# Chapter 1 – Integers

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Class 7th Mathematics chapter ‘Integers‘ is an essential chapter, as it forms the basis of higher-level mathematics. It covers all the critical topics related to integers and numbers. It is also used in successive chapters of class 7th mathematics, so a clear understanding of integers will make understanding other mathematical concepts easier.

The chapter ‘Integers’ covers the following topics:

• Natural and whole numbers
• Properties of Integers for addition and subtraction
• Properties of Integers for multiplication and division
• Representation of Integers on the number line

#### What are Natural and Whole Numbers?

Natural numbers are a set of positive numbers starting from 1. It does not include 0.

Whole numbers are all positive numbers, along with 0. It is a collection of both 0 and natural numbers.

#### What are Integers?

Integers are all whole numbers along with their negatives. It includes both positive and negative whole numbers.

#### Properties of Addition And Subtraction of Integers

Following are the integrative properties of addition and subtraction of integers:

• Closure under Addition: If there are 2 integers x and y, then x+y is also an integer.
• Closure under Subtraction: If there are 2 integers x and y, then x-y is also an integer.
• Associative Property of Integers: If there are 3 integers x, y and z, then (x+y)+z = x+(y+z).
• Commutative Property of Integers: If there are 2 integers x and y, then x+y = y+x.

Additive identity is the number which, when added to any integer, number remains the same. Additive identity for any integer is 0 as x+0 = 0+x = x where x is an integer. For example: 5+0 = 0+5 = 5.

Additive inverse is any number which, when added to an integer, the answer is equal to 0. Additive inverse of any integer is the negative of that integer as x+(-x) = 0, where x is an integer. For example, 2 is the additive inverse of (-2) and -3 is the additive inverse of 3.

#### Multiplication of Integers

The result of the multiplication of two integers is as follows:

• Multiplication of any two positive integers is a positive integer. For example: (+4) × (+6) = +24
• Multiplication of any two negative integers is a positive integer. For example: (-4) × (-6) = +24
• When a positive and a negative integer are multiplied, then the result is a negative integer. For example: (+4) × (-6) = -24

#### Integrative Properties of Multiplication

Following are the integrative properties of multiplication:

• Closure under Multiplication: If there are 2 integers x and y, then x multiplied by y is also an integer.
• Associative Property of Multiplication: If there are 3 integers a, b and c, then (a×b) ×c = a× (b×c).
• Commutative Property of Multiplication of Integers: If there are 2 integers a and b, then a×b = b×a.
• Distributive Property: The distributive property of Integers is used in the case of multiplication and addition to make calculations easier. If there are 3 integers a, b and c, then a×(b+c) = (a×b) + (a×c).
• Multiplicative Identity: Multiplicative identity is the number that, when multiplied to any integer, remains the same. Multiplicative identity for any integer is 1 as a×1 = 1×a = a where a is an integer. For example: 5×1 = 1×5 = 5.

#### Division of Integers

The result of the division of two integers is as follows:

• The division of any two positive integers is a positive integer. For example: (+4)÷(+6) = +24
• The division of any two negative integers is a positive integer. For example: (-4)÷(-6) = +24
• The division of a positive integer and a negative integer is a negative integer. For example: (+4)÷(-6) = -24 and (-4)÷(+6) = -24.

#### Representation of Integers on a Number Line

A number line is a single axis line that has integer markings at an equal interval. Addition and subtraction of the integers are represented on a number line in the following ways:

• A positive integer is added to any integer by moving to the right on a number line.
• Any negative integer is added to any other integer by moving to the left on a number line.
• A positive integer is subtracted from any integer by moving to the left on a number line.
• A negative integer is subtracted from any integer by moving to the right on a number line.

#### Conclusion

The chapter ‘Integers’ is an important topic for class 7th mathematics, and an essential concept for advanced and higher-level mathematics. This chapter will smoothen your journey through the upcoming mathematics chapters like algebra, coordinate geometry, statistics, and calculus.

#### FAQs

1. What are Integers in math?
Integers are all whole numbers along with their negatives. It includes both positive and negative whole numbers.
2. What is the rule for integers?
• The addition of any two positive integers is a positive integer.
• The addition of any two negative integers is a negative integer.
• The addition of a positive integer and a negative integer is the difference between the integers. The resultant integer bears the sign of the bigger integer.
• Multiplication of any two positive integers is a positive integer.
• Multiplication of any two negative integers is a positive integer.
• When a positive and a negative integer are multiplied, then the result is a negative integer.
3. What are the types of integers?
Integersare of three types:

• Zero
• Positive integers
• Negative integers
4. What is an integer of 4?
4 is a positive integer and a rational number. The negative integer of 4 is (-4).
5. Is 0 a positive or a negative integer?
0 is neither a positive nor a negative integer.

‘Integers‘ is an exciting chapter of mathematics. So, the visual representation of this chapter is really important. The MSVgo app is a video library platform that helps you comprehend topics through exploratory representations and practical models. MSVgo helps you to comprehend the Math & Science behind concepts through interesting visual animations and videos. So, do check out the videos at MSVgo for better understanding.

### High School Physics

• Alternating Current
• Atoms
• Communication Systems
• Current Electricity
• Dual nature of Radiation and Matter
• Electric Charges and Fields
• Electricity
• Electromagnetic Induction
• Electromagnetic Waves
• Electrons and Photons
• Electrostatic Potential and Capacitance
• Fluid Pressure
• Force and Acceleration
• Force And Laws Of Motion
• Gravitation
• Internal Energy
• Kinetic Theory
• Law of motion
• Light – Reflection And Refraction
• Magnetic Effects Of Electric Current
• Magnetism and Matter
• Management Of Natural Resources
• Mechanical properties of Fluids
• Mechanical properties of Solids
• Motion
• Motion in a plane
• Motion in a straight line
• Moving Charges and Magnetism
• Nuclear Energy
• Nuclei
• Oscillations
• Our Environment
• Paths of Heat
• Physical world
• Ray optics and optical instruments
• Semiconductor Devices
• Semiconductor Electronics: Materials, Devices and Simple Circuits
• Simple Machines
• Sound
• Sources Of Energy
• Specific and Latent Heats
• Spherical Mirrors
• Static Electricity
• Systems of Particles and Rotational motion
• Thermal properties of matter
• Thermodynamics
• Units and Measurement
• Vectors, Scalar Quantities and Elementary Calculus
• Wave Optics
• Waves
• Work, Power and Energy

### High School Chemistry

• Acids, Bases and Salts
• Alcohols, Phenols and Ethers
• Aldehydes, Ketones and Carboxylic Acids
• Aliphatic and Aromatic Hydrocarbons
• Alkyl and Aryl Halides
• Amines
• Analytical Chemistry
• Atomic Structure
• Atoms And Molecules
• Basic concepts of Chemistry
• Biomolecules
• Carbon And Its Compounds
• Carboxylic acids and Acid Derivatives
• Chemical Bonding and Molecular Structures
• Chemical Energetics
• Chemical Equilibria
• Chemical Kinetics
• Chemical Reactions And Equations
• Chemical Reactions and Their Mechanisms
• Chemistry in Everyday Life
• Chemistry of p-Block elements
• Chemistry of Transition and Inner Transition
• Classification of Elements
• Coordination Compounds
• Cyanide, Isocyanide, Nitro compounds and Amines
• Electrochemistry
• Electrolysis
• Elements, Compounds and Mixtures
• Environmental Chemistry
• Equilibrium
• Ethers and Carbonyl compounds
• Haloalkanes and Haloarenes
• Hydrocarbons
• Hydrogen
• Ideal solutions
• Introduction to Organic Chemistry
• Ionic equilibria
• Matter
• Matter Around Us
• Matter In Our Surroundings
• Metallurgy
• Metals And Non-Metals
• Mole Concept and Stoichiometry
• Natural Resources
• Organic Chemistry – Basic Principles
• Periodic Classification of Elements
• Physical and Chemical Changes
• Physical and Chemical Properties of Water
• Polymers
• Preparation, Properties and Uses of Compounds
• Principles and Processes of Isolation of Elements
• Redox Reactions
• Relative Molecular Mass and Mole
• States of Matter
• Structure Of The Atom
• Study of Compounds
• Study of Gas Laws
• Study of Representative Elements
• Surface Chemistry
• The d-block and f-block elements
• The Gaseous State
• The p-Block Elements
• The Periodic Table
• The s-Block Elements
• The Solid State
• Thermodynamics

### High School Biology

• Absorption and Movement of Water in Plants
• Anatomy of Flowering Plants
• Animal Kingdom
• Bacteria and Fungi-Friends and Foe
• Biodiversity and Conservation
• Biofertilizers
• Biological Classification
• Biomedical Engineering
• Biomolecules
• Biotechnology and its Applications
• Biotic Community
• Body Fluids and Circulation
• Breathing and Exchange of Gases
• Cell – Unit of Life
• Cell Cycle and Cell Division
• Cell Division and Structure of Chromosomes
• Cell Reproduction
• Cellular Respiration
• Chemical Coordination and Integration
• Circulation
• Control And Coordination
• Crop Improvement
• Digestion and Absorption
• Diversity In Living Organisms
• Ecosystem
• Environmental Issues
• Excretory Products and their Elimination
• Flowering Plants
• Genes and Chromosomes
• Health and Diseases
• Health and Its Significance
• Heredity And Evolution
• Heredity and Variation
• How Do Organisms Reproduce?
• Human Diseases
• Human Eye And Colourful World
• Human Health and Disease
• Human Population
• Human Reproduction
• Hygiene
• Improvement In Food Resources
• Integumentary System- Skin
• Kingdom Fungi
• Kingdom Monera
• Kingdom Protista
• Life Processes
• Locomotion and Movement
• Microbes in Human Welfare
• Mineral Nutrition
• Molecular Basis of Inheritance
• Morphology of Flowering Plants
• Neural Control And Coordination
• Nutrition in Human Beings
• Organism and Population
• Photosynthesis
• Photosynthesis in Higher Plants
• Plant Growth and Development
• Plant Kingdom
• Pollination and Fertilization
• Pollution; Sources and its effects
• Principles of Inheritance and Variation
• Reproduction and Development in Angiosperms
• Reproduction in Organisms
• Reproductive Health
• Respiration in Human Beings
• Respiration in Plants
• Respiratory System
• Sexual Reproduction in Flowering Plants
• Strategies for Enhancement in Food Production
• Structural Organisation in Animals
• Structural Organisation of the Cell
• The Endocrine System
• The Fundamental Unit Of Life
• The Living World
• The Nervous System and Sense Organs
• Tissues
• Transpiration
• Transport in Plants

### High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
• Algebra – Polynomials
• Algebra – Principle of Mathematical Induction
• Binomial Theorem
• Calculus – Applications of Derivatives
• Calculus – Applications of the Integrals
• Calculus – Continuity and Differentiability
• Calculus – Differential Equations
• Calculus – Integrals
• Geometry – Area
• Geometry – Circles
• Geometry – Conic Sections
• Geometry – Constructions
• Geometry – Introduction to Euclid’s Geometry
• Geometry – Three-dimensional Geometry
• Geometry – Lines and Angles
• Geometry – Straight Lines
• Geometry – Triangles
• Linear Programming
• Matrices and Determinants
• Mensuration – Areas
• Mensuration – Surface Areas and Volumes
• Number Systems
• Number Systems – Real Numbers
• Permutations and Combinations
• Probability
• Sequence and Series
• Sets and Functions
• Statistics
• Trignometry – Height and Distance
• Trignometry – Identities
• Trignometry – Introduction

### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
• Body Movements
• Carbon and Its Compounds
• Cell – Structure And Functions
• Changes Around Us
• Chemical Effects Of Electric Current
• Coal And Petroleum
• Combustion And Flame
• Components Of Food
• Conservation Of Plants And Animals
• Crop Production And Management
• Electric Current And Its Effects
• Electricity And Circuits
• Elements and Compounds
• Fibre To Fabric
• Food production and management
• Force And Pressure
• Forests: Our Lifeline
• Friction
• Fun With Magnets
• Garbage In, Garbage Out
• Getting To Know Plants
• Health and Hygiene
• Heat
• Hydrogen
• Life Processes: Nutrition in Animals and Plants
• Materials: Metals And Non-Metals
• Matter and Its States
• Metals and Non-metals
• Micro Organisms: Friend And Foe
• Motion And Measurement Of Distances
• Motion And Time
• Nutrition In Animals
• Nutrition In Plants
• Organization in Living Things
• Our Environment
• Physical And Chemical Changes
• Pollution and conservation
• Pollution Of Air And Water
• Reaching The Age Of Adolescence
• Reproduction In Animals
• Reproduction In Plants
• Respiration In Organisms
• Rocks and Minerals
• Separation Of Substances
• Simple Machines
• Soil
• Some Natural Phenomena
• Sorting Materials Into Groups
• Sound
• Stars And The Solar System
• Structure of Atom
• Synthetic Fibers And Plastics
• The Living Organisms And Their Surroundings
• Transfer of Heat
• Transformation of Substances
• Transportation In Animals And Plants
• Universe
• Waste-water Story
• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time