Maths Chapter 01: Integers
Class 07 Maths NCERTIntegers are a bigger collection of numbers which is formed by whole numbers and their negatives. Integers are closed for addition and subtraction both. 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.
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.
Division
- When a positive integer is divided by a negative integer, the quotient obtained is negative and vice-versa.
- Division of a negative integer by another negative integer gives positive as quotient.
For any integer a, we have
- a ÷ 0 is not defined
- a ÷ 1 = a