NCERT Solutions for Class 7 Maths

Chapter 1 - Integers

In this chapter, students will learn what is an integer, and what is its relation to the natural and whole numbers. Terms such as additive inverse will be introduced. Exercise 1.1 has 10 questions in total. After completing exercise 1, students will learn about the properties of addition and subtraction of integers. Exercise 1.2 is based on the properties of integers and has 4 questions. Next, students will learn about the Multiplication of integers and the properties of the multiplication of integers. Exercise 1.3 contains 9 questions based on the above-mentioned concepts. The next concept that the students are going to learn is the division of integers. The last exercise, exercise 1.4 has 7 questions on the division of integers.

1. Exercise 1.1 This exercise asks you to represent integers on a number line. The number line is a visual representation of numbers, with positive numbers to the right of zero and negative numbers to the left. You'll likely be given some integers and asked to mark their corresponding points on the number line.

2. Exercise 1.2 This exercise deals with expanding numerals. A numeral is another way of writing a number, like the digits you use to write a whole number. Expanding a numeral means writing it out in terms of its place values. For instance, the expanded form of 253 would be 2 x 100 + 5 x 10 + 3 x 1. In this exercise, you'll probably be given some numerals and asked to write them out in their expanded form.

3. Exercise 1.3 This exercise is about writing integers in words. Here, you'll likely be given some integers and asked to write them out in words. For example, you might be asked to write 3,456 as "three thousand four hundred fifty six".

In Class 7 Maths Chapter 1 we cover the following:

• 1.1 Introduction

• 1.2 Recall

• 1.3 Properties of Addition and Subtraction of Integers

• 1.4 Multiplication of Integers

• 1.5 Properties of Multiplication of Integers

• 1.6 Division of Integers

• 1.7 Properties of Division of Integers

Given below are the links for the exercise solutions for questions from Chapter 1 of the Class 7 Maths NCERT textbook.

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Chapter 2 - Fractions and Decimals

In this chapter, students will learn about the various types of fractions such as proper fractions, improper fractions, mixed fractions, addition and subtraction of fractions, comparison of fractions, equivalent fractions, representation of fractions on a number line and order of fractions. Exercise 2.1 has 8 questions based on the above-mentioned concepts. Next comes the multiplication of fractions and exercise 2.2 has 8 questions on that. Exercise 2.3 has 8 questions on the multiplication of a fraction with a fraction. The next exercise, exercise 2.4 contains 4 questions on the division of fractions. Exercise 2.5 has 9 questions on the revision of decimals. Exercise 2.6 has 5 questions on the multiplication of decimals. The next concept is the division of decimals and has 6 questions in the last exercise, exercise 2.7.

1. Exercise 2.1 focuses on finding equivalent fractions. Remember, equivalent fractions represent the same quantity though written differently. You'll practice finding fractions that have the same value as the given ones.

2. Exercise 2.2 deals with visualizing fractions on a number line. The number line helps represent numbers graphically. Here, you'll learn to mark positions of fractions on the number line.

3. Exercise 2.3 covers addition and subtraction of fractions with the same denominator. Fractions with the same denominator simply mean they have the same base (the number of parts the whole is divided into). You'll practice adding and subtracting these fractions.

4. Exercise 2.4 extends addition and subtraction of fractions to cases where the fractions have different denominators. Here, you'll learn how to convert fractions to make their denominators the same before adding or subtracting them.

5. Exercise 2.5 introduces converting between fractions and decimals. Decimals are another way to represent parts of a whole, using a point and place values. You'll learn how to change fractions into decimals and vice versa.

In Class 7 Maths Chapter 2 we cover the following:

• 2.1 Introduction

• 2.2 How Well Have You Learnt About Fractions?

• 2.3 Multiplication of Fractions

• 2.4 Division of Fractions

• 2.5 How Well Have You Learnt About Decimal Numbers

• 2.6 Multiplication of Decimal Numbers

• 2.7 Division of Decimal Numbers

Given below are the links for the exercise solutions for questions from Chapter 2 of the Class 7 Maths NCERT textbook.

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Chapter 3 - Data Handling

Chapter 3 of the NCERT textbook will teach students about the various types of data, collection of data, organization of data, and arithmetic mean. Exercise 3.1 has 9 questions based on these concepts. The students will then learn about the mode and median and will solve 5 questions in exercise 3.2. The next concept to be learned will be the use of bar graphs and students will be required to solve 6 questions in exercise 3.3. Exercise 3.4 has 3 questions on chances and probability.

1. Exercise 3.1 focuses on methods of data collection and organizing data. This exercise might ask you to find the range or mean (average) of a set of numbers, or how to arrange data in a table.

2. Exercise 3.2 gets into different ways to represent data visually. This could include histograms or frequency tables that you might have already seen.

3. Exercise 3.3 dives deeper into specific types of visual representations of data, such as bar charts and pie charts. You'll learn how to interpret and create these charts to understand data better.

In Class 7 Maths Chapter 3 we cover the following:

• 3.1 Introduction

• 3.2 Collecting Data

• 3.3 Organisation of Data

• 3.4 Representative Values

• 3.5 Arithmetic Mean

• 3.6 Mode

• 3.7 Median

• 3.8 Use of Bar Graphs With A Different Purpose

• 3.9 Chance and Probability

Given below are the links for the exercise solutions for questions from Chapter 3 of the Class 7 Maths NCERT textbook.

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Chapter 4 - Simple Equations

Simple equations can help greatly in solving mathematical problems by forming a relationship between two expressions on both sides of the equal symbol.  This is going to be an interesting chapter for the students as the students will learn about equations in this chapter. They will learn what an equation is and how to set up an equation. They will also learn how to solve equations and from solutions to equations. Students will learn how to apply equations in practical life. There are a total of 4 exercises in this chapter.

1. Exercise 4.1: Focuses on translating word problems into mathematical equations (e.g., sum, difference) and vice-versa.

2. Exercise 4.2: Likely involves checking whether given values satisfy the equations (verifying solutions).

3. Exercise 4.3: Expands on solving equations by introducing techniques like transposition (moving terms from one side to another) and potentially dividing/multiplying both sides by a number to isolate the variable.

In Class 7 Maths Chapter 4 we cover the following:

• 4.1 A Mind-Reading Game!

• 4.2 Setting Up of An Equation.

• 4.3 Review of What We Know.

• 4.4 What Equation Is?

• 4.5 More Equations.

• 4.6 From Solution To Equation.

• 4.7 Applications of Simple Equations To Practical Situations.

Given below are the links for the exercise solutions for questions from Chapter 4 of the Class 7 Maths NCERT textbook.

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Chapter 5 - Lines and Angles

Our lives revolve around lines and angles. They are found almost everywhere. Hence, it is very important that students learn about them to be able to calculate lengths and measures of lines and angles, in order to excel both in exams and in real life. Chapter 5 of the NCERT textbook of Class 7 will introduce the basics of geometry to the students. They will learn about line segments, endpoints, angles and types of angles. Exercise 5.1 has 14 questions on types of angles. The next exercise (Ex 5.2) has 6 questions based on pairs of lines.

1. Exercise 5.1 This exercise focuses on identifying various types of angles. You'll be asked to recognize and classify angles as acute, obtuse, right, reflex, or straight angles based on their measure.

2. Exercise 5.2 In this exercise, you'll get some hands-on practice with drawing different angles. You'll likely be required to use a protractor and ruler to construct acute angles, obtuse angles, right angles, reflex angles, and straight angles with specific measurements.

In Class 7 Maths Chapter 5 we cover the following:

• 5.1 Introduction.

• 5.2 Related Angles.

• 5.3 Pairs of Lines.

• 5.4 Checking For Parallel Lines.

Given below are the links for the exercise solutions for questions from Chapter 5 of the Class 7 Maths NCERT textbook.

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Chapter 6 - The Triangle and its Properties

The next chapter - The Triangle and its Properties is based on the geometrical shape Triangle and its properties as suggested by the name of the chapter. The chapter has total 5 exercises and the concepts and topics discussed in the chapter are - medians of a triangle, altitudes of a triangle, exterior angle of a triangle and its property, angle sum property of triangle, Two special triangles - Isosceles and Equilateral, Sum of lengths of two sides of a triangle, right-angled triangle, and Pythagoras property.

1. Exercise 6.1: Focuses on identifying triangles based on their sides (scalene, isosceles, equilateral).

2. Exercise 6.2: Relates to angle properties of triangles (acute, right-angled, obtuse angled) and their relationships.

3. Exercise 6.3: Covers using the triangle sum property (sum of angles in a triangle is 180°) to find missing angles.

4. Exercise 6.4: Applies the Pythagoras theorem to solve problems in right-angled triangles. (a^2 + b^2 = c^2 where a and b are legs and c is the hypotenuse)

5. Exercise 6.5: Includes mixed problems involving various triangle properties and their applications.

In Class 7 Maths Chapter 6 we cover the following:

• 6.1 Introduction.

• 6.2 Medians of A Triangle.

• 6.3 Altitudes of A Triangle.

• 6.4 Exterior Angle of A Triangle and Its Property.

• 6.5 Angle Sum Property of A Triangle.

• 6.6 Two Special Triangles: Equilateral and Isosceles.

• 6.7 Sum of The Lengths of Two Sides of A Triangle.

• 6.8 Right-Angled Triangles and Pythagoras Property.

Given below are the links for the exercise solutions for questions from Chapter 6 of the Class 7 Maths NCERT textbook.

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Chapter 7 - Comparing Quantities

In our everyday life, we keep on comparing two or more things. By the time students reach class 7, they also start comparing. But, they should know what actual comparison means and how they should compare mathematically. This chapter helps them understand all these concepts. They will learn about equivalent ratios, solve 10 questions in Ex 7.1, Ratios to percentages, Price related to an item buying or selling, Simple Interest, and solve 11 questions in Ex 7.2.

1. Exercise 7.1: This might focus on practicing how to express comparisons between quantities. It could involve writing things like "greater than," "less than," "equal to," or using symbols like "<", ">", and "=".

2. Exercise 7.2: This exercise likely dives into concepts related to profit and loss. It might involve scenarios where you calculate the difference between a buying price and selling price of an item to determine if there was a profit (money gained) or a loss (money lost).

In Class 7 Maths Chapter 6 we cover the following:

• Ratio

• Writing Ratios

• Finding Ratios

• Properties of Ratios

• Percentage

• Converting Between Ratios and Percentages

• Applications of Percentages

Given below are the links for the exercise solutions for questions from Chapter 7 of the Class 7 Maths NCERT textbook.

Other Related Links for Class 7 Maths Chapter 7 The Triangle and Its Properties

Chapter 8 - Rational Numbers

The importance of rational numbers is that they help describe certain quantities or measures that simply integers cannot. Rational numbers are used to measure quantities like length, mass, time, or other quantities. Now, in this chapter, they will be introduced to Rational numbers, what is the need for Rational numbers, what is a rational number, 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 are the concepts to be learned in this chapter. There are 2 exercises.

1. Exercise 8.1: Focuses on identifying rational numbers and expressing them in their simplest form. You might be asked to find rational numbers between two given rational numbers or represent a given situation using rational numbers.

2. Exercise 8.2: Explores comparing and ordering rational numbers. You'll likely practice techniques to compare rational numbers with different denominators by finding a common denominator.

In Class 7 Maths Chapter 8 we cover the following:

• 8.1 Introduction

• 8.2 Need For Rational Numbers.

• 8.3 What Are Rational Numbers?

• 8.4 Positive and Negative Rational Numbers.

• 8.5 Rational Numbers On A Number Line.

• 8.6 Rational Numbers In Standard Form.

• 8.7 Comparison of Rational Numbers.

• 8.8 Rational Numbers Between Two Rational Number.

• 8.9 Operations On Rational Numbers.

Given below are the links for the exercise solutions for questions from Chapter 8 of the Class 7 Maths NCERT textbook.

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Chapter 9 - Perimeter and Area

Perimeter and area are two very important topics in mathematics that help greatly in quantifying physical objects and spaces. In this chapter, students will learn how to find the perimeter and area of different geometrical shapes. They will learn about the perimeter and area of squares and rectangles, triangles as part of rectangles, area of parallelograms, area of a triangle, the circumference of a circle, area of a circle, conversion of units, applications of perimeter and area in practical life, and the students will have to solve 4 exercises in this chapter.

1. Exercise 9.1 focuses on finding the perimeter of various shapes. The perimeter is the total length of all the sides of a closed figure added together, like the total length of fencing you would need to enclose a garden.

2. Exercise 9.2 deals with finding the area of various shapes. The area refers to the amount of space a flat shape fills, like the amount of carpet you would need to cover the floor.

In Class 7 Maths Chapter 9 we cover the following:

• 9.1 Introduction.

• 9.2 Squares and Rectangles.

• 9.3 Area of A Parallelogram.

• 9.4 Area of A Triangle.

• 9.5 Circles.

• 9.6 Conversion of Units.

• 9.7 Applications.

Given below are the links for the exercise solutions for questions from Chapter 9 of the Class 7 Maths NCERT textbook.

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Chapter 10 - Algebraic Expressions

This chapter is all about algebra. How algebraic expressions are 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 are the concepts that the students will learn in this chapter. There are a total of 4 exercises in this chapter.

1. Exercise 10.1 This exercise focuses on representing real-world situations using algebraic expressions. You'll learn how to translate phrases like "subtraction of z from y" or "one-fourth of the product of numbers p and q" into mathematical expressions using variables and arithmetic operations like addition, subtraction, multiplication, and division.

2. Exercise 10.2 Here, you'll practice evaluating algebraic expressions. You'll be given an expression with variables and specific numerical values for those variables. Your task is to substitute those values into the expression and simplify it using the order of operations (PEMDAS) to arrive at a final answer.

In Class 7 Maths Chapter 10 we cover the following:

• 10.1 Introduction.

• 10.2 How Are Expressions Formed?

• 10.3 Terms of An Expression.

• 10.4 Like and Unlike Terms.

• 10.5 Monomials, Binomials, Trinomials and Polynomials.

• 10.6 Addition and Subtraction of Algebraic Expressions.

• 10.7 Finding The Value of An Expression.

• 10.8 Using Algebraic Expressions – Formulas and Rules.

Given below are the links for the exercise solutions for questions from Chapter 10 of the Class 7 Maths NCERT textbook.

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Chapter 11 - Exponents and Powers

Exponents and powers help us shorten or abbreviate values that would otherwise be difficult or too cumbersome to write and make easily readable.  This chapter will teach about exponents, the law of exponents, applying the law of exponents, and decimal number systems. There are 3 exercises in this chapter.

1. Exercise 11.1 This exercise focuses on evaluating expressions with exponents. You'll get to practice applying the basic rules of exponents, especially understanding exponents as repeated multiplication of the base.

2. Exercise 11.2 Here, you'll compare expressions that involve exponents. This will require simplifying the expressions first and then using their values to determine which one is greater or smaller.

3. Exercise 11.3 This exercise introduces exponents with negative bases. You'll explore the rules for simplifying expressions with negative exponents and learn the importance of following the order of operations (PEMDAS) when evaluating them.

In Class 7 Maths Chapter 11 we cover the following:

• 11.1 Introduction.

• 11.2 Exponents.

• 11.3 Laws of Exponents.

• 11.4 Miscellaneous Examples Using The Laws of Exponents.

• 11.5 Decimal Number System.

• 11.6 Expressing Large Numbers In The Standard Form.

Given below are the links for the exercise solutions for questions from Chapter 11 of the Class 7 Maths NCERT textbook.

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Chapter 12 - Symmetry

Symmetry is very important since it helps us identify, study, and discover objects in an organized and systematic manner. Symmetrical objects are easier to study and work with. In this chapter, the geometrical concept of symmetry is introduced. Lines of symmetry for regular polygons and rotational symmetry are taught in this chapter and the students will have to solve 3 exercises.

1. Exercise 12.1 Focuses on identifying lines of symmetry in shapes. You'll practice recognizing both horizontal and vertical lines of symmetry. Imagine folding the shape along the line, and if the two halves exactly overlap, it's a line of symmetry.

2. Exercise 12.2 Introduces shapes with rotational symmetry. Here, you'll find shapes with a center point. You can rotate the shape around this center point, and if it looks exactly the same after rotation, it has rotational symmetry.

3. Exercise 12.3 Combines your understanding of linear and rotational symmetry. You'll be challenged with shapes that might have both types of symmetry, and you'll need to identify all of them.

In Class 7 Maths Chapter 11 we cover the following:

• 12.1 Introduction: Symmetry

• 12.2 Lines of Symmetry For Regular Polygons.

• 12.3 Rotational Symmetry.

• 12.4 Line Symmetry and Rotational Symmetry.

Given below are the links for the exercise solutions for questions from Chapter 12 of the Class 7 Maths NCERT textbook.

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Chapter 13 - Visualising Solid Shapes

In this chapter, students will learn about the various solid shapes that we see around us in everyday life. The faces, edges, vertices, nets for 3D shapes, drawing solids on a flat surface, visualizing solid objects, viewing different sections of a solid, shadow play, and different angles of viewing an object are the concepts that students will learn in this chapter. There are 4 exercises in this chapter.

1. Exercises 13.1 & 13.2: These exercises deals with basic definitions related to solids. You might be asked about properties of solids like faces, edges, vertices, and nets.

2. Exercise 13.3: This exercise might involve drawing different types of sketches for 3D shapes. There could be concepts like oblique sketches (focusing on overall form) and isometric sketches (where measurements are proportional).

3. Exercise 13.4: This exercise likely involves visualizing how a 3D shape would look from different angles or after cutting it in a specific way. You might be asked to identify the resulting 2D shape (the cross-section).

In Class 7 Maths Chapter 11 we cover the following:

• 13.1 Introduction: Plane Figures and Solid Shapes.

• 13.2 Faces, Edges, and Vertices.

• 13.3 Nets For Building 3-D Shapes.

• 13.4 Drawing Solids On A Flat Surface.

• 13.5 Viewing Different Sections of A Solid.

Given Below are the links for the exercise solutions for questions from Chapter 13 of the Class 7 Maths NCERT textbook.

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