## 12 January 2014

Operations on Integers • When two positive integers are added, we get a positive integer; 9 + 2 = 11.
• When two negative integers are added, we get a negative integer; -2 + (-3) = -5.
• When a positive and a negative integer are added, the sing of the sum is always the sing of the bigger number of the two, without considering their sign 55 + -25 = 30 and -55 + 25 = -30.
• The additive inverse of any integer a is -a , and the additive inverse of (-a ) is a . Integer (-12) = Additive Inverse (12).
• Subtraction is the opposite of addition and therefore, we add the additive inverse of the integer that is being subtracted, to the other integer.Hence, 23 - 43 =23 + Additive Inverse of 43 + 23 + (-43) = -20.
• The product of a positive and a negative integer is a negative integer.
• If the number of negative integers in a product is even, then the product is a positive integer, and if the number of negative integers in a
• product is odd, then the product is a negative integer.
• Division is the inverse operation of multiplication.
• The division of a negative integer by a positive integer results in a negative integer.
• The division of a positive integer by a negative integer results in a negative integer.
• The division of a negative integer by a negative integer results in a positive integer.
• For any integer p, p multiplied with zero is equal to zero multiplied with p, which is equal to zero.
• For any integer p, p divided by zero is not defined, and zero divided by p is equal to zero, where p is not equal to zero.

Properties of Integers

• Integers are closed under addition and subtraction. 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 .
• Integers are closed under multiplication. That is, a × b is an integer, for any two integers a and b .
• Multiplication is commutative for integers. That is, a × b = b × a for any integers a and b .
• The integer 1 is the identity under multiplication, i.e., 1 × a = a × 1 = a, for any integer a .
• Multiplication is associative for inters, i.e.,(a × b) × c = a × (b × c), for any three integers a, b and c.
• Distributive property of multiplication over addition: For any integers a, b, c we have a × (b + c) = a × b + a × c.
• Distributive property of multiplication integers a, b, c we have a × (b - c) = a × b - a × c.

 With our free PDF notes you can get success in any competitive or entrance exams like CTET,  KVS, NET, CAT, MAT, CMAT, SSC, B.ED, IBPS Recruitment, IAS, CSAT, State Civil Services Exams, UPTET, PSTET, HTET & many more. It also provides NCERT solutions, CBSE, NTSE, Olympiad study material, Indian General Knowledge, English, Hindi, Mathematics, Current affairs, Science, S.ST, model test papers, important Questions and Answers asked in CBSE examinations.