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Class Vii Maths Ncert Solutions Pdf

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Moreover, to help students solve complex math problems of class 7, our expert teachers have created in-depth solutions for CBSE 7th Class Maths subject. These solutions are made available free of cost. You can simply access them through the links given above. So, if you want to practice CBSE 7th Class Maths chapter wise, then you can refer to the list of maths chapters given above.

NCERT Solutions for Class 7 Maths (Chapter-wise Description)

Chapter 1: Integers

Introduction: The concept of integers was first introduced in NCERT Class 6 Maths textbook. You learnt that integers comprise 0, positive and negative numbers. Positive numbers along with 0 constitute whole numbers.

As you now know the basic difference between integers and whole numbers, you will be able to understand the properties and operations of integers in a better manner. In this chapter, you will first revisit the concept of representation of integers on a number line.

Next, you will learn the properties of integers satisfied by addition and subtraction. Find out how addition and multiplication are commutative and associative for integers. Besides, these two operations also show a property known as distributive property.

The main purpose of learning these properties is to make the calculations easier. Once you are well-versed with all the following concepts, you can attempt exercise questions, which are 33 in total. You may take reference from NCERT Solutions for Class 7 Maths Chapter-1 for cross-checking your answers.

List of Topics in "Integers"

  1. Number Line
  2. Properties Of Addition And Subtraction Of Integers
  3. Multiplication Of Integers
  4. Properties Of Multiplication Of Integers
  5. Division Of Integers

Important Properties of "Integers"

1. Properties of Addition and Subtraction
(a). Commutative
        a + b = b + a for all integers a and b
 (b). Associative
       (a + b) + c = a + (b + c) for all integers a, b and c
2. Properties under Multiplication
(a). Commutative
        a ✖ b = b ✖ a for any integers a and b
 (b).  Associativity
       (a ✖ b) ✖ c = a ✖ (b ✖ c) for any three integers a, b and c
3. Distributive Property under Addition and Multiplication
      a ✖ (b + c) = a ✖ b + a ✖ c for any three integers a, b and c

Chapter 2: Fractions and Decimals

Introduction: In chapter-2 of NCERT Class 7 Maths, you will first revisit basic concepts of fractions and decimals that you learnt in earlier classes. In fractions, you were taught how to represent proper, improper and mixed fractions. Basic topics of decimals include their addition and subtraction, comparison, and their representation on the number line.

In class 7, your will understand how fractions and decimals can be multiplied and divided. To get the product of two fractions, you need to multiply their numerators and denominators. The sign of multiplication can also be written as 'of'.

A reciprocal of a fraction can be obtained by inverting the fraction upside down, i.e. the numerator and the denominator interchange their places. In the case of division of two numbers, you need to reciprocate the second number and multiply it with the first number.

For finding the product of two decimals, you first have to multiply them as whole numbers. Next, start counting the number of digits from the right-hand side in both the decimal numbers. In the case of division of two decimals, you first divide them as whole numbers and then put the decimal point. There are 50 questions across 7 exercises in this chapter.

List of Topics in "Fractions and Decimals"

  1. Fractions
  2. Multiplication of Fractions
  3. Division of Fractions
  4. Decimal Numbers
  5. Multiplication of Decimal Numbers
  6. Division of Decimal Numbers


Chapter 3: Data Handling

Introduction: In the previous edition of NCERT Maths textbook, you have learnt to convert raw data into a bar graph. This year, you will take a step further towards representing data into many more meaningful ways.

The first and foremost step when processing data is to collect raw data. Generally, data is extracted from authentic sources and then organized to make it look easy-to-understand. As the values are now arranged, you can find the average of given values with the help of arithmetic mean.

Further, you will learn to obtain the range of data when you are given multiple observations. The range of the observation is obtained when the the lowest observation is subtracted from the higher observation.

As discussed above, there are three ways of measuring central tendency. Depending upon the different requirements, different measures of central tendencies are used. The arithmetic mean is applicable wherever you need to find the average while the mode is used to find the set of observations that occurs most often.

Finally, the median provides us with the middle value after the data is organized in ascending or descending order. This chapter comprises 23 exercise questions that are based on the following concepts.

List of Topics in "Data Handling"

  1. Collection of Data
  2. Organisation of Data
  3. Representative Values
  4. Arithmetic Mean
  5. Mode
  6. Median
  7. Use of Bar Graphs for Different Purposes
  8. Chance and Probability

Important Formulas of "Data Handling"

  1. Arithmetic Mean = Sum of all observations/ Total Number of Observations
  2. Range = Highest observation - Lowest observation
  3. Mode = Count of observations that occur most often
  4. Median = Middle observation of the data arranged in ascending or descending order
  5. Measure of two complementary angles = 90°
  6. Measure of two supplementary angles = 180°


Chapter 4: Simple Equations

Introduction: Before you start this chapter, you must have a basic understanding of key concepts of algebra, including constants, variables, expressions, and terms. Also, recall that the solution of the equation is the value of the variable that satisfies the equation.

In other words, the left-hand side of the equation should be equal to the right-hand side. In some algebraic equations, you will find the value of a variable using addition, subtraction, multiplication or division with the same number so that the balance remains undisturbed.

Another method of solving an equation is the method of transposing. As the name suggests, transposition of a number has the same effect as that of balancing an equation. When you move a number from one side of the equation to the other side, its sign changes.

To conclude, you can form simple algebraic expressions corresponding to practical situations. This chapter consists of 19 questions across four exercises, which you can attempt after covering the following topics.

List of Topics in "Simple Equations"

  1. Setting up of Equation
  2. An Equation
  3. More Equations
  4. From Solution to Equation
  5. Applications of Simple Equations in Practical Situations


Chapter 5: Lines and Angles

Introduction: Recall the definitions of a line, a line segment and an angle from the previous class. A line can be formed when we extend it from both the ends. A line segment, on the other hand, can be formed when we join both ends. Unlike a line, the line segment cannot be extended infinitely.

An angle is formed when lines or line segments meet at a common point. In this chapter, you will study five types of angles, namely complementary, supplementary, adjacent, linear pair, and vertically opposite angles.

In the second exercise of NCERT Class 7 Maths Chapter-5, you will find questions based on the key concepts, including intersecting lines, transversal, a transversal of parallel lines etc. To begin with, the point of intersection is defined as the junction or meeting point of two lines.

Two lines are said to be parallel when they do not meet at a common point on a sheet of paper. When two lines intersect, then they form two pairs of opposite angles.

List of Topics in "Lines and Angles"

1. Related Angles
(a). Complementary Angles
 (b). Supplementary Angles
 (c). Adjacent Angles
 (d). Linear Pair
 (e). Vertically Opposite Angles
2. Pairs of Lines
(a). Intersecting Lines
 (b). Transversal
 (c). Angles made by a Transversal
 (d). Transversal of Parallel Lines
3. Parallel Lines

Chapter 6: The Triangle and its Properties

Introduction: Let us recollect basic knowledge about triangles before we jump into its properties. A triangle is a three-sided simple closed curve, which also contain three angles and three vertices. In the past, you also learnt how to classify triangles based on the number of sides and measure of angles.

Based on the number of sides, there are three types of triangles, namely equilateral, isosceles, and scalene. On the basis of angles, triangles can be categorised into acute-angled, obtuse-angled, and right-angled triangle.

In NCERT Class 7 Maths Chapter-6, you will first study about median and altitudes of a triangle. Median is termed as a line segment that connects a vertex of a triangle to the midpoint of the opposite side.

An altitude is a height shown by the line segment that starts from vertex A and gets connected with the opposite side. An altitude makes an angle of 90 degrees with the line segment with which it connects.

Further, you will develop an understanding of the angle sum property and exterior angle property. The last topic of the chapter will introduce you to the concept of Pythagoras property. Apart from the examples, you can practise 21 NCERT back-exercise questions.

List of Topics in "The Triangle and its Properties"

  1. Medians of a Triangle
  2. Altitudes of a Triangle
  3. Exterior Angle of a Triangle and its Property
  4. Angle Sum Property of a Triangle
  5. Two Special Triangles: Equilateral and Isosceles
  6. Sum of the Lengths of Two Sides of a Triangle
  7. Right-Angled Triangles and Pythagoras Property

Important Properties of "The Triangle and its Properties"

1. Angle Sum Property
    Measure of interior angles of a triangle = 180°
2. Measure of each angle of an equilateral triangle = 60°
3. Pythagoras Property
    h 2 = p2  + b2

Chapter 7: Congruence of Triangles

Introduction: In the last chapter, you proved that the addition of two sides of a triangle is always larger than its third side. Besides, you covered all the basic properties of a triangle with which you can calculate the measure of an unknown angle.

You are now ready to proceed with an important geometrical concept called congruence. Two shapes are said to be congruent when they appear exact copies of each other on getting superimposed. To prove two triangles congruent, you need to prove their corresponding parts equal.

There are four criteria for proving two triangles congruent SSS, ASA, SAS and RHS. SSS congruence rule is applicable if the three sides of one triangle are equal to the three corresponding sides of the second. Under SAS congruence, two triangles are called congruent if their two sides and the angle included between them are equal.

To prove two triangles congruent by ASA criterion, their two angles and the side between them must be equal. Lastly, RHS criterion is applicable where two right-angled triangles have an equal hypotenuse and a side.

Now, you can put your knowledge to test by practising the exercise questions. Consider taking reference from our NCERT Solutions for cross-checking your answers.

List of Topics in "Congruence of Triangles"

  1. Congruence of Plane Figures
  2. Congruence among Line Segments
  3. Congruence of Angles
  4. Criteria for Congruence of Triangles
  5. Congruence among Right-Angled Triangles


Chapter 8: Comparing Quantities

Introduction: Having prior knowledge of ratios will make the learning process of NCERT Class 7 Maths Chapter-8 more streamlined. A ratio can be expressed in the form of a fraction, but it is represented by the symbol of (:). Two ratios are said to be equivalent when their values of numerators and denominators are the same.

The ratio is the most common method of comparing quantities. Another way of comparing quantities is the percentage that you are already familiar. Before you jump into the concept of simple interest, you must know how to convert fractions to percentages, decimals to percentages, percentages to fractions/ decimals etc.

Next, you need to know the formulae of increase or decrease percent to find out the increase or decrease in quantity. In the third exercise of chapter-8, you will come across questions related to profit and loss. If the value of selling price (SP) is more than the cost price (CP), then you can find their difference to get profit.

When the value of the cost price is greater than the selling price, then you can obtain the value of loss incurred. In case the difference between the selling price and cost price comes out to be zero, then you are in neither profit nor loss.

The most important concept of this chapter is to find the simple interest on borrowed money. Word problems related to simple interest will indicate either of the two values out of the principal amount, rate, and time period. Overall, there are 25 questions that are framed from the following concepts.

List of Topics in "Comparing Quantities"

  1. Equivalent Ratios
  2. Percentage- Another Way of Comparing Quantities
  3. Use of Percentages
  4. Prices Related to an Item or Buying and Selling
  5. Simple Interest or Charge Given on Borrowed Money

Important Formulae of "Comparing Quantities"

  1. If SP > CP, Profit = Selling Price - Cost Price
  2. If CP > SP, Loss = Cost Price - Selling Price
  3. If CP = SP, Neither Profit nor Loss
  4. Simple Interest = (P ✖ R ✖ T) / 100
  5. Amount = Principal + Interest


Chapter 9: Rational Numbers

Introduction: Rational numbers are represented in the form of a fraction where the value of the denominator can never be equal to zero. So far, we have covered natural numbers, whole numbers, and integers. This collection of numbers is known as real numbers. In NCERT Class 7 Maths, we will extend the number system further.

Why do we need rational numbers? There are many situations that involve the use of fractional numbers. For instance, we can represent a distance of 250 m above sea level as 1/4 km. As you proceed, you will be applying the operations of addition, subtraction, multiplication, and division into rational numbers.

In the second chapter 'Whole Numbers' of NCERT Class 6 Maths, you have learnt how to represent positive and negative numbers on the number line. Likewise, you can also indicate rational numbers on a number line. For example, ½ and -½ can be represented at an equal distance from 0 in the positive and negative direction, respectively.

The types of questions that are in the first exercise include conversion of rational numbers to its standard form, finding rational numbers between two rational numbers, and more. The second exercise of the chapter consists of questions based on operations of rational numbers. At the end of this chapter, you will find 14 questions covering the following concepts.

List of Topics in "Rational Numbers"

  1. Need for Rational Numbers
  2. Rational Numbers
  3. Positive and Negative Rational Numbers
  4. Rational Numbers on a Number Line
  5. Rational Numbers in Standard Form
  6. Comparison of Rational Numbers
  7. Rational Numbers Between Two Rational Numbers
  8. Operations on Rational Numbers


Chapter 10: Practical Geometry

Introduction: To understand NCERT Class 7 Maths Chapter-10 properly, you should consider practising the construction of a line segment, a line perpendicular to a given line segment, an angle, an angle bisector, a circle etc. In this chapter, you will learn to construct parallel lines and different types of triangles.

For the construction of triangles, you must revisit the chapters on properties and congruence of triangles. To begin with, the exterior angle of a triangle is equal in measure to the sum of opposite interior angles. The angle-sum property suggests that the sum of the measure of three interior angles of a triangle is 180 degrees.

Recall the third property of a triangle which suggests that the sum of its two sides is always greater than its third side. You also learnt to prove two triangles congruent based on SSS, SAS, ASA, and RHS criterion.

Using the criteria of congruence mentioned above, you will learn to construct triangles. This chapter includes 16 questions in total.

List of Topics in "Practical Geometry"

  1. How to Construct a Line Parallel to a Given Line?
  2. Construction of Triangles
  3. Construction of Triangles by SSS Criterion
  4. Construction of Triangles by SAS Criterion
  5. Construction of Triangles by ASA Criterion
  6. Construction of Triangles by RHS Criterion


Chapter 11: Perimeter and Area

Introduction: Previously, you studied the formulae of the perimeter of plane figures and areas of squares and rectangles. Recall the definition of the perimeter, it helps you calculate the distance along the boundary of a closed figure. On the other hand, you calculate the area for finding out the region occupied by the closed figure.

In the second exercise of NCERT Solutions for Class 7 Maths Chapter-11, you will come across questions which will require you to apply areas and perimeters of various figures. These include the area of a parallelogram and the area of a triangle.

When attempting questions of the third exercise, the formulae of area and perimeter of a circle come into use. In the final exercise, you will find questions based on the applications related to plane shapes you have covered till now. Below are the list of topics and important formulae of this chapter.

List of Topics in "Perimeter and Area"

  1. Squares and Rectangles
  2. Area of a Parallelogram
  3. Area of a Triangle
  4. Circles
  5. Conversion of Units
  6. Applications of Perimeter and Area

Important Formulae of "Area and Perimeter"

  1. Area of a Square = Side ✖ Side
  2. Area of a Rectangle = Length ✖ Breadth
  3. Perimeter of a Square = 4 ✖ Side
  4. Perimeter of a Rectangle = 2 ✖ (length + breadth)
  5. Area of a Parallelogram = Base ✖ Height
  6. Area of a Triangle = ½ ✖ Base ✖ Height
  7. Area of a Circle = πr 2
  8. Circumference of a Circle = 2πr
  9. 1 cm2  = 100 mm2
  10. 1 m2  = 10000 cm2
  11. 1 hectare = 10000 m2

Chapter 12: Algebraic Expressions

Introduction: In the previous class, you were taught algebraic expressions and how they are useful in forming equations. In algebra, every concept revolves around expressions, their formation and combination, and their use. Expressions are formed by combining variables and constants using operations such as addition, subtraction, multiplication and division.

In an expression, terms are separated by operations of addition and subtraction. A single term can be obtained by multiplying or dividing variables and constants. Factors can be extracted from the terms. For example- 3, x and y are factors of term 3xy.

Coefficients can be found by separating the numerical factor from the variable factors. Here, the numerical factor can be considered as the numerical coefficient of the term. Based on the number of terms, a polynomial can be classified into monomial, binomial and trinomial.

In NCERT Solutions for Class 7 Maths Chapter-12, you will find various questions based on substitution of values in place of variables for obtaining the result of an expression.

List of Topics in "Algebraic Expressions"

  1. How to Form Expressions?
  2. Terms of an Expression
  3. Like and Unlike Terms
  4. Monomials, Binomials, Trinomials, and Polynomials
  5. Addition and Subtraction of Algebraic Expressions
  6. Finding the Value of an Expression
  7. Using Algebraic Expressions (Formulas and Rules)

Chapter 13: Exponents and Powers

Introduction: The distance between our planet and the sun is very large. Also, the mass of all celestial objects can only be represented in large numbers, but are difficult to read and understand. In this chapter, you will learn to write large numbers in shorter form using exponents. For example- the number 1,00,000 can be written as 10 5 .

In the first exercise of this chapter, you will learn to simplify exponents and express them as a product of powers. Next, you will learn to apply the laws of exponents for converting complex expressions into simpler ones. Finally, the last exercise will contain questions asking you to express large numbers in the standard form or convert standard into expanded form.

List of Topics in "Exponents and Powers"

  1. Exponents
  2. Laws of Exponents
  3. Miscellaneous Examples using the Laws of Exponents
  4. Decimal Number System
  5. Expressing Large Numbers in the Standard Form

Important Formulae of "Algebraic Expressions"

  1. a m ✖ a n = a m+n
  2. a m ÷ a n = a m-n , m > n
  3. (a m ) n = a mn
  4. a m ✖ b m = (ab) m
  5. am  ÷ bm  = (a/b)m
  6. a 0 = 1
  7. (-1) even number = 1
  8. (-1)odd number = -1

Chapter 14: Symmetry

Introduction: In Mathematics, two objects are said to be symmetrical when they are of the same size and shape. However, both objects have a different orientation. In NCERT Class 6 Maths textbook, you have already covered the concept of "line symmetry". A line of symmetry is drawn to see whether the left side of the object appears similar to its right side or not.

In the case of regular polygons, the number of lines of symmetry is equal to its sides. For example, an equilateral triangle has three sides and three lines of symmetry. The concept of line symmetry is similar to that of mirror reflection, i.e. one half of the image is the mirror image of the other half.

When we speak of rotating objects such as the blades of a ceiling fan, the wheel of a bicycle or a windmill, they all exhibit rotational symmetry. For instance, a windmill has four positions when it looks exactly the same. Thus, we will say that a windmill has rotational symmetry of order 4 about its centre.

Later, you will discover that there are some shapes that have both rotational as well as line symmetry, like the letter "H". The chapter-14 of NCERT Class 7 Maths includes a total of 19 questions across 3 exercises.

List of Topics in "Symmetry"

  1. Lines of Symmetry for Regular Polygons
  2. Rotational Symmetry
  3. Line Symmetry and Rotational Symmetry

Chapter 15: Visualising Solid Shapes

Introduction: In earlier classes, we have already discussed plane figures, including circle, quadrilateral, rectangle, square, and triangles. These shapes are called two-dimensional figures. When we speak of solid shapes such as a cube, cuboid, cylinder, cone, sphere, and pyramid, we refer to them as three-dimensional shapes.

When we draw solid shapes on paper, we call it a two-dimensional representation of a 3-D solid. Each solid shape has its vertices, edges, and faces. For example- a cuboid has 8 vertices, 12 edges, and 6 faces.

A net is a flattened out three-dimensional solid that can be folded to make it. Further, you will study two types of sketches of a solid- oblique sketch and isometric sketch. After you complete this chapter, you will learn to see hidden parts of the solid shape.

List of Topics in "Visualising Solid Shapes"

  1. Faces, Edges and Vertices
  2. Nets for Building 3-D Shapes
  3. Drawing Solids on a Flat Surface
  4. Viewing Different Sections of a Solid

Benefits of Studying with NCERT Class 7 Maths Solutions

The NCERT Maths Class 7 Solutions offered by Goprep are created by experts keeping in mind the comfort of the students. The maths textbook solutions come with zero percent error and are based on the latest exam pattern of CBSE. Given below are some of the advantages that students can experience by studying class 7 NCERT solutions.

  • Our NCERT maths solutions for class 7 are prepared by expert teachers.
  • Step by step solutions has been provided for each problem to help students clear their doubts and better understand complex concepts.
  • Every question has been solved using the most effective method of solving a particular problem.
  • Formulas are placed in between the steps to enable students to learn them quickly.
  • Besides helping in clearing the doubts, our NCERT Solutions for Maths provide thorough knowledge to students about topics.
  • Important questions in each chapter are also highlighted to help students revise them thoroughly and prepare better for the exam.

Final Words

As the level of difficulty in maths subject has increased considerably over the years, classroom study is not enough to score good marks. Therefore, it gets important to supplement your math preparation through NCERT maths solutions for class 7 by Gradeup school. The solutions are targeted towards developing a better understanding of the basic and complex concepts to assist students to score better marks in the exam.

Class Vii Maths Ncert Solutions Pdf

Source: https://goprep.co/ncert-solutions/ncert-solutions-for-class-7-maths

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