-a } = 0 = {-a } + a
• Integers a and –a are called OPPOSITES or NEGATIVE
or ADDITIVE INVERSE of each other.
EXAMPLE:- {-1 } + {1} =0 and 1+{-1}
=0,:.,{-1 }+{1}= 0 ={1}+{-1 }
NOTE:- THE ADDITIVE INVERSE OF 0 IS 0.

4. ABSOLUTE VALUE OF
INTEGERS
 The absolute value of an integer is the numerical
value of the integer regardless of its sign.
 The absolute value of an integer is denoted by |a|.

5. OPERATIONS ON
INTEGERS
 The four basic operations namely:-
 ADDITION
 SUBTRACTION
 MULTIPLICATION
 DIVISION
 Can easily be done on integers.

6. ADDITION OF
INTEGERS{properties}
 PROPERTY 1- Closure PROPERTY 3- Associative
property of addition law of addition; If a,b,c
 The sum of two integers are any three integers
is always an integer. then {a+b}+c=a+{b+c}
 PROPERTY 2- PROPERTY 4- If a is any
Commutative property of integer then a+0=a and
addition 0+a=a
 If a and b are any two PROPERTY 5- The sum of
integers then a+b=b+a. an integer and its
. opposite is 0.

7. ADDITION OF
INTEGERS{RULES}
• RULE 1- If two positive positive and a negative
integers or two negative integer, we find the
integers are added, we difference between their
add their values absolute values regardless
regardless of their signs of their signs and give the
and give their common sign of the greater integer
sign to the sum. to it.
• EXAMPLE:- +1+4=+5 EXAMPLE:- -3+2=-1
• RULE 2- To add a -

8. SUBTRACTION OF
INTEGERS{Properties and Rules}
 PROPERTY 1- Closure property
 If a and b are integers then{a-b}is also an integer.
 PROPERTY 2- If a is any integer then {a-0}=a.
 PROPERTY 3- If a , b and c are integers and a>b
then{a-c}>{b-c}.
 RULE 1- To subtract one integer from another, we
take the additive inverse of the integer to be
subtracted and add it to the other integer.
 Thus, if a and b are two integers then a-b=a+{-b}.
 EXAMPLE:- 2-7=+5

9. MULTIPLICATION OF
INTEGERS{properties}
 PROPERTY 1- Closure property of multiplication ;The
product of two integers is always an integer.
 PROPERTY 2- Commutative law for multiplication ; For any
two integers a and b ,we have a*b=b*a.
 PROPERTY 3- Associative law for multiplication ; If a ,b and
c are any three integers then {a*b}*c=a*{b*c}.
 PROPERTY 4- Distributive law ; If a, b and c are any three
integers then a*{b + c}=a*b + a*c.
 PROPERTY 5- For any integer a we have a*1=a.1 is known as
the multiplicative identity for integers.
 PROPERTY 6- For any integer a we have a*0=0.

10. MULTIPLICATION OF
INTEGERS{Rules}
 RULE 1- To find the product of two integers with
unlike signs ,we find the product of their values
regardless of their signs and give a minus sign to
the answer. Example- -5*7=-35
 RULE 2- To find the product of two integers with
the same sign ,we find the product of their values
regardless of their signs and give a plus sign to the
answer. Example- -18*{-10}=+180.

11. DIVISION OF
INTEGERS{properties}
 PROPERTY 1-If a and b are integers then {a/b} is not
necessarily an integer.
 PROPERTY 2- If a is an integer and a is not equal to 0 then
{a/a}=1
 PROPERTY 3- if a is an integer then {a/1 }= a
 PROPERTY 4- if a is a non –zero number then {0/a }=0 but
{a/0}is not meaningful.

12. Division of integers
{rules}
RULE 1 - for dividing one integer by another , the
two having unlike signs we divide their values
regardless of their sign and give a minus {-} sign to
the quotient EXAMPLE {–36}/4={ -9 }
RULE 2- for dividing one integer by another , the two
having like signs , we divide their values regardless
of their signs and give a plus{+} sign to the
quotient.
EXAMPLE{-26}/{-2}=+13