Notes On Operations on Integers - CBSE Class 7 Maths
The set of natural numbers, zero and the negatives of natural numbers form the set of Integers. The set of integers includes all the whole numbers. There is no smallest integer. Addition of Integers The sum of two positive integers results in a positive integer.   Ex: 8 + 2 = 10 The sum of two negative integers results in a negative integer. Ex:  (– 6) + (– 3) = – 9 The sum of a positive and a negative integer is the difference of the numbers with the sign of the larger integer of the two. Ex:  45 + (– 25) = 20 and (– 45) + 20 = – 25 The additive inverse of any integer 'a' is '– a', and the additive inverse of '– a' is 'a'. Ex: Additive inverse of (– 12) = – (– 12) = 12 Subtraction of Integers Subtraction is the opposite of addition, Therefore, to subtract two integers, we add the additive inverse of the integer that is being subtracted to the other integer.  Ex:  23 – 43 = 23 + (Additive inverse of 43) = 23 + (– 43) = – 20 Multiplication of Integers The product of two positive integers is a positive integer. The product of a positive and a negative integer is a negative integer. The product of two negative integers is a positive integer. If the number of negative integers in a product is even, then the product is a positive integer. Similarly, if the number of negative integers in a product is odd, then the product is a negative integer.  Division of Integers Division is the inverse operation of multiplication. The division of a positive integer by a positive integer results in a positive integer. 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 'a', a × 0 = 0 × a = 0.  a ÷ 0 is not defined. 0 ÷ a = 0, where a is not equal to zero.

Summary

The set of natural numbers, zero and the negatives of natural numbers form the set of Integers. The set of integers includes all the whole numbers. There is no smallest integer. Addition of Integers The sum of two positive integers results in a positive integer.   Ex: 8 + 2 = 10 The sum of two negative integers results in a negative integer. Ex:  (– 6) + (– 3) = – 9 The sum of a positive and a negative integer is the difference of the numbers with the sign of the larger integer of the two. Ex:  45 + (– 25) = 20 and (– 45) + 20 = – 25 The additive inverse of any integer 'a' is '– a', and the additive inverse of '– a' is 'a'. Ex: Additive inverse of (– 12) = – (– 12) = 12 Subtraction of Integers Subtraction is the opposite of addition, Therefore, to subtract two integers, we add the additive inverse of the integer that is being subtracted to the other integer.  Ex:  23 – 43 = 23 + (Additive inverse of 43) = 23 + (– 43) = – 20 Multiplication of Integers The product of two positive integers is a positive integer. The product of a positive and a negative integer is a negative integer. The product of two negative integers is a positive integer. If the number of negative integers in a product is even, then the product is a positive integer. Similarly, if the number of negative integers in a product is odd, then the product is a negative integer.  Division of Integers Division is the inverse operation of multiplication. The division of a positive integer by a positive integer results in a positive integer. 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 'a', a × 0 = 0 × a = 0.  a ÷ 0 is not defined. 0 ÷ a = 0, where a is not equal to zero.

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