Class 7 Chapter 1: Integers

# Class 7 Chapter 1: Integers

Important Concepts and Formulas

1.      Numbers below zero are negative numbers.

2.      Negative numbers together with whole numbers are called integers … –3, –2, –1, 0, 1, 2, 3, … are integers.

3.      The numbers 1, 2, 3, 4, … are positive integers and –1, –2, –3, … are negative integers.

4.      The number 0 is neither positive nor negative.

5.      The absolute value of an integer is always positive and is equal to the numerical value of that integer.

6.      Every positive integer is greater than 0 and every negative integer is smaller than 0.

7.      The greatest negative integer is −1 and the smallest positive integer is 1.

8.      Integers are closed under addition and subtraction, i.e., if a and b are any two integers, then (a + b) and (a – b) are also integers.

9.      Addition of integers is commutative. For any two integers a and b, we have a + b = b + a.

10.  Addition of integers is also associative. For any three integers a, b and c, we have (a + b) + c = a + (b + c).

11.  For every integer, 0 is the identity element under addition, i.e., a + 0 = a = 0 + a.

12.  Integers are closed under multiplication, i.e., for any two integers a and b, (a × b) is an integer.

13.  Multiplication is commutative for integers, i.e., for any two integers a and b, a × b = b × a.

14.  Multiplication of integers is associative, i.e., for any three integers a, b and c, we have (a × b) × c = a × (b × c).

15.  Multiplication of integers is distributive, i.e., if a, b and c are integers, then a × (b + c) = a × b + a × c and a × (b – c) = a × b – a × c.