1. WHAT ARE INTEGERS
2. ADDITION OF INTEGERS
2.1. RULES
2.1.1. rule 1
2.1.1.1. (+2 )+(+2 ) = + 4
2.1.1.2. (-2 ) + (-2) = - 4
2.1.1.3. if two positive or or negative integers are added , we add their VALUES regardless of their SIGNS
2.1.1.3.1. and give common SAME SIGN
2.1.1.4. (+) + ( + ) = +
2.1.1.5. ( - ) + ( - ) = +
2.1.2. rule 2
2.1.2.1. (+2) + ( - 4) = difference is 2 and sign of greater value 4 is - , so answer is = - 2
2.1.2.2. for adding positive and negative integers 1) we find difference between their values 2) we give the sign of greater value
2.1.2.2.1. (- ) + ( + ) = FIND DIFFERENCE AND GIVE SIGN OF GREATER VALUE
2.2. PROPERTIES
2.2.1. CLOSURE PROPERTY OF ADDITION
2.2.1.1. a+b= integer
2.2.1.2. a+ (-b) = integer
2.2.1.3. (-a)+(-b)=integer
2.2.2. COMMUTATIVE LAW OF ADDITION
2.2.2.1. a+b = b+ a
2.2.2.1.1. +2 + ( -5) = (-5 ) + 2 -3 = -3
2.2.3. ASSOCIATIVE LAW OF ADDITION
2.2.3.1. a + ( b + c) = ( a+b)+c
2.2.3.1.1. 1for adding positive and negative integers 1) we find difference between their values for adding positive and negative integers 1) we find difference between their values 2) we give the sign of greater value for adding positive and negative integers 1) we find difference between their values 2) we give the sign of greater value 2) we give the sign of greater value 1+ ( 2+ 3)= ( 1 + 2 ) + 3 1 + 5 = 3 + 3 6 6
2.2.4. EXISTENCE OF ADDDITIVE IDENTITY
2.2.4.1. a+ ( -a) = (-a )+ a = 0
2.2.4.1.1. 2 + ( -2) = 0 (-2) + 2 = 0
3. ABOUT ME
4. SUBTRACTION OF INTEGERS
4.1. RULES
4.1.1. RULE 1
4.1.1.1. a-b=a+(-b)
4.1.1.1.1. this rule helps us to understand that if something like this comes in a problem +(- ) it has to be subtracted
4.1.2. RULE 2
4.1.2.1. a - ( - b ) = a + b
4.1.2.1.1. this rule helps us to understand that if something like this comes in a problem -( -) it has to be added
4.2. PROPERTIES
4.2.1. CLOSURE PROPERTY OF SUBTRACTION
4.2.1.1. a - b = integer
4.2.1.2. a- ( - b) = integer
4.2.1.3. ( - a ) - ( - b ) = integer
4.2.1.4. IF A AND B ARE TWO INTEGERS THEN A - B IS ALWAYS AN INTEGER
4.2.2. COMMUTATIVE LAW OF SUBTRACTION
4.2.2.1. A - B =/= B - A
4.2.2.1.1. A - B IS NOT EQUAL TO B - A
4.3. ASSOCIATIVE LAW OF SUBTRACTION
4.3.1. A - ( B - C ) =/= (A - B ) - C
4.3.1.1. SUBTRACTION OF INTEGERS IS NOT ASSOCIATIVE
4.3.1.1.1. 5 - ( 3-2 ) NOT EQUAL TOO ( 5-3 ) - 2
5. MULTIPLICATION OF INTEGERS
5.1. RULES
5.1.1. RULE 1
5.1.1.1. A X B = C
5.1.1.2. -A X - B = C
5.1.2. RULE 2
5.1.2.1. A X - B = - C
5.1.2.2. - A X B = - C
5.2. PROPERTIES
5.2.1. CLOSURE PROPERTY OF MULTIPLICATION
5.2.1.1. A X B = INTEGER
5.2.2. COMMUTATIVE LAW OF MULTIPLICATION
5.2.2.1. A X B = B X A
5.2.3. ASSOCIATIVE LAW OF MULTIPLICATION
5.2.3.1. A X ( B X C ) = ( A X B ) X C
5.2.4. DISTRIBUTIVE LAW OF MULTIPLICATION OVER ADDITION
5.2.4.1. A X ( B + C ) = A X B + A X C
5.2.5. EXISTENCE OF MULTIPLICATIVE IDENTITY
5.2.5.1. A X 1 = 1 X A = A
5.2.6. EXISTENCE OF MULTIPLICATIVE INVERSE
5.2.6.1. A X 1 /A = I/A X A
5.2.6.1.1. 6 X 1/6 = 1/6 X 6
6. DIVISION OF INTEGERS
6.1. RULES
6.1.1. RULE 1
6.1.1.1. A/-B = - C
6.1.1.2. -A / B = - C
6.1.2. RULE 2
6.1.2.1. -A / - B = C
6.2. PROPERTIES
6.2.1. CLOSURE PROPERTY OF DIVISION
6.2.1.1. A/B MAY NOT AN INTEGER ALWAYS
6.2.2. DIVISION OF SAME INTEGERS COME TO 1
6.2.2.1. A/A = 1
6.2.2.1.1. EXAMPLES :
6.2.3. ANY INTEGER DIVIDED BY 1 IS SAME INTEGER
6.2.3.1. A/1 = A
6.2.3.1.1. - A / 1 = - A
6.2.4. ANY INTEGER DIVIDED BY 0 IS SAME INTEGER
6.2.4.1. A / 0 = A
6.2.4.1.1. 3/0 = 3
6.2.5. IF ZERO IS DIVIDED BY INTEGER = 0
6.2.5.1. 0/3 = 0 . 0/ - 9 = 0
6.2.5.2. 0/ A = 0