NCERT Solutions for Class 7 Maths

The right approach to use NCERT solutions for class 7 Maths

Scoring good marks in class 7 Maths is every child's dream and it can be fulfilled by proper strategies and planning. Students must understand the right process to become experts in Maths. One must understand that maths is the subject of concepts, and its applications so start with the following tips.

1. Conceptual understanding: This is key to scoring good marks in class 7 Maths, students must understand the concepts very well in class or tuition, while learning in class always ask your doubts and try to clear all your questions during the class. Listen carefully to what your teacher is teaching it is always a good practice if you read the chapter which is going to be taught in class this will give you additional confidence to understand the concept very well.

2. Application of concepts in questions: Lots of students understood the concept explained in the class but while solving the NCERT exercise they feel problems, this is because students accept that the questions must be solved in one attempt which is not the right way, don’t jump into NCERT solutions for class 7 Maths to check the solution. The right approach is solving the questions given in the NCERT exercise many times and still, you can’t crack it then only go and take the reference from NCERT solutions for class 7 Maths.

3. Tips to score good marks-To score good marks in class 7 Maths and build up the right foundation in maths students must start making notes of every chapter, write down all important formulas in each chapter and try to remember formulas very well that will help you a lot while solving the questions given in the NCERT exercise. Secondly, practice as many questions as you can. To score good marks understand the weightage in the exam which is as follows.

CBSE Class 7 Maths Unit-wise Marks Weightage

• Chapter-1 Integer (Weightage-15%)
• Chapter 2 - Fractions and Decimals (Weightage-17.5%)
• Chapter 3 - Data Handling (Weightage-17.5%)
• Chapter 4 - Simple Equations (Weightage-17.5%)
• Chapter 5 - Lines and Angles (Weightage-17.5%)
• Chapter 6 - The Triangles and Its Properties (Weightage-12%)
• Chapter 7 - Congruence of Triangles (Weightage-12%)
• Chapter 8 - Comparing Quantities (Weightage-14%)
• Chapter 9 - Rational Numbers (Weightage-7%)
• Chapter 10 - Practical Geometry (Weightage-12%)
• Chapter 11 - Perimeter and Area (Weightage-14%)
• Chapter 12 - Algebraic Expressions (Weightage-13%)
• Chapter 13 - Exponents and Powers (Weightage-14%)
• Chapter 14 - Symmetry and (Weightage-10%)
• Chapter 15 - Visualising Solid Shapes (Weightage-5%)

Brief explanations of Chapter-wise NCERT solutions for class 7 Maths

Chapter-1: Integers Exercises and Number of Questions given in NCERT textbook Exercise

About Chapter-1-Integers

The whole numbers can be represented on the number line, as shown below:

Remarks :

Integers: All natural numbers, negatives of natural numbers, and 0, together form the set Z or I of all integers. Thus, Z = {…... – 3, - 2 , - 1, 0, 1, 2, 3, …..} = N∪{0}∪N^-

Remarks :

NCERT Solutions for Class 7 Maths Chapter-1-Integers

• Exercise 1.1-10 Questions
• Exercise 1.2-4 Questions
• Exercise 1.3-9 Questions
• Exercise 1.4-7 Questions

• Natural Numbers: The counting numbers are called natural numbers. Thus, N = {1, 2, 3, 4, 5, …} is the set of all-natural numbers.

• Representation of Natural Numbers on Number Line: Draw a line. Mark points at equal intervals of length as shown below. Label these points as 1, 2, 3, 4, 5, ….. . Then these points will represent the natural numbers 1, 2, 3, 4, 5, ….. respectively on the number line. The arrowhead at one end of the number line indicates the continuation of these numbers indefinitely.

• Whole Numbers: All natural numbers together with 0 (zero) form the set W of all whole numbers. Thus, W = {0, 1, 2, 3, 4, 5, …..} is the set of all whole numbers. Clearly, W = N∪{0}.

1. Every natural number is a whole number.
2. 0 is a whole number which is not a natural number.

NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals

Chapter-2: Fractions and Decimals Exercises and Number of Questions given in NCERT textbook Exercise

About Chapter 2 Fractions and Decimals

1. The set Z+ = {1, 2, 3, 4, 5, …} = N is the set of all positive integers.
2. The set Z^- = {-1, -2, -4, -5, …} is the set of all negative integers.
3. The integers are also known as directed numbers.

• Exercise 2.1 8 Questions
• Exercise 2.2 8 Questions
• Exercise 2.3 8 Questions
• Exercise 2.4 4 Questions
• Exercise 2.5 9 Questions
• Exercise 2.6 5 Questions
• Exercise 2.7 6 Questions

Example :

1. 3.42 has 2 decimal places (ii) 19.205 has 3 decimal places.
2. Like Decimals : Decimals having the same number of decimal places are called like decimals.

Example :

1. 0.1, 22.5, 3214.2, 893.7 are like decimals, each having one decimal place.
2. 1.234, 22.038, 197.105, 0.678 are like decimals, each having three decimal places.

Unlike Decimals: Some given decimals, all not having the same number of decimal places, are called unlike decimals.

Example :

1. 0.321, 3.21 and 32.1 are unlike decimals.
2. 348.111, 432.89, 999.9, 26.3512 are unlike decimals.

An important result : Annexing zeros to the extreme right of the decimal part of a decimal does not change its value.

e.g. 1.2 =12/10=120/100=1.20 and 1.20 =120/100=1200/1000=1.200

∴1.2 = 1.20 = 1.200 etc.

To Convert a Decimal into a Fraction :

• Step 1. Write the given decimal without the decimal point as numerator.
• Step 2. Take 1 annexed with as many zeros as is the number of decimal places in the given decimal as denominator.
• Step 3. Reduce the above fraction in simplest form. e.g. 13.484 =13484/1000=13484/1000=3371/250=13 ¹²¹/₂₅₀ .

To Convert a Fraction into a Decimal by Division Method :

• Step 1. Divide the numerator by the denominator.
• Step 2. Complete the division. Let a non-zero remainder be left.
• Step 3. Insert a decimal point in the dividend and the quotient.
• Step 4. Put a zero on the right of the decimal point in the dividend as well as on the right of the remainder. Divide again just like whole numbers.
• Step 5. Repeat step 4 till either the remainder is zero or the requisite number of decimal places have been obtained.

NCERT Solutions for Class 7 Maths Chapter 3 Data Handling

Chapter-3: Data Handling Exercises and Number of Questions given in NCERT textbook Exercise

About Chapter 3 Data Handling

• Decimals: The fractions having denominators 10 or some positive integral power of 10 such as  5/10, 63/100, 328/100, etc. can be written in the decimal form as 0.5, 0.63 3.28, etc. Such fractions are known as decimal numbers or simply decimals. Thus, each of the numbers 0.5, 0.63, and 3.28 is a decimal.
• A decimal has two parts: The whole number part and the Decimal part. These parts are separated by a dot (.), called a decimal point. The digits lying to the left of the decimal point form the whole number part. The decimal point together with the digits lying to its right form the decimal part.
• Example: In the decimal 32.65, the whole number part is 32 and the decimal part is .65
• Decimal Places: The number of digits contained in the decimal part of a decimal gives the number of its decimal places.

• Exercise 3.1 9 Questions
• Exercise 3.2 5 Questions
• Exercise 3.3 6 Questions
• Exercise 3.4 4 Questions

•  Bar graph: A bar graph is a pictorial representation of data in which usually bars of uniform width are drawn with equal spacing between them on one axis and values of variables are shown on other axes. It is of three types:
•  Double bar graph: A bar graph showing two sets of data simultaneously. It is useful for the comparison of the data. 
•  Multiple bar graph: Sets of two or more related phenomena can be represented by multiple bar diagrams.
•  Component bar graph: If a given magnitude can be broken into parts of which it is composed, then bars are drawn corresponding to different total values of the variables.
• Histogram: This is a form of representation like the bar graph, but it is used for continuous class intervals.
• Pictograph: It is a pictorial representation of data using symbols.
• Pie chart: In a pie chart, the various observations or components are represented by the sectors of a circle and the whole circle represents the sum of the values of all components.

Number of individual items = Total No Of Items / 360°×Central angle of an Item

NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations

Chapter-4: Simple Equations Exercises and Number of Questions given in NCERT textbook Exercise

• Exercise 4.1 6 Questions
• Exercise 4.2 4 Questions
• Exercise 4.3 4 Questions
• Exercise 4.4 4 Questions

A brief introduction to Chapter 4 Simple Equations

Rules for Solving Linear Equations in One Variable.

We learned the rules for solving an equation in one variable. Let us recall them. They are:

• Rule 1: Same quantity (number) can be added to both sides of an equation without changing the equality.
• Rule 2: Same quantity can be subtracted from both sides of an equation without changing the equality.
• Rule 3: Both sides of an equation may be multiplied by the same non-zero number without changing the equality.
• Rule 4: Both sides of an equation may be divided by the same non-zero number without changing the equality.

It should be noted that some complicated equations can be solved by using two or more of these rules together.

SOLVING Equations having variable terms on the side and number(s) on the other side

These problems involve relations among unknown quantities (variables) and known quantities (numbers) and are often stated in words. That is why we often refer to these problems as word problems. A word problem is first translated in the form of an equation containing unknown quantities (variables) and known quantities (numbers or constants) and then we solve it by using any one of the methods discussed in the earlier section. The procedure to translate a word problem in the form of an equation is known as the formulation of the problem. Thus, the process of solving a word problem consists of two parts, namely, formulation and solution.

The following steps should be followed to solve a word problem

• Step I: Read the problem carefully and note what is given and what is required.
• Step II: Denote the unknown quantity with some letters say x, y, z, etc.
• Step III: Translate the statements of the problem into mathematical statements.
• Step IV: Using the condition(s) given in the problem, form the equation.
• Step V: Solve the equation for the unknown.
• Step VI: Check whether the solution satisfies the equation.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

Chapter-5: Lines and Angles Exercises and Number of Questions given in NCERT textbook Exercise

• Exercise 5.1 14 Questions
• Exercise 5.2 6 Questions

NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and its Properties

Chapter-6:The Triangle and its Properties Exercises and Number of Questions given in NCERT textbook Exercise

• Exercise 6.1 3 Questions
• Exercise 6.2 2 Questions
• Exercise 6.3 2 Questions
• Exercise 6.4 6 Questions
• Exercise 6.5 8 Questions

What you will learn in Chapter 6 The Triangles and its Properties

The learner will investigate the language and symbols of geometry by utilizing the terms of points, lines, planes, segments, midpoints, rays, angles, angle pairs, and perpendicular bisectors, as well as analyze two-dimensional and three-dimensional figures and relate to life-related problems.

The learner will:

 

•  find angle relationships such as vertical angles, linear pairs, complementary angles, and supplementary angles.
•  identify relationships between and among points, lines, and planes, such as betweenness of points, midpoint, distance, collinear, and coplanar.....
•  find the intersection of lines, planes, and solids.
•  connect geometric diagrams with algebraic representations.
•  integrate constructions such as segments and angles, segment bisectors, and angle bisectors.
•  use relationships among one-and two-dimensional measures.
•  represent geometric figures and properties using coordinates.
•  connect the concepts of distance and midpoint to coordinate geometry.

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles

Chapter-7: Congruence of Triangles Exercises and Number of Questions given in NCERT textbook Exercise

• Exercise 7.1 4 Questions
• Exercise 7.2 10 Questions

Introduction to Chapter 7 Congruence of Triangles

The learner will investigate the types of relationships of triangles using the properties that relate to the segments and angles of triangles including inequalities, perpendicular bisectors, altitudes, and medians, determine missing measures using diagrams and appropriately apply theorems/corollaries for equilateral, isosceles, scalene triangles and interior/exterior angle properties to solve problems.

The learner will:

 

• connect geometric diagrams with algebraic representations.
•  integrate constructions such as segment bisectors, perpendiculars, and polygons.
•  describe, draw, and construct two-dimensional figures.
•  use angle and side relationships such as triangle inequalities, isosceles and equilateral triangle properties, altitude, and median.

A. Lesson 1: Angles in Triangles

Read the definitions for acute angle, obtuse angle, right angle, acute triangle, right triangle, and obtuse triangle.

You are now to create a collage of the different types of triangles that are in your world. You will need at least three pictures for each of these triangles: acute triangle, right triangle, and obtuse triangle. These pictures can come from the Internet or magazines or your own photographs. After you have located your pictures, then display them on a poster board, appropriately labeled.

B. Lesson 2: Measuring Angles

This lesson will review measuring angles with a protractor. To measure an angle with a protractor, you need to place the measuring line with the center, usually a hole, on the vertex and a line of the angle. Then, look at the angle measurements on the protractor to read the angle measurement. Keep in mind that an acute angle is less than 90° and that an obtuse angle is greater than 90°.

NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities

Chapter-8: Comparing Quantities Exercises and Number of Questions given in NCERT textbook Exercise

• Exercise 8.1 3 Questions
• Exercise 8.2 10 Questions
• Exercise 8.3 11 Questions

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers

Chapter-9: Rational Numbers Exercises and Number of Questions given in NCERT textbook Exercise

• Exercise 9.1 10 Questions
• Exercise 9.2 4 Questions

NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry

Chapter-10: Practical Geometry Exercises and Number of Questions given in NCERT textbook Exercise

• Exercise 10.1 3 Questions
• Exercise 10.2 4 Questions
• Exercise 10.3 3 Questions
• Exercise 10.4 3 Questions
• Exercise 10.5 3 Questions

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area

Chapter-11: Perimeter and Area Exercises and Number of Questions given in NCERT textbook Exercise

• Exercise 11.1 11 Questions
• Exercise 11.2 5 Questions
• Exercise 11.3 6 Questions
• Exercise 11.4 3 Questions

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions

Chapter-12: Algebraic Expressions Exercises and Number of Questions given in NCERT textbook Exercise

• Exercise 12.1 7 Questions
• Exercise 12.2 6 Questions
• Exercise 12.3 10 Questions
• Exercise 12.4 2 Questions

The algebraic expression has been studied in previous classes. We are familiar with the terms, monomials, binomials, trinomials etc. In this chapter, we will extend our study to the wide application of algebraic expressions in modern algebra. Different operations on algebraic expressions viz. addition, subtraction, multiplication and division will be studied in this chapter. Applications of standard identities will also be treated in this chapter.

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers

Chapter-13: Exponents and Powers Exercises and Number of Questions given in NCERT textbook Exercise

• Exercise 13.1 8 Questions
• Exercise 13.2 5 Questions
• Exercise 13.3 4 Questions

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Chapter-14: Symmetry Exercises and Number of Questions given in NCERT textbook Exercise

• Exercise 14.1 10 Questions
• Exercise 14.2 2 Questions
• Exercise 14.3 7 Questions

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes

Chapter-15: Visualizing Solid Shapes Exercises and Number of Questions given in NCERT textbook Exercise

• Exercise 15.1 5 Questions
• Exercise 15.2 5 Questions
• Exercise 15.3 1 Questions
• Exercise 15.4 3 Questions

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Important points about NCERT Solutions for class 7 maths

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NCERT Solutions for Class 7 Maths contains detailed explanations, with examples and numerical. The solutions are structured to help students understand the concepts well.

NCERT Solutions for class 7 maths contains solutions for all the chapters in a chapter-wise manner. This is a complete package that helps students in their revisions, exams, competitive tests, etc.