NCERT Solutions for Class 7 Mathematics

Chapter 1: Integers

In this chapter the main key concepts you will be learning are Properties of Addition and Subtraction of Integers, Closure under Addition and Subtraction, Commutative Property, Associative Property, Additive Identity, Multiplication of Integers, Multiplication of a Positive and a Negative Integer, Multiplication of two Negative Integers, Product of three or more Negative Integers, Properties of Multiplication of Integers, Closure under Multiplication, Commutativity of Multiplication, Multiplication by Zero, Multiplicative Identity, Associativity for Multiplication, Distributive Property, Making Multiplication Easier, Division of Integers, Properties of Division of Integers

Chapter 2: Fractions and Decimals

In this chapter the main key concepts you will be learning are How Well Have You Learnt About Fractions? Multiplication of Fractions, Multiplication of a Fraction by a Whole Number, Multiplication of a Fraction by a Fraction, Division of Fractions, Division of Whole Number by a Fraction, Division of a Fraction by a Whole Number, Division of a Fraction by Another Fraction, How Well Have You Learnt About Decimal Numbers, Multiplication of Decimal Numbers, Multiplication of Decimal Numbers by 10, 100 and 1000, Division of Decimal Numbers, Division by 10, 100 and 1000, Division of a Decimal Number by a Whole Number, Division of a Decimal Number by another Decimal Number.

Chapter 3: Data Handling

In this chapter the main key concepts you will be learning are Collecting Data, Organisation of Data, Representative Values, Arithmetic Mean, Range, Mode, Mode of Large Data, Median, and Use of Bar Graphs with a Different Purpose, Choosing a Scale, Chance and Probability, Chance.

Chapter 4: Simple Equations

In this chapter the main key concepts you will be learning are A Mind-Reading Game! Setting Up of an Equation, Review of What We Know, What Equation Is? Solving an Equation, More Equations, From Solution to Equation, Applications of Simple Equations to Practical Situations

Chapter 5: Lines and Angles

In this chapter the main key concepts you will be learning are Related Angles, Complementary Angles, Supplementary Angles, Adjacent Angles, Linear Pair, Vertically Opposite Angles, Pairs of Lines, Intersecting Lines, Transversal, and Angles Made by a Transversal, Transversal of Parallel Lines, and Checking for Parallel Lines.

Chapter 6: Triangles and its Properties

In this chapter the main key concepts you will be learning are Medians of a Triangle, Altitudes of a Triangle, Exterior Angle of a Triangle and Its Property, Angle Sum Property of a Triangle, Two Special Triangles: Equilateral and Isosceles, Sum of The Lengths of Two Sides of a Triangle, Right-Angled Triangles and Pythagoras Property

Chapter 7: Congruence of Triangles 

In this chapter the main key concepts you will be learning are Congruence of Plane Figures, Congruence among Line Segments, Congruence of Angles, Congruence of Triangles, Criteria for Congruence of Triangles, and Congruence among Right-Angled Triangles.

Chapter 8: Comparing Quantities

In this chapter the main key concepts you will be learning are Equivalent Ratios, Percentage – Another Way of Comparing Quantities, Meaning of Percentage, Converting Fractional Numbers to Percentage, Converting Decimals to Percentage, Converting Percentages to Fractions or Decimals, Fun with Estimation, Use of Percentages, Interpreting Percentages, Converting Percentages To “How Many”, Ratios to Percent’s, Increase or Decrease as Percent, Prices Related to An Item or Buying and Selling, Profit or Loss as A Percentage, Charge Given on Borrowed Money or Simple Interest, Interest for Multiple Years.

Chapter 9: Rational Numbers 

In this chapter the main key concepts you will be learning are Need for Rational Numbers, What Are Rational Numbers?, Positive and Negative Rational Numbers, Rational Numbers on a Number Line, Rational Numbers in Standard Form, Comparison of Rational Numbers, Rational Numbers between Two Rational Numbers, Operations on Rational Numbers, Addition, Subtraction, Multiplication, Division.

Chapter 10: Practical Geometry

In this chapter the main key concepts you will be learning are Construction of A Line Parallel To A Given Line, Through A Point Not On The Line, Construction of Triangles, Constructing A Triangle When the Lengths of Its Three Sides Are Known (SSS Criterion), Constructing A Triangle When the Lengths of Two Sides and The Measure of The Angle Between Them Are Known. (SAS Criterion), Constructing A Triangle When the Measures of Two of Its Angles and The Length of The Side Included Between Them Is Given. (ASA Criterion), Constructing A Right-Angled Triangle When the Length of One Leg and Its Hypotenuse Are Given (RHS Criterion). 

Chapter 11: Perimeter and Area 

In this chapter the main key concepts you will be learning are Squares and Rectangles, Triangles as Parts of Rectangles, Generalising for Other Congruent Parts of Rectangles, Area of A Parallelogram, Area of A Triangle, Circles, Circumference of A Circle, Area of Circle, Conversion of Units, Applications.

Chapter 12: Algebraic Expressions 

In this chapter the main key concepts you will be learning are How Are Expressions Formed? Terms of an Expression, Like and Unlike Terms, Monomials, Binomials, Trinomials and Polynomials, Addition and Subtraction of Algebraic Expressions, Finding the Value of an Expression, Using Algebraic Expressions – Formulas and Rules.

Chapter 13: Exponents and Powers

In this chapter the main key concepts you will be learning are Exponents, Laws of Exponents, Multiplying Powers with the Same Base, Dividing Powers with the Same Base, Taking Power of a Power, Multiplying Powers with the Same Exponents, Dividing Powers with the Same Exponents, Miscellaneous Examples Using the Laws of Exponents, Decimal Number System, Expressing Large Numbers in the Standard Form.

Chapter 14: Symmetry

In this chapter the main key concepts you will be learning are Lines of Symmetry for Regular Polygons, Rotational Symmetry, Line Symmetry and Rotational Symmetry.

Chapter 15: Visualising Solid Shapes 

In this chapter the main key concepts you will be learning are Plane Figures and Solid Shapes, Faces, Edges and Vertices, Nets for Building 3-D Shapes, Drawing Solids on A Flat Surface, Oblique Sketches, Isometric Sketches, Visualising Solid Objects, Viewing Different Sections of a Solid, One Way to View an Object Is by Cutting Or Slicing, Another Way Is by Shadow Play, A Third Way Is by Looking at It From Certain Angles To Get Different Views.

Chapter 1: Integers

In this chapter the main key concepts you will be learning are Properties of Addition and Subtraction of Integers, Closure under Addition and Subtraction, Commutative Property, Associative Property, Additive Identity, Multiplication of Integers, Multiplication of a Positive and a Negative Integer, Multiplication of two Negative Integers, Product of three or more Negative Integers, Properties of Multiplication of Integers, Closure under Multiplication, Commutativity of Multiplication, Multiplication by Zero, Multiplicative Identity, Associativity for Multiplication, Distributive Property, Making Multiplication Easier, Division of Integers, Properties of Division of Integers

Chapter 2: Fractions and Decimals

In this chapter the main key concepts you will be learning are How Well Have You Learnt About Fractions? Multiplication of Fractions, Multiplication of a Fraction by a Whole Number, Multiplication of a Fraction by a Fraction, Division of Fractions, Division of Whole Number by a Fraction, Division of a Fraction by a Whole Number, Division of a Fraction by Another Fraction, How Well Have You Learnt About Decimal Numbers, Multiplication of Decimal Numbers, Multiplication of Decimal Numbers by 10, 100 and 1000, Division of Decimal Numbers, Division by 10, 100 and 1000, Division of a Decimal Number by a Whole Number, Division of a Decimal Number by another Decimal Number.

Chapter 3: Data Handling

In this chapter the main key concepts you will be learning are Collecting Data, Organisation of Data, Representative Values, Arithmetic Mean, Range, Mode, Mode of Large Data, Median, and Use of Bar Graphs with a Different Purpose, Choosing a Scale, Chance and Probability, Chance.

Chapter 4: Simple Equations

In this chapter the main key concepts you will be learning are A Mind-Reading Game! Setting Up of an Equation, Review of What We Know, What Equation Is? Solving an Equation, More Equations, From Solution to Equation, Applications of Simple Equations to Practical Situations

Chapter 5: Lines and Angles

In this chapter the main key concepts you will be learning are Related Angles, Complementary Angles, Supplementary Angles, Adjacent Angles, Linear Pair, Vertically Opposite Angles, Pairs of Lines, Intersecting Lines, Transversal, and Angles Made by a Transversal, Transversal of Parallel Lines, and Checking for Parallel Lines.

Chapter 6: Triangles and its Properties

In this chapter the main key concepts you will be learning are Medians of a Triangle, Altitudes of a Triangle, Exterior Angle of a Triangle and Its Property, Angle Sum Property of a Triangle, Two Special Triangles: Equilateral and Isosceles, Sum of The Lengths of Two Sides of a Triangle, Right-Angled Triangles and Pythagoras Property

Chapter 7: Congruence of Triangles 

In this chapter the main key concepts you will be learning are Congruence of Plane Figures, Congruence among Line Segments, Congruence of Angles, Congruence of Triangles, Criteria for Congruence of Triangles, and Congruence among Right-Angled Triangles.

Chapter 8: Comparing Quantities

In this chapter the main key concepts you will be learning are Equivalent Ratios, Percentage – Another Way of Comparing Quantities, Meaning of Percentage, Converting Fractional Numbers to Percentage, Converting Decimals to Percentage, Converting Percentages to Fractions or Decimals, Fun with Estimation, Use of Percentages, Interpreting Percentages, Converting Percentages To “How Many”, Ratios to Percent’s, Increase or Decrease as Percent, Prices Related to An Item or Buying and Selling, Profit or Loss as A Percentage, Charge Given on Borrowed Money or Simple Interest, Interest for Multiple Years.

Chapter 9: Rational Numbers 

In this chapter the main key concepts you will be learning are Need for Rational Numbers, What Are Rational Numbers?, Positive and Negative Rational Numbers, Rational Numbers on a Number Line, Rational Numbers in Standard Form, Comparison of Rational Numbers, Rational Numbers between Two Rational Numbers, Operations on Rational Numbers, Addition, Subtraction, Multiplication, Division.

Chapter 10: Practical Geometry

In this chapter the main key concepts you will be learning are Construction of A Line Parallel To A Given Line, Through A Point Not On The Line, Construction of Triangles, Constructing A Triangle When the Lengths of Its Three Sides Are Known (SSS Criterion), Constructing A Triangle When the Lengths of Two Sides and The Measure of The Angle Between Them Are Known. (SAS Criterion), Constructing A Triangle When the Measures of Two of Its Angles and The Length of The Side Included Between Them Is Given. (ASA Criterion), Constructing A Right-Angled Triangle When the Length of One Leg and Its Hypotenuse Are Given (RHS Criterion). 

Chapter 11: Perimeter and Area 

In this chapter the main key concepts you will be learning are Squares and Rectangles, Triangles as Parts of Rectangles, Generalising for Other Congruent Parts of Rectangles, Area of A Parallelogram, Area of A Triangle, Circles, Circumference of A Circle, Area of Circle, Conversion of Units, Applications.

Chapter 12: Algebraic Expressions 

In this chapter the main key concepts you will be learning are How Are Expressions Formed? Terms of an Expression, Like and Unlike Terms, Monomials, Binomials, Trinomials and Polynomials, Addition and Subtraction of Algebraic Expressions, Finding the Value of an Expression, Using Algebraic Expressions – Formulas and Rules.

Chapter 13: Exponents and Powers

In this chapter the main key concepts you will be learning are Exponents, Laws of Exponents, Multiplying Powers with the Same Base, Dividing Powers with the Same Base, Taking Power of a Power, Multiplying Powers with the Same Exponents, Dividing Powers with the Same Exponents, Miscellaneous Examples Using the Laws of Exponents, Decimal Number System, Expressing Large Numbers in the Standard Form.

Chapter 14: Symmetry

In this chapter the main key concepts you will be learning are Lines of Symmetry for Regular Polygons, Rotational Symmetry, Line Symmetry and Rotational Symmetry.

Chapter 15: Visualising Solid Shapes 

In this chapter the main key concepts you will be learning are Plane Figures and Solid Shapes, Faces, Edges and Vertices, Nets for Building 3-D Shapes, Drawing Solids on A Flat Surface, Oblique Sketches, Isometric Sketches, Visualising Solid Objects, Viewing Different Sections of a Solid, One Way to View an Object Is by Cutting Or Slicing, Another Way Is by Shadow Play, A Third Way Is by Looking at It From Certain Angles To Get Different Views.