# Chapter 1 Integers Class 7 Notes Maths

Integers Class 7 Notes Maths is given on this page that will provide a quick glimpse of the chapter and improve the learning experience. NCERT Notes becomes a vital resource for all the students to self-study from NCERT textbooks carefully. Chapter 1 Class 7 Maths Notes will help in understanding the complex topics easily and boost their preparation and assessment of understood concepts. Class 7 Maths Revision Notes are prepared by Studyrankers experts who have great experience in Maths subject.

Integers

â€¢ Integers are the collection of whole numbers and theirÂ  negatives. Positive Integers are 1, 2, 3 ... . Negative Integers are 1, 2, 3 ... .

â€¢ Every positive integers is greater than every negative integers.

â€¢ Zero is less than every positive integers and greater than every negative integers.

â€¢ Number line : On a number line, when we
(a) add a positive integer, we move to the right.
(b) add a negative integer, we move to the left.
(c) subtract a positive integer, we move to the left.
(d) subtract a negative integer, we move to the right.

Whole Numbers

â€¢ Whole Numbers are all natural numbers along with zero (0) are called whole numbers.

â€¢ Zero is the only whole number that is not a natural number.

â€¢ When two positive integers are added we get a positive integer. Example: 44+ 71 = 116.

â€¢ When two negative integers are added we get a negative integer. Example: (-44) + (-71)=-116.

â€¢ When one positive and one negative integers is added, we take their difference and place the sign of the bigger integer. Example: (-44) + (71) = 27

â€¢ The additive inverse of any integer a is a and additive inverse of (-a) is a.

â€¢ Closure Property:Â For any two integers a and b, a+b is an integer.Â Example: 20+10 = 30 is an integer and -8 + 5 =-3 is an integer.

â€¢ CommutativityÂ Property: For any two integers a and b, a + b = b + a. Example: 7+(-6)=-1 and (-7) + 6 =-1 So, 6+(-7)= (-7) +6.

â€¢ Associativity Property:Â For any three integers a, b, and c, we have a +(b + c) = (a +b) +C Example: (-7) + [(-2) + (-1)] = [(-7) + (-1)] +(-2) = -10.

â€¢ Zero is an additive identity for integers. For any integer a, a + 0 = a = 0 + a.

Subtraction

â€¢ Closure Property: For any two integers a and b, a-b is an integer. Example: 20-10 = 10 is an integer.

â€¢ CommutativityÂ Property:Â The subtraction is not commutative for whole numbers. For example, 20 â€“ 30 = -10 and 30 â€“ 20 = 10. So, 20 â€“ 30Â â‰  30 â€“ 20.

â€¢ Subtraction is not associative for integers.

Multiplication

â€¢ Product of a positive integer and a negative integer is a negative integer. a Ã— (â€“b) = â€“ ab, where a and b are integers.

â€¢ Product of two negative integers is a positive integer. (â€“a) Ã— (â€“b) = ab, where a and b are integers.

â€¢ Product of even number of negative integers is positive, where as the product of odd number of negative integersÂ is negative.

â€¢ Closure Property: For all integers a and b, aÃ—b is an integer. For example: (-3) (-5) = 150 is an integer.

â€¢ CommutativityÂ Property: For any two integers a and b, aÃ—b = bÃ—a. For example: (-3) Ã— (-5) = (-5) Ã— (-5) = -15.

â€¢ Associativity Property: For any three integers a,b and c, (aÃ—b) Ã— c = aÃ— (b Ã— c). For example, (-7) Ã—Â [(-2) Ã—Â (-1)] = [(-7) Ã—Â (-1)] Ã—(-2) = -14.

â€¢ Distributivity Property:Â For any three integers a,b and c, aÃ—(b + c)= a Ã— b + aÃ—c Example: (-2) (3 + 5) = [(-2)Ã—3] + [(-2)Ã—Â 5] =-16.

â€¢ The product of a integer and zero is again zero.

â€¢Â 1 is the multiplicative identity for negative integers.

Division

â€¢ When a positive integer is divided by a negative integer or vice-versa and the quotient obtained is an integer, then it is a negative integer.Â  a Ã· (â€“b) = (â€“a) Ã· b = â€“ a/b , where a and b are positive integers and a/b is an integer.

â€¢ When a negative integer is divided by another negative integer to give an integer, then it gives a positive integer. (â€“a) Ã· (â€“b) = a/b, where a and b are positive integers and a/b is also an integer.

â€¢ For any integer a, a Ã· 1 = a and a Ã· 0 is not defined.
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