CBSE Class–VII | CHAPTER – 1 Integers | NMMS Revision Notes

 Here is the NMMS  Revision Notes  CBSE Class–VII  | CHAPTER – 1 Integers |

• Integers are a bigger collection of numbers which is formed by whole numbers and their negatives.
• 
  
• You have studied in the earlier class, about the representation of integers on the number line and their addition and subtraction.
• We now study the properties satisfied by addition and subtraction.
  (a) 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.
  (b) Addition is commutative for integers, i.e., a + b = b + a for all integers a and b.
  (c) Addition is associative for integers, i.e., (a + b) + c = a + (b + c) for all integers a, b and c.
  (d) Integer 0 is the identity under addition. That is, a + 0 = 0 + a = a  for every integer a.
• We studied, how integers could be multiplied, and found that product of a positive and a negative integer is a negative integer, whereas the product of two negative integers is a positive integer. For example, – 2 × 7 = – 14 and – 3 × – 8 = 24.
• 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.
  (a) Integers are closed under multiplication. That is, a × b is an integer for any two integers a and b.
  (b) Multiplication is commutative for integers. That is, a × b = b × a for any integers a and b.
  (c) The integer 1 is the identity under multiplication, i.e., 1 × a = a × 1 = a for any integer a.
  (d) 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.
• We also learnt how to divide integers. We found that,
  (a) When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice-versa.
  (b) Division of a negative integer by another negative integer gives a positive integer as quotient.
• For any integer a, we have
  
  

For More :-

CBSE Class–VII  | CHAPTER – 1 Integers |  NMMS  Revision Notes  à Click Here

Tracing Changes Through a Thousand Years | NMMS Revision Notes | Class 7 | Social  à Click Here

New Kings and Kingdoms | NMMS Revision Notes | Class 7 | Social  à Click Here

The Delhi Sultanate | NMMS Revision Notes | Class 7 Social à Click Here

The Mughal Empire | NMMS Revision Notes | Class 7 Social à Click Here

Tribes Nomads and Settled Communities | NMMS Revision Notes | Class 7 Social à Click Here

Devotional Paths to the Divine | NMMS Revision Notes | Class 7 Social à Click Here

The Making of Regional Cultures | NMMS Revision Notes | Class 7 Social à Click Here

Eighteenth Century Political Formations | NMMS Revision Notes | Class 7 Social à Click Here

Environment | NMMS Revision Notes | Class 7 Social à Click Here

Inside Our Earth | NMMS Revision Notes | Class 7 Social à Click Here

Our Changing Earth | NMMS Revision Notes | Class 7 Social à Click Here

Air | NMMS Revision Notes | Class 7 Social  à Click Here

Water | NMMS Revision Notes | Class 7 Social à Click Here

Human Environment Interactions the Tropical | NMMS Revison Notes | Class 7 Social à Click Here

Life in the Deserts | NMMS Revision Notes | Class 7 Social à Click Here

On Equality | NMMS Revision Notes | Class 7 Social à Click Here

How the State Government Works | NMMS Revision Notes | Class 7 Social à Click Here

Role of the Government in Health | NMMS Revision Notes | Class 7 Social à Click Here

Growing up as Boys and Girls | NMMS Revision Notes | Class 7 Social à Click Here

Women Change the World | NMMS Revision Notes | Class 7 Social à Click Here

Understanding Media | NMMS Revision Notes | Class 7 Social à Click Here

Markets Around Us | NMMS Revision Notes | Class 7 Social à Click Here

A Shirt in the Market | NMMS Revision Notes | Class 7 Social à Click Here

Nutrition in Plants | NMMS Revision Notes | Class 7 Science à Click Here

Nutrition in Animals | NMMS Revision Notes | Class 7 Science à Click Here

Heat | NMMS Revision Notes | Class 7 Science à Click Here

Acids Bases And Salts | NMMS Revision Notes | Class 7 Science à Click Here

Physical And Chemical Changes | NMMS Revision Notes | Class 7 Science  à Click Here

Respiration In Organisms | NMMS Revision Notes | Class 7 Science à Click Here     

Transportation in Animals and Plants | NMMS Revision Notes | Class 7 Science à Click Here

Force and Pressure | NMMS Quick  Revision Notes | Class: 8 Physics à Click Here

Reproduction In Plants | NMMS Revision Notes | Class 7 Science à Click Here

Motion And Time | NMMS Revision Notes | Class 7 Science à Click Here

Electric Current and its Effects | NMMS Revision Notes | Class 7 Science à Click Here

Light | NMMS Revision Notes | Class 7 Science à Click Here

Waste Water Story | NMMS Revision Notes | Class 7 Science à Click Here

How When and Where | NMMS Revision Notes | Class 8 Social à Click Here

From Trade to Territory | NMMS Revision Notes | Class 8 Social à Click Here

Ruling the Countryside | NMMS Revision Notes | Class 8 Social à Click Here

Tribals Dikus and Vision of Golden Age | NMMS Revision Notes | Class 8 Social à Click Here

When People Rebel | NMMS Revision Notes | Class 8 Social à Click Here

Weavers Iron Smelters and Factory Owners | NMMS Revision Notes | Class 8 Social à Click Here

Civilising the Native Educating the Nation | NMMS Revision Notes | Class 8 Social à Click Here

Women Caste and Reform | NMMS Revision Notes | Class 8 Social à Click Here