RBSE Class 7 Maths Notes Chapter 1 Integers

These comprehensive RBSE Class 7 Maths Notes Chapter 1 Integers will give a brief overview of all the concepts.

RBSE Class 7 Maths Chapter 1 Notes Integers

→ Integers are a bigger collection of numbers, which is formed by whole numbers and their negatives.

→ Numbers ................ - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, ................. are integers.

→ 1, 2, 3, 4, are positive integers and ................. - 4, - 3, - 2, - 1 are negative integers.

→ 0 is neither negative nor positive integer.

→ On a number line, the integers to the right of 0 are positive integers and to the left of 0 are negative integers.

→ 0 is less than all positive integers and greater than all negative integers.

→ All positive integers are greater than all negative integers.

→ Integers are closed under addition and subtraction. In general, for any two integers a and b, a + b and a - b both are integers.

→ Addition is commutative for integers. Thus for any two integers a and 6, we can say a + b = b + a.

→ Addition is associative for integers. Thus for any integers a, b and c, we can say (a + b) + c = a + (b + c).

→ Zero is an additive identity for integers. In general, for any integer a, a + 0 = 0 + a = a.

→ Product of a positive and a negative integer is a negative integer, whereas the product of two negative integers is a positive integer.

→ Product of even number of negative integers is positive, whereas the product of odd number of negative integers is negative.

→ Integers show some properties under multiplication:

• 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 integers, i.e., (a × b) × c = a × (b × c) for any three integers a, b and c.

→ Under addition and multiplication, integers show a property called distributive property. That is, a × (b + c) = a × b + a × c for any three integers a, b and c.

→ The properties of commutativity, associativity under addition and multiplication and the distributive property help us to make our calculations easier.

→ When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice-versa.

→ Division of a negative integer by another negative integer gives a positive integer as quotient.

→ For any integer a, we have :

• a ÷ 0 is not defined.
• a ÷ 1 = a
• 0 + a = 0 (if a ≠ 0).