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

• Integers are the collection of whole numbers and their  negatives. Positive Integers are 1, 2, 3 ... . Negative Integers are 1, 2, 3 ... .

• Every positive integers is greater than every negative integers.

• Zero is less than every positive integers and greater than every negative integers.

• 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

• Whole Numbers are all natural numbers along with zero (0) are called whole numbers.

• Zero is the only whole number that is not a natural number.

Addition

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

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

• 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

• The additive inverse of any integer a is a and additive inverse of (-a) is a.

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

• Commutativity 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.

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

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

Subtraction

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

• Commutativity Property: The subtraction is not commutative for whole numbers. For example, 20 – 30 = -10 and 30 – 20 = 10. So, 20 – 30 ≠ 30 – 20.

• Subtraction is not associative for integers.

Multiplication

• Product of a positive integer and a negative integer is a negative integer. a × (–b) = – ab, where a and b are integers.

• Product of two negative integers is a positive integer. (–a) × (–b) = ab, where a and b are integers.

• Product of even number of negative integers is positive, where as the product of odd number of negative integers is negative.

• Closure Property: For all integers a and b, a×b is an integer. For example: (-3) (-5) = 150 is an integer.

• Commutativity Property: For any two integers a and b, a×b = b×a. For example: (-3) × (-5) = (-5) × (-5) = -15.

• Associativity Property: For any three integers a,b and c, (a×b) × c = a× (b × c). For example, (-7) × [(-2) × (-1)] = [(-7) × (-1)] ×(-2) = -14.

• Distributivity Property: For any three integers a,b and c, a×(b + c)= a × b + a×c Example: (-2) (3 + 5) = [(-2)×3] + [(-2)× 5] =-16.

• The product of a integer and zero is again zero.

• 1 is the multiplicative identity for negative integers.

Division

• 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.  a ÷ (–b) = (–a) ÷ b = – a/b , where a and b are positive integers and a/b is an integer.

• When a negative integer is divided by another negative integer to give an integer, then it gives a positive integer. (–a) ÷ (–b) = a/b, where a and b are positive integers and a/b is also an integer.

• For any integer a, a ÷ 1 = a and a ÷ 0 is not defined.