assignment for class 6 maths chapter 1

NCERT Solutions Class 6 Maths Chapter 1 Knowing Our Numbers

NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers will help the students take their understanding of numbers a bit further and explore topics like shifting digits, expanding brackets, roman numerals, estimating sum or difference, products, outcomes of number situations, and many more. This chapter will also help the students revise all the operations on numbers like multiplication , addition , subtraction , and division covered in the previous classes. Presented below is an in-depth analysis of Class 6 Maths NCERT Solutions Chapter 1.

These solutions will help the students understand large numbers through real-life examples while also exploring their unit conversions. They will also get to learn about the International and Indian systems of numeration along with an introduction to the concept of roman numerals. Let us now take a deeper look at the different sub-topics covered in NCERT Solutions Class 6 Maths Chapter 1 and also you can find some of these in the exercises given below.

• NCERT Solutions Class 6 Maths Chapter 1 Ex 1.1
• NCERT Solutions Class 6 Maths Chapter 1 Ex 1.2
• NCERT Solutions Class 6 Maths Chapter 1 Ex 1.3

NCERT Solutions for Class 6 Maths Chapter 1 PDF

NCERT Solutions Class 6 Maths Chapter 1 Knowing Our Numbers contains all the important questions, images, explanations, and formulas covered in the chapter. These solutions are aimed at helping the students understand and solve complex concepts such as the use of commas in larger numbers. Commas are used to mark thousands, lakhs, and crores. Let us do a detailed exercise-wise overview of this chapter using the PDF links given below :

☛ Download Class 6 Maths NCERT Solutions Chapter 1 Knowing Our Numbers

NCERT Class 6 Maths Chapter 1   Download PDF

NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers

Students must have already studied the formation of numbers in the previous classes. In this chapter, they will be introduced to the concept of arranging numbers in ascending as well as in descending order and shifting the digits to form new numbers. All these ideas are explained along with real-life examples in the NCERT Solutions Class 6 Maths Chapter 1 Knowing Our Numbers.

• Class 6 Maths Chapter 1 Ex 1.1 - 4 Questions
• Class 6 Maths Chapter 1 Ex 1.2 - 12 Questions
• Class 6 Maths Chapter 1 Ex 1.3 - 5 Questions

☛ Download Class 6 Maths Chapter 1 NCERT Book

Topics Covered: The important topics covered under Class 6 maths NCERT Solutions Chapter 1 are natural numbers , comparison of numbers, place value of a digit, estimation of the numbers, roman numerals , and importance of brackets. Questions related to all these topics must be practiced regularly to score excellent marks in the exams.

Total Questions: Class 6 Maths Chapter 1 Knowing Our Numbers has a total of 21 well-researched questions out of which 12 are straightforward, 3 are of moderate level, and 6 are complex level problems. 

List of Formulas in NCERT Solutions Class 6 Maths Chapter 1

NCERT solutions class 6 maths chapter 1 does not cover any formulas . However, there are some pointers that the students must remember while solving problems from this chapter. These pointers will help them avoid mistakes while giving a crystal clear understanding of the topics covered in this chapter. Let us now go through these pointers one by one :

• Given two numbers, if one has a large number of digits, then it is greater. In the case where the number of digits is the same, the number with the larger leftmost digit is considered to be the greater number.
• We put commas after 3 digits in the Indian system. These commas are put after 3,5,7, thus separating the thousand, lakh, and crore. However, in the International System, we put commas after every 3 and 6 digits from right, separating thousands, billions, and further billions.
• We use estimation in order to get a rough figure of the numbers involved. This gives us a quick idea of the answer. Estimation is done by rounding numbers.

Important Questions for Class 6 Maths NCERT Solutions Chapter 1

FAQs on NCERT Solutions for Class 6 Maths Chapter 1

Why are ncert solutions class 6 maths chapter 1 important.

NCERT Solutions Class 6 Maths Chapter 1 will help kids identify pain points and find ways to solve questions in an efficient manner. They focus on some of the fundamental concepts that act as a building block for a kid’s mathematical journey. Topics such as estimation have practical applications in our daily life as it gives an idea of the quantity. Thus these solutions are extremely important for students considering their utility in everyday life.

Do I Need to Practice all Questions Provided in NCERT Solutions for Class 6 Maths Knowing Your Numbers?

All the questions in NCERT Solutions are curated by experts covering a range of topics. NCERT Solutions for Class 6 Maths Chapter 1 will help you explore all the topics in detail by solving a range of problems. Thus practicing all the questions of this chapter is important for a strong mathematical foundation.

What are the Important Topics Covered in NCERT Solutions Class 6 Maths Chapter 1?

NCERT Solutions Class 6 Maths Chapter 1 covers a range of essential topics such as estimating numbers, use of commas, place value, expanding brackets, and roman numerals. Questions related to all these topics are explained in a step-wise manner in the NCERT solutions.

How Many Questions are there in Class 6 Maths NCERT Solutions Chapter 1 Knowing Your Numbers?

There are a total of 21 sums in the NCERT Solutions Class 6 Maths Chapter 1 Knowing Your Numbers. These questions are distributed in 3 exercises. Out of 21 questions, 10 are easy sums, 5 are moderately difficult problems, while 6 are complex sums that need brainstorming.

How can CBSE Students utilize NCERT Solutions for Class 6 Maths Chapter 1 effectively?

In order to effectively utilize the NCERT Solutions Class 6 Maths Chapter 1 students must go through the detailed solutions of all the questions, explore the chapter summary, and theory of the chapter. Students must give adequate time to all the exercises and solve questions in a step-wise manner.

Why Should I Practice NCERT Solutions Class 6 Maths Knowing Your Numbers?

NCERT Solutions Class 6 Maths Chapter 1 Knowing Your Numbers will help you revise the previous concepts from earlier classes like place values, whole numbers, number system, etc. Apart from that, this chapter will help you understand the applications of interesting concepts in your day-to-day life.

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Home » 6th Class » NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers | Question Answer PDF

NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers | Question Answer PDF

NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers has been published by Aglasem. You can now download the Class 6 Maths Ch 1 Questions and Answers PDF here. This NCERT Solutions for Class 6 Maths contains answers of all questions asked in Chapter 1 in textbook, Mathematics . Therefore you can refer it to solve Knowing Our Numbers exercise questions and learn more about the topic.

NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers

Class – Class 6 Subject – Maths Chapter – Ch 1 Chapter Name – Knowing Our Numbers Book – Mathematics Study Material – NCERT Solutions

NCERT Solutions for Class 6 Maths Chapter 1 PDF

While you can read NCERT Solutions for Class 6 Maths Ch 1 for all exercises here on aglasem. You can also download this NCERT Solutions PDF to refer ncer question answer at anytime when you study Knowing Our Numbers. Here it is.

NCERT Solutions for Class 6 Maths Chapter 1 PDF Download Link – Click Here to Download Solutions PDF

How to download NCERT Solutions for Class 6 Maths Chapter 1 PDF?

You can download the complete NCERT solutions for chapter 1 of this NCERT Book i.e. Mathematics with following steps.

• First search NCERT Solutions for Class 6 Maths Ch 1 PDF aglasem and come to this page.
• Now you will see the exercise questions answers of Knowing Our Numbers and download pdf link on it.
• Click the Download PDF link to obtain the Knowing Our Numbers questions with answers document.

NCERT Solutions for Class 6 Maths

There are more chapters to study besides Knowing Our Numbers in this subject. So here are NCERT solutions for all topics of Maths taught in 6th class here at aglasem.

• Chapter 1 Knowing Our Numbers
• Chapter 2 Whole Numbers
• Chapter 3 Playing With Numbers
• Chapter 4 Basics Geometrical Ideas
• Chapter 5 Understanding Elementary Shapes
• Chapter 6 Integers
• Chapter 7 Fractions
• Chapter 8 Decimals
• Chapter 9 Data Handling
• Chapter 10 Mensuration
• Chapter 11 Algebra
• Chapter 12 Ratio and Proportion

NCERT Solutions for Class 6

Just like you got Maths Ch 1 solutions here. You can see exercise questions answers of other subjects and their topics too on aglasem. Here are NCERT solutions for all subjects of 6th standard NCERT books.

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NCERT Solutions for Class 6 Maths Chapter 1 – An Overview

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NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers

Get here the NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers and Class 6 Maths Chapter 1 Try These Solutions and Practice Tests for revision. It is given here in Hindi and English Medium prepared for academic session 2024-25. According to rationalised syllabus and new books for class 6 Mathematics for CBSE 2024-25, there are only two exercises in chapter 1 Knowing our numbers.

6th Maths Chapter 1 Solutions for CBSE Board

• Class 6 Maths Chapter 1 Try These
• Class 6 Maths Exercise 1.1 in English
• Class 6 Maths Exercise 1.2 in English

6th Maths Chapter 1 Solutions for State Boards

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• Class 6 Maths Chapter 1 Exercise 1.2
• Class 6 Maths Chapter 1 Exercise 1.3
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Class 6 Maths Chapter 1 Practice Test 6th Maths Chapter 1 Test 1 6th Maths Chapter 1 Test 2 6th Maths Chapter 1 Test 3 6th Maths Chapter 1 Test 4 6th Maths Chapter 1 Test 5 6th Maths Chapter 1 Test 6

Get class VI Maths Exercise 1.1 and 1.2 at Tiwari Academy in simplified way. 6th Maths Solutions PDF and Video in English and Hindi Medium are prepared in such a way that student can understand it easily. We have updated it for new session based on latest textbooks from NCERT (https://ncert.nic.in/) website. Find the Solutions of Prashnavali 1.1 and 1.2 in Hindi. We are following the latest CBSE Syllabus 2024-25. We work for your help free of cost. Separate links are given to download solutions in PDF file format. In case of any hassle in finding the solutions, please inform us. We will help you at our level best.

These NCERT Solutions are based on latest CBSE – NCERT Textbooks for the CBSE exams 2024-25. Download NCERT Solutions in PDF format to use it offline or use as it is online without downloading.

In 6 Maths Chapter 1 Knowing Our Numbers, we will study about comparing the number (smaller or greater), selecting the smallest or greatest numbers, order of numbers (ascending or descending).

Ascending order: Ascending order means arrangement from the smallest to the greatest. Descending order: Descending order means arrangement from the greatest to the smallest.

Concepts of Place values, face values and questions based on the numbers as follow: Starting from the greatest 6-digit number, write the previous five numbers in descending order. Starting from the smallest 8-digit number, write the next five numbers in ascending order. The Indian System of Numeration: In our Indian System of Numeration, Commas are used to mark thousands, lakhs and crores. We use ones, tens, hundreds, thousands and then lakhs and crores. The first comma comes after hundreds place and marks thousands. The second comma comes two digits later. It comes after ten thousands place and marks lakh. The third comma comes after another two digits. It comes after ten lakh place and marks crore.

Important Questions on 6 Maths Chapter 1

Fill in the blank: 1 lakh = _______________ ten thousand.

Fill in the blank: 1 lakh = 10 ten thousand

Place commas correctly and write the numerals: Seventy-three lakh seventy-five thousand three hundred seven.

Insert commas suitable and write the names according to indian system of numeration: 87595762.

8,75,95,762 Eight crore seventy-five lakh ninety-five thousand seven hundred sixty-two.

Estimate each of the following using general rule: 730 + 998

730 round off to 700 998 round off to 1000 Estimated sum 1700

Estimate the following product using general rule: 578 x 161

578 x 161 578 round off to 600 161 round off to 200 The estimated product = 600 x 200 = 1,20,000

We are here to help you. For educational help any time you can leave a message, we will call you with in 24 hours. Our prime motive is to help the students without any delay free of cost. NCERT Books and their solutions are given in offline as well as online mode.

How many exercises, questions, and examples are there in chapter 1 of class 6th Maths?

There are 2 exercises in chapter 1 (Knowing our Numbers) of class 6th Maths. In the first exercise (Ex 1.1), there are 4 questions. Questions 1 and 2, each having five parts, and questions 3 and 4, each having four parts. In the second exercise (Ex 1.2), there are 12 word problem questions. So, there are in all 16 questions in chapter 1 (Knowing our Numbers) of class 6th Maths. There are 6 examples in chapter 1 (Knowing our Numbers), which are good for exams point of view.

What are the main topics to study in chapter 1 of class 6th Maths?

In chapter 1 of class 6th Maths, students will study:

• 1. Comparing Numbers.
• 2. How many numbers can you make?
• 3. Shifting digits.
• 4. Introducing 10,000.
• 5. Revisiting place value.
• 6. Introducing 1, 00,000.
• 7. Larger numbers.
• 8. An aid in reading and writing large numbers.
• 9. Use of commas.
• 10. Large Numbers in Practice.

Is chapter 1 of class 6th Maths difficult?

Chapter 1 of class 6th Maths is neither too easy nor too difficult. It lies in the middle of easy and difficult because some parts of this chapter are easy, and some are difficult. However, the difficulty level of any chapter varies from student to student. So, Chapter 1 of class 6th Maths is easy or not depends on students also. Some students find it complicated, some find it simple, and some find it in the middle of simple and difficult.

How much time, students need to do chapter 1 of class 6th Maths?

Students need a maximum of 5-6 days to do chapter 1 of class 6th Maths if they give at least 1-2 hours per day to this chapter. This time is an approximate time. This time can vary because no students have the same working speed, efficiency, capability, etc.

Chapter 2: Whole Numbers »

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NCERT Solutions Class 6 Maths Chapter 1

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NCERT Solutions for Class 6 Maths Chapter 1 – Knowing Our Numbers

Chapter 1 of the NCERT Textbook “Knowing Our Numbers”begins with comparing numbers, shifting digits, revisiting place value, larger numbers, and so on.  The NCERT solutions of this chapter will help them to strengthen basic concepts and help them excel in the examination. Subject experts at Extramarks create the solutions for Class 6 Maths Chapter 1. This will help boost the student’s confidence in learning mathematical concepts at an early age.

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As all the solutions are prepared based on the CBSE guidelines and as per the marking scheme provided by NCERT, these will help clear the concepts about use of commas, revisiting place value, large numbers, reading and writing large numbers etc. Additionally, students will get a fair idea of the exam pattern, get enough practice and need not look for any kind of help elsewhere. The NCERT Solutions for Class 6 Chapter 1 Maths can be accessed from Extramarks.

NCERT Solutions Class 6 Maths Other Related Chapters

NCERT Solutions for Class 6 Maths Chapter 1

The first chapter of NCERT’s Class 6 Maths book is “Knowing Our Numbers’. It is not so that students learn about numbers for the first time. They are already aware of various operations such as addition, multiplication, division and subtraction. In this particular chapter, students will be learning some advanced concepts such as ideas on larger numbers, operations using more significant numbers, comparisons, shifting of digits, commas, etc. Students will also be learning about the process of estimating numbers and rounding off. The beginning of the chapter includes topics on comparing numbers, commas, ascending and descending order, large numbers, reading and writing large numbers and  other concepts. 

Access NCERT Solutions for Class 6 Maths Chapter 1- Knowing Our Numbers

Subject experts and experienced teachers at Extramarks who draft the NCERT solutions  prepare NCERT solutions after conducting extensive research. Students can rely on these solutions to understand every topic with examples, gamified content and graphics to make it colourful and interesting. These solutions also help students in completing their assignments and adequately prepare for their exams. The solutions are available at the official website of Extramarks.

NCERT Solutions Class 6 of Maths Chapter-Wise 

If you can practise the NCERT books exercise regularly, it will be easier to understand the concepts. You will cover all the topics equally and have a better idea about every topic given in the book. The total number of questions in every exercise of Chapter 1 is given below::

As the chapter includes more significant numbers, students need to learn the usage of commas and should have a clear idea about the different number systems: Indian and International. As soon as students understand the formation of the numbers, they can move on to comparisons and arrangement  of numbers. Usually, this is done by ascending and descending order, shifting digits to form new numbers. Students will be learning about reading and writing large numbers using tablets and other indicators. The chapter-wise solutions are  available on Extramarks.

Knowing Our Numbers: NCERT Class 6 Maths Chapter 1 Solutions Summary

Numbers involve counting and measuring. With the help of numbers, it becomes easy to perform simple operations such as addition, subtraction, multiplication and division. In this chapter, students will learn how to compare numbers and expand the numbers. Also, make the largest and the smallest numbers using digits. 

Chapter 1 – Knowing Our Numbers

Chapter 1 “knowing our numbers” covers many important topics. These include ideas on larger numbers, operations using more significant numbers, comparisons, shifting of digits, commas, etc. The NCERT Solutions for Chapter 1 Maths help students in understanding all the concepts easily. 

1.1 Introduction

The first part is the basic introduction of the chapter “Knowing Our Numbers”. Here one can revise the old concepts of numbers, such as the Indian system, the International system and many more. Solved sums are given in the NCERT textbook and the exercise to ensure that students understand the concepts and the topics mentioned. 

1.2 Comparing Numbers

Once the students know the number system and its structure, then they learn about comparisons. The comparison of more significant numbers using the number systems and the arrangement of numbers in ascending and descending order.  

1.3 Large Numbers in Practise

Large numbers in practice involve practising through real-life examples. 

1.4 Using Brackets

The use of brackets and the Indian and international numeration system are covered in this section. 

1.5 Roman Numerals

The Roman numerals involve the Hindu Arabic system of numerals. This is a particular system of writing numerals in the form of the Roman number system. There are specific rules which are listed in this section. Students are advised to keep these rules in mind while writing or reading the roman numerals.

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Q.1 Fill in the blanks:

(a) 1 lakh = _______ ten thousand.

(b) 1 million = _______ hundred thousand.

(c) 1 crore = _______ ten lakh.

(d) 1 crore = _______ million.

(e) 1 million = _______ lakh.

(a) 1 lakh = __ 10 ___ ten thousand.

(b) 1 million = __ 10 __ hundred thousand.

(c) 1 crore = __ 10 __ ten lakh.

(d) 1 crore = _ 10 __ million.

(e) 1 million = _ 10 __ lakh.

Q.2 Place commas correctly and write the numerals:

(a) Seventy three lakh seventy five thousand three hundred seven.

(b) Nine crore five lakh forty one.

(c) Seven crore fifty two lakh twenty one thousand three hundred two.

(d) Fifty eight million four hundred twenty three thousand two hundred two.

(e) Twenty three lakh thirty thousand ten.

(a) 73,75,307

(b) 9,05,00,041

(c) 7,52,21,302

(d) 58,423,202

(e) 23,30,010

Q.3 Insert commas suitably and write the names according to Indian System of Numeration:

(a) 87595762 (b) 8546283

(c) 99900046 (d) 98432701

(a) 8,75,95,762

Eight crore seventy five lakh ninety five thousand seven hundred sixty two

(b) 85,46,283

Eighty five lakh forty six thousand two hundred eighty three

(c) 9,99,00,046

Nine crore ninety nine lakh forty six

(d) 9,84,32,701

Q.4 Nine crore eighty four lakh thirty two thousand seven hundred one

Insert commas suitably and write the names according to International System of Numeration:

(a) 78921092 (b) 7452283

(c) 99985102 (c) 48049831

(a) 78,921,092

Seventy eight million nine hundred twenty one thousand ninety two

(b) 7,452,283

Seven million four hundred fifty two thousand two hundred eighty three

(c) 99,985,102

Ninety nine million nine hundred eighty five thousand one hundred two

(d) 48, 049,831

Forty eight million forty nine thousand eight hundred thirty one

Q.5 A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final day was respectively 1094, 1812, 2050 and 2751. Find the total number of tickets sold on all the four days.

Q.6 Shekhar is a famous cricket player. He has so far scored 6,980 runs in test matches. He wishes to complete 10,000 runs. How many more runs does he need?

Runs scored = 6,980

Runs desired = 10,000

Runs needed = 10,000 – 6,980 = 3,020

Q.7 In an election, the successful candidate registered 5,77,500 votes and his nearest rival secured 3,48,700 votes. By what margin did the successful candidate win the election?

Q.8 Find the difference between the greatest and the least 5-digit number that can be written using the digits 6, 2, 7, 4, 3 each only once.

Let us form the greatest and the least number using the digits 6, 2, 7, 4, 3 only once.

So, we have

Greatest number = 76432

Least number = 23467

Difference = 76432 – 23467 = 52965

Therefore, the required difference is 52,965.

Q.9 A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?

Screws manufactured in one day = 2,825

Days in January = 31

Screws produced in 31 days = 2825 × 31 = 87575

Therefore, screws produced in the month of January = 87,575

Q.10 A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer?

(7236 × 65) – (7236 × 56) = 7236 × (65 – 56)

Therefore, student’s answer was greater than the correct answer by 65,124.

Q.11 To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain?

Cloth required for one shirt = 2 m 15 cm

= 200 cm + 15 cm

Total cloth = 40 m = 40 × 100 = 4000 cm

Number of shirts that can be stitched out of 4000 cm =

Therefore, 18 shirts can be stitched and 130 cm cloth will remain.

Q.12 Medicine is packed in boxes, each weighing 4 kg 500g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg?

Q.13 The distance between the school and a student’s house is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days.

Distance between school and house = 1 km 875 m

Now, 1 km = 1000 m

So, 1 km 875 m = (1000 + 875) m = 1875 m

Distance covered in 1 day = 1875 × 2 = 3750 m

Distance covered in 6 days = 3750 × 6 = 22,500

Therefore, distance covered in 6 days = 22,500 m

= 22 km 500 m

Q.14 A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?

We know that

1 litre = 1000 ml

Capacity of vessel = 4 litres and 500 ml

= (4000 + 500) ml

Capacity of a glass = 25 ml

Number of glasses that can be filled = 4500/25 = 180

Therefore, 180 glasses can be filled.

Estimate each of the following using general rule:

(a) 730 + 998 (b) 796 – 314 (c) 12,904 +2,888 (d) 28,292 – 21,496

Q.15 Make ten more such examples of addition, subtraction and estimation of their outcomes.

(a) 730 + 998

We round off the given numbers to hundreds.

Number 730 rounds off to 700 and 998 rounds off to 1000.

Estimated sum = 700 + 1000 = 1700

(b) 796 – 314

Number 796 rounds off to 800 and 314 rounds off to 300.

Estimated difference = 800 – 300 = 500

(c) 12904 + 2888

We round off the given numbers to thousands.

Number 12904 rounds off to 13000 and 2888 rounds off to 3000.

Estimated sum = 13000 + 3000 = 16000

(d) 28,292 − 21,496

Number 28,2962 rounds off to 28000 and 21,496 rounds off to 21000.

Estimated difference = 28000 − 21000 = 7000

Q.16 Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens) :

(a) 439 + 334 + 4,317 (b) 1,08,734 – 47,599 (c) 8325 – 491 (d) 4,89,348 – 48,365

Make four more such examples.

(a) 439 + 334 + 4317

Number 439 rounds off to 400, 334 rounds off to 300 and 4317 rounds off to 4300.

Estimated sum = 400 + 300 + 4300 = 5000

Now, we round off the given numbers to tens.

Number 439 rounds off to 440, 334 rounds off to 330 and 4317 rounds off to 4320.

Estimated sum = 440 + 330 + 4320= 5090

(b) 1,08,734 − 47,599

Number 1,08,734 rounds off to 1,08,700 and 47,599 rounds off to 47,600.

Estimated difference = 1,08,700 – 47,600 = 61,100

Number 1,08,734 rounds off to 1,08,730 and 47,599 rounds off to 47,600.

Estimated difference = 1,08,730 – 47,600 = 61,130

(c) 8325 − 491

Number 8325 rounds off to 8300 and number 491 rounds off to 500.

Estimated difference = 8300 – 500 = 7,800

Number 8325 rounds off to 8330 and number 491 rounds off to 490.

Estimated difference = 8330 – 490 = 7,840

(d) 4,89,348 − 48,365

Number 4,89,348 rounds off to 4,89,300 and number 48,365 rounds off to 48,400.

Estimated difference = 4,89,300 – 48,400 = 4,40,900

Number 4,89,348 rounds off to 4,89,350 and number 48,365 rounds off to 48,370.

Estimated difference = 4,89,350 – 48,370 = 4,40,980

Q.17 Estimate the following products using general rule:

(a) 578 × 161 (b) 5281 × 3491 (c) 1291 × 592 (d) 9250 × 29

(a) 578 × 161

Number 578 rounds off to 600 and number 161 rounds off to 200.

Estimated product = 600 × 200 = 1,20,000

(b) 5281 × 3491

We round off 5281 to nearest thousands and so 5281 rounds off to 5000.

We round off 3491 to nearest hundreds and so 3491 rounds off to 3500.

Estimated product = 5000 × 3500 = 1,75,00,000

(c) 1291 × 592

Number 1291 rounds off to 1300 and number 592 rounds off to 600.

Estimated product = 1300 × 600 = 7,80,000

(d) 9250 × 29

We round off 9250 to 9000 and 29 to 30.

Estimated product = 9,000 × 30 = 2,70,000

Q.18 Kirti bookstore sold books worth ₹ 2,85,891 in the first week of June and books worth ₹ 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?

Worth of Books sold in 1 st week = ₹2,85,891

Worth of books sold in 2 nd week = ₹4,00,768

Total sale = Sale in 1 st week + Sale in 2 nd week

= ₹2,85,891 + ₹4,00,768 = ₹6,86,659

Thus, the sale for the two weeks together was ₹6,86,659.

Also, 4,00,768 – 2,85,891 = 1,14,877

Thus, the sale in 2 nd week was greater than the sale in 1 st week by ₹1,14,877.

Q.19 A merchant had ₹78,592 with her. She placed an order for purchasing 40 radio sets at ₹1200 each. How much money will remain with her after the purchase?

Cost of one radio set = ₹1200

So, cost of 40 radio sets = ₹1200 × 40 = ₹48000

Merchant had ₹78,592 with her before purchase.

So, after purchase, she will have ₹(78,592 – 48,000),i.e. ₹30,592.

Therefore, ₹30,592 will remain with her after the purchase.

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Faqs (frequently asked questions), 1. where can i get the ncert class 6 maths syllabus in hindi.

You will get the Class 6 Maths syllabus from Extramarks’ official website.

2. How many chapters are there in the NCERT Maths Class 6 syllabus?

There are 14 chapters in the NCERT  Maths Class 6 syllabus.

3. What are the different topics covered in Chapter 1 of Class 6 Maths?

The different topics covered in NCERT solutions for Class 6 Maths are:

• Introduction to numbers
• Comparing numbers
• Ascending order and Descending order
• How many numbers can be formed using a certain number of digits?
• Shifting digits
• Place value
• Larger Numbers and Estimates
• Estimating sum or difference
• Estimating products of numbers
• Using Brackets

NCERT Solutions Related Links

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NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers

• Exercise 1.1 Chapter 1 Class 6 Maths NCERT Solutions
• Exercise 1.2 Chapter 1 Class 6 Maths NCERT Solutions
• Exercise 1.3 Chapter 1 Class 6 Maths NCERT Solutions

NCERT Solutions for Class 6 Maths Chapters:

What are the benefits of NCERT Solutions for Chapter 1 Knowing Our Numbers Class 6 NCERT Solutions?

How many exercises in chapter 1 knowing our numbers, how to compare numbers, what is international numeration system, contact form.

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Assignments For Class 6 Mathematics

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Assignments for Class 6 Mathematics as per CBSE and NCERT pattern

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Assignments for Class 6 Mathematics as per CBSE NCERT pattern

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CBSE Worksheets for Class 6 Maths | MCQ Questions for Class 6 Maths

CBSE Worksheets for Class 6 Maths: One of the best teaching strategies employed in most classrooms today is Worksheets. CBSE Class 6 Maths Worksheet for students has been used by teachers & students to develop logical, lingual, analytical, and problem-solving capabilities. So in order to help you with that, we at WorksheetsBuddy have come up with Kendriya Vidyalaya Class 6 Maths Worksheets for the students of Class 6. All our CBSE NCERT Class 6 Maths practice worksheets are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance. These chapter wise test papers for Class 6 Maths will be useful to test your conceptual understanding.

Board: Central Board of Secondary Education(www.cbse.nic.in) Subject: Class 6 Maths Number of Worksheets: 145

CBSE Class 6 Maths Worksheets PDF

All the CBSE Worksheets for Class 6 Maths provided in this page are provided for free which can be downloaded by students, teachers as well as by parents. We have covered all the Class 6 Maths important questions and answers in the worksheets which are included in CBSE NCERT Syllabus. Just click on the following link and download the CBSE Class 6 Maths Worksheet. CBSE Worksheets for Class 6 Math can also use like assignments for Class 6 Maths students.

• MCQ Questions for Class 6 Maths
• Class 6 Knowing Our Numbers Worksheets
• Class 6 Whole Numbers Worksheets
• Class 6 Playing with Numbers Worksheets
• Class 6 Basic Geometrical Ideas Worksheets
• Class 6 Understanding Elementary Shapes Worksheets
• Class 6 Integers Worksheets
• Class 6 Fractions Worksheets
• Class 6 Decimals Worksheets
• Class 6 Data Handling Worksheets
• Class 6 Mensuration Worksheets
• Class 6 Algebra Worksheets
• Class 6 Ratio and Proportion Worksheets
• Class 6 Symmetry Worksheets
• Class 6 Practical Geometry Worksheets

Factors and Multiples

• CBSE Worksheets for Class 6 Maths Factors and Multiples Assignment 1
• CBSE Worksheets for Class 6 Maths Factors and Multiples Assignment 2
• CBSE Worksheets for Class 6 Maths Factors and Multiples Assignment 3

Perimeter And Area

• CBSE Worksheets for Class 6 Maths Perimeter And Area Assignment

Class 6 Maths Worksheets and MCQ Questions

• CBSE Worksheets for Class 6 Maths Assignment 1
• CBSE Worksheets for Class 6 Maths Assignment 2
• CBSE Worksheets for Class 6 Maths Assignment 3
• CBSE Worksheets for Class 6 Maths Assignment 4
• CBSE Worksheets for Class 6 Maths Assignment 5
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• CBSE Worksheets for Class 6 Maths Assignment 11
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• CBSE Worksheets for Class 6 Maths Assignment 13
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• CBSE Worksheets for Class 6 Maths Assignment 21
• CBSE Worksheets for Class 6 Maths Assignment 22

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NCERT Maths Class 6 Try These Solutions Chapter 1

Try these page 2

Try These Page 4

Numbers are the highest degree of knowledge. It is knowledge itself. Pluto

Table of Contents

• Ascending Order
• Descending Order
• Place value

Expanded Form

Ascending order- This is also known as increasing Order.

Numbers should be arranged from smallest to greatest.

Descending Order – This is also known as decreasing order.

Numbers should be arranged from greatest to the smallest.

NCERT Maths Class 6 Try These Solutions Chapter 1 Page 6

• Arrange the following numbers in ascending order

a) 847, 9754, 8320, 571

Solution- Arranging numbers in ascending order, first look at the highest

place digit number. For digit number is always greater than a three-digit number.

Now comparing thousand place values of 9754 and 8320

we know 9 > 8. so, 9754 > 8320

now comparing three digits numbers. we know 5 < 8. so, 571 < 847

Now, arranging numbers in ascending orders are

571 < 847 < 8320 < 9754

b) 9801, 25751, 36501, 38802

solution-Numbers in Ascending or increasing orders are

9801< 25751<36501<38802

2. Arrange the following numbers in descending order .

a) 5000, 7500, 85400, 7861

Solution- Numbers in descending or decreasing orders are

85400 > 7861 > 7500 > 5000

b) 1971, 45321, 88715, 92547

92547 > 88715 > 45321 > 1971

Place value-

NCERT Maths Class 6 Try These Solutions Chapter 1 Page 8

Read and Expand the numbers

Try These Page 9

Read and expand the numbers

NCERT Maths Class 6 Try These Solutions Page 13

Read these numbers. write them using Shagufta’s boxes and then write their expanded form.

Solution- four lakh seventy-five thousand three hundred twenty

ii) 9847215

Solution- Ninety-eight lakh forty-seven thousand two hundred fifteen

iii) 97645310

Solution- Nine crores seventy-six lakh forty-five thousand three hundred ten

iv ) 30458094

Solution-Three crore four lakh fifty-eight thousand ninety-four

a) Which is the smallest number?

Solution – The smallest number is 475320

b) Which is the greatest number?

Solution- The greatest number is 97645310

c) Arrange these numbers in ascending or descending order.

Solution- Arranging numbers in descending orders are

97645310 > 30458094 > 9847215 > 475320

Arranging numbers in ascending orders are

475320 < 9847215 < 30458094 < 97645310

2. i) 527864 ii) 95432 iii) 18950049 iv) 70002509

a) Write these numbers using commas

Solution- i) 5,27,864 – Five lakhs twenty-seven thousand eight hundred sixty-four

ii) 95,432 – ninety-five thousand four hundred thirty-two

iii) 1,89,50,049 – one crore eighty nine lakh fifty thousand forty nine

iv) 7,00,02,509- Seven crore two thousand five hundred nine

b) Which is the smallest number?

Solution- The smallest number is 95,432

c) Which is the greatest number?

Solution- The greatest number is 7,00,02,509

d) Arrange these in ascending and descending order.

Solution- Numbers in ascending orders are

95,432 < 5,27,864 < 1,89,50,049 < 7,00,02,509

Numbers in descending orders are

7,00,02,509 > 1,89,50,049 > 5,27,864 > 95,432

NCERT Maths Class 6 Try These Solutions Page 14

• You have the following digits 4, 5, 6, 0, 7, and 8. Using them make five numbers each with six digits.

a) Put commas for ease of reading.

Solution-a) Five six digits numbers using commas are

8,76,540 ; 8,67,540 ; 8,67,450 ; 7,86, 405 ; 7,68,045

b) Arrange them in ascending and descending order.

Solution- Arranging numbers in ascending orders are

7,68,045 < 7,86,405 < 8,67,450 < 8,67,540 < 8,76,540

Arranging numbers in descending orders are

8,76,540 > 8,67,540 > 8,67, 450 > 7,86,405 > 7,68,045

2. Take the digits 4, 5, 6, 7, 8, and 9. make any three numbers each with 8 digits.

Put commas for ease of reading.

Solution- Three numbers with 8 digits are

9,98,76,544 ; 9,89,67,454; 8,75,69,495

3. From the digits 3.0, and 4 make five numbers each with 6 digits . Use commas.

Solution- five numbers with six digits are

4,43,034 ; 3,34,003 ; 4,30,004 ; 4,00,344; 4,03,343

NCERT Chapter 1Try These Solutions Page 16

• How many centimeters make a kilometer?

Ans- We know, 1 meter = 100 centimeter

1 Kilometer = 1000 meter = 1000 x 100 centimeters = 100000 centimeters

2. Name five large cities in India. Find thei r populations. Also, find the distance in kilometers between

each pair of these cities .

The population of Mumbai is 25,882, 773

The population of Delhi is 20, 782, 883

The population of Bangalore is 15, 771, 231

The population of Chennai is 10, 231, 828

The population of Kolkata is 8, 029, 819

The distance between Delhi and Mumbai is 1, 411. 9 km

The distance between Delhi and Bangalore is 2,174.8 km

The distance between Delhi and Chennai is 2,208 km

The distance between Kolkata and Chennai is 1,662.8 km

• How many Milligrams make one kilogram?

Ans- 1 gram = 1000 miligram

one kilogram = 1000 gram = 1000 x 1000 miligram = 1,000,000 miligrams

2. A box of medicines tablets contains 2,000,000 tablets each weighing 20 mg. What is the total weight of all the tablets

in the box in grams and in kilograms?

1 tablet weighs 20 mg

2,000,000 tablets weigh 20 mg x 2,000,000 = 40,000,000 mg

we know 1000 mg = 1 g

so, 40,000,000 mg = =\frac{1}{1000}\times 40,000,000 =40,000 g

We know 100 g = 1 kg

so, 40, 000 g = =\frac{1}{1000}\times 40,000 =40 kg

so, 40,000,000 mg = 40,000 g = 40 kg

NCERT Class 6 Chapter 1Try These Page 17

• A bus started its journey and reached different places at a speed of 60km/hr. The journey is shown below.

A to B is 4170 km, B to C is 3410 km, C to D is 2160 km, D to E is 8140 km, E to F is 4830 km, F to G is 2550 km,

G to A is 1290 km

i) Find the total distance covered by the bus from A to D.

Solution- Total Distance covered by the bus from A to D is

the Distance covered from A to B + B to C + C to D =4170 km + 3410 km + 2160 km = 9740 km

ii) Find the total distance covered by the bus from D to G

Solution- Total distance = the distance from D to E + E to F + F to G = 8140 lm + 4830 km + 2550 km = 15,520km

iii) Find the total distance covered by the bus, if it starts from A and returns back to A

Solution – 4170 km+ 3410 + 2160 + 8140 + 4830 + 2550 + 1290 = 26,550km

iv) Can you find the difference of distances from C to D and D to E?

Solution – Difference of distance = Distance from D to E – Distance from C to D = 8140 km – 2160 km = 5980 km

NCERT Class 6 Maths Chapter 1 Try These Page 23

Round these numbers to the nearest tens.

Solution -Unit digit of 28 is 8, which is more than 5. so add 1 to tens place digit and write zero in-unit digit.

Rounding 28 to the nearest ten is 30

Solution- Unit digit of 32 is 2, which is less than 5. so write tens place digit as it is and write zero in-unit digit.

Rounding 32 to the nearest ten is 30

Solution – Unit digit of 52 is 2, which is less than 5. so write tens place digit as it is and write zero in-unit digit.

Rounding 52 to the nearest ten is 50

Solution -Unit digit of 41 is 1, which is less than 5. so write tens place digit as it is and write zero in-unit digit.

Rounding 41 to the nearest ten is 40

Solution – Unit digit 9 is more than 5. Add 1 to the tens place digit and write 0 in the unit place digit.

39 rounding to 40

Solution- unit place digit of 48 is 8 which is more than 5. add 1 to the tens place digit and write 0 in the unit place digit

48 rouning to the number 50

Solution- unit place digit of 64 is 4 which is less than 5. write the tens place digit as it is and 0 in the unit place digit

64 rouning to the number 60

Solution- unit place digit of 59 is 9 which is more than 5. add 1 to the tens place digit and write 0 in the unit place digit

59 rouning to the number 60

Solution- unit place digit of 99 is 9 which is more than 5. add 1 to the tens place digit and write 0 in the unit place digit

99 rouning to the number 100

Solution- unit place digit of 215 is 5 which is more than 5. add 1 to the tens place digit and write 0 in the unit place digit

215 rouning to the number 220

Solution- unit place digit of 1453 is 3 which is less than 5. write 0 in the unit place digit

1453 rouning to the number 1450

Solution -Unit digit of 1493 is 6, which is more than 5. so add 1 to tens place digit and write zero in-unit digit.

2936 rounded to the nearest ten is 2940

Try These Page 24

Round off the numbers to the nearest tens, hundreds, and thousands.

solution- a) Unit digit f the number is 7, which is more than 5, so, write 0 in unit place and add 1 to the tens place.

75847 rounded off to the nearest ten is 75850

b) Tens place digit of the number is 4, which is less than 5. so write 0 in tens and unit place digit and write the hundred place

digit as it is.

so, 75847 rounded off to the nearest hundred is 75800

c) Hundred place digit of the number is 8, which is less than 5. so write 0 in tens and unit place digit and write the hundred place

so, 75847 rounded off to the nearest thousand is 76000

d) Thousands place digit of the number is 5, which is equal to 5. so write 0 in thousands, hundreds. tens and unit place digit and add 1 to the ten thousand places

so, 75847 rounded off to the nearest thousand is 80000

NCERT Class 6 knowing our numbers Try These Page 28

Estimation of Numbers

Estimate the following products:

a) 87 x 313

solution- 87 rounded off to the nearest tens is 90

313 rounded off to the nearest hundreds is 300

so, estimated product is 90 x 300 = 27000

solution- 9 rounded off to the nearest tens is 10

795 rounded off to the nearest hundreds is 800

so, estimated product is 10 x 800 = 8000

c) 898 x 785

solution- 898 rounded off to the nearest hundreds is 900

785 rounded off to the nearest hundreds is 800

so, estimated product is 900 x 800 = 7,20,000

d) 958 x 387

solution- 958 rounded off to the nearest hundreds is 1000

387 rounded off to the nearest hundreds is 400

so, estimated product is 1000 x 400 = 4,00,000

NCERT Class 6 chapter 1 Try These Page 29

Using Brackets

• Write the expressions for each of the following using brackets.

a) Four multiplied by the sum of nine and two.

solution- 4(9+2)

b) Divide the difference between eighteen and six by four

solution- \frac{(18-6)}{4}

c) Forty divided by three times the sum of three and two

Solution- \frac{45}{3(3+2)}

NCERT Class 6 chapter 1 Try These Page 32

Roman Numerals

solution- 73=70+3= 50 +20 + 3 = LXXIII

Solution- 92 = 90+2 = 100-10+2= XCII

solution – 54 = 50+4 = LIV

solution- 66 = 60+6 = 50 + 10 + 5+ 1= LXVI

Solution- 87 = 80 + 7 = 50 + 30 +5+2 = LXXXVII

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NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

NCERT Solutions for Class 6 Maths

NCERT Solutions for Class 6 Maths is a very important resource for students of Class 6. CBSE 6th class maths textbook solutions includes answers of all questions except the ones which are not in the syllabus anymore. NCERT class 6 maths solutions have been provided by the most experienced teachers. A very simple approach has been followed while solving the questions and designing the class 6 maths NCERT solutions. Students will find it extremely easy to understand the problems and how to go about solving them. You can also practice  Extra Questions for Class 6 Maths  on LearnCBSE.in

NCERT Solutions for Class 6 Maths are given below for all chapters.

• Chapter 1 Knowing Our Numbers
• Chapter 2 Whole Numbers
• Chapter 3 Playing With Numbers
• Chapter 4 Basic Geometrical Ideas
• Chapter 5 Understanding Elementary Shape
• Chapter 6 Integers
• Chapter 7 Fractions
• Chapter 8 Decimals
• Chapter 9 Data Handling
• Chapter 10 Mensuration
• Chapter 11 Algebra
• Chapter 12 Ratio and Proportion
• Chapter 13 Symmetry
• Chapter 14 Practical Geometry

Click on the name of the chapter for which you want to check the solutions and you will be directed to the page for that chapter. You can then go through the detailed, step-wise CBSE 6th class maths questions and answers for each and every question for that chapter.

NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers

• Class 6 Maths Knowing our Numbers Exercise 1.1
• Class 6 Maths Knowing our Numbers Exercise 1.2
• Class 6 Maths Knowing our Numbers Exercise 1.3
• Knowing Our Numbers Class 6 Extra Questions

NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers

• Class 6 Maths Whole Numbers Exercise 2.1
• Class 6 Maths Whole Numbers Exercise 2.2
• Class 6 Maths Whole Numbers Exercise 2.3
• Whole Numbers Class 6 Extra Questions

NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers

• Playing with Numbers Class 6 Ex 3.1
• Playing with Numbers Class 6 Ex 3.2
• Playing with Numbers Class 6 Ex 3.3
• Playing with Numbers Class 6 Ex 3.4
• Playing with Numbers Class 6 Ex 3.5
• Playing with Numbers Class 6 Ex 3.6
• Playing with Numbers Class 6 Ex 3.7
• Playing with Numbers Class 6 Extra Questions

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

• Class 6 Maths Basic Geometrical Ideas Exercise 4.1
• Class 6 Maths Basic Geometrical Ideas Exercise 4.2
• Class 6 Maths Basic Geometrical Ideas Exercise 4.3
• Class 6 Maths Basic Geometrical Ideas Exercise 4.4
• Class 6 Maths Basic Geometrical Ideas Exercise 4.5
• Class 6 Maths Basic Geometrical Ideas Exercise 4.6
• Basic Geometrical Ideas Class 6 Extra Questions

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shape

• Understanding Elementary Shapes Class 6 Ex 5.1
• Understanding Elementary Shapes Class 6 Ex 5.2
• Understanding Elementary Shapes Class 6 Ex 5.3
• Understanding Elementary Shapes Class 6 Ex 5.4
• Understanding Elementary Shapes Class 6 Ex 5.5
• Understanding Elementary Shapes Class 6 Ex 5.6
• Understanding Elementary Shapes Class 6 Ex 5.7
• Understanding Elementary Shapes Class 6 Ex 5.8
• Understanding Elementary Shapes Class 6 Ex 5.9
• Understanding Elementary Shapes Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 6 Integers

• Integers Class 6 Ex 6.1
• Integers Class 6 Ex 6.2
• Integers Class 6 Ex 6.3
• Integers Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 7 Fractions

• Fractions Class 6 Ex 7.1
• Fractions Class 6 Ex 7.2
• Fractions Class 6 Ex 7.3
• Fractions Class 6 Ex 7.4
• Fractions Class 6 Ex 7.5
• Fractions Class 6 Ex 7.6
• Fractions Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 8 Decimals

• Class 6 Maths Decimals Exercise 8.1
• Class 6 Maths Decimals Exercise 8.2
• Class 6 Maths Decimals Exercise 8.3
• Class 6 Maths Decimals Exercise 8.4
• Class 6 Maths Decimals Exercise 8.5
• Class 6 Maths Decimals Exercise 8.6
• Decimals Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 9 Data Handling

• Class 6 Maths Data Handling Exercise 9.1
• Class 6 Maths Data Handling Exercise 9.2
• Class 6 Maths Data Handling Exercise 9.3
• Class 6 Maths Data Handling Exercise 9.4
• Data Handling Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 10 Mensuration

• Class 6 Maths Mensuration Exercise 10.1
• Class 6 Maths Mensuration Exercise 10.2
• Class 6 Maths Mensuration Exercise 10.3
• Mensuration Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 11 Algebra

• Class 6 Maths Algebra Exercise 11.1
• Class 6 Maths Algebra Exercise 11.2
• Class 6 Maths Algebra Exercise 11.3
• Class 6 Maths Algebra Exercise 11.4
• Class 6 Maths Algebra Exercise 11.5
• Algebra Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 12 Ratio and Proportion

• Class 6 Maths Ratio and Proportion Exercise 12.1
• Class 6 Maths Ratio and Proportion Exercise 12.2
• Class 6 Maths Ratio and Proportion Exercise 12.3
• Ratio and Proportion Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 13 Symmetry

• Class 6 Maths Symmetry Exercise 13.1
• Class 6 Maths Symmetry Exercise 13.2
• Class 6 Maths Symmetry Exercise 13.3
• Symmetry Class 6 Extra Questions

Class 6 Maths NCERT Solutions Chapter 14 Practical Geometry

• Class 6 Maths Practical Geometry Exercise 14.1
• Class 6 Maths Practical Geometry Exercise 14.2
• Class 6 Maths Practical Geometry Exercise 14.3
• Class 6 Maths Practical Geometry Exercise 14.4
• Class 6 Maths Practical Geometry Exercise 14.5
• Class 6 Maths Practical Geometry Exercise 14.6
• Practical Geometry Class 6 Extra Questions

Maths Formulas for Class 6 RD Sharma Class 6 Solutions Maths NCERT Solutions

Mathematics is an interesting subject. Unfortunately, many students find it difficult. But that’s not because Mathematics is really a difficult subject. Students find it difficult because most of them do not have their basics clear for the subject. Lack of sufficient practice tool is a reason why solving Mathematical problems seems a tough nut to crack.

Unlike other subjects, rote learning cannot help you to excel this subject. Even for other subjects, rote learning is not recommended as it won’t be of much use after a point of time. And Mathematics, from the very beginning, needs one to think logically. But just because the subject needs logical thinking and analytical skills does not mean it is tough. Mathematics needs practice and with practice, anything can be perfected, even the way you think and analyze. So, it is of utmost importance to take Mathematics seriously right from your early school life. Getting your basics clear at this point will make it easier for you to handle difficult concepts as you grow older.

Mathematics of Class 6, 7 and 8 standard play a vital role in strengthening the fundamentals of the subject. It is at this point, Mathematics goes beyond simple addition, subtraction, multiplication, and division and move onto more complex concepts. So, one must prepare for this subject in a serious manner and get all their doubts clear. Otherwise, they won’t be able to cope with the subject later, especially if they are planning to take up Science in their Higher Secondary level.

Class 6 Maths Chapter 1 Knowing Our Numbers

• Introduction
• Comparing Numbers Worksheet
• Large Numbers In Practice
• Using Brackets
• Roman Numerals Chart

Class 6 Maths Chapter 2 Whole Numbers

• Whole Numbers
• The Number Line
• Properties of Whole Numbers
• Patterns In Whole Numbers

Class 6 Maths Chapter 3 Playing With Numbers

• Factors And Multiples Worksheet
• Prime And Composite Numbers Chart and Worksheets
• Divisibility Rules 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3,2
• Common Factors And Common Multiples
• Some More Divisibility Rules
• Prime Factorisation Worksheets
• Highest Common Factor Worksheets
• Lowest Common Multiple Worksheet
• Hcf And Lcm Formulas, Problems with Solutions

Class 6 Maths Chapter 4 Basic Geometrical Ideas

• Points, A Line Segment, Ray, and A Line
• Intersecting Lines and Parallel Lines
• Types of Polygons
• What is Angle in Geometry
• Median, altitude of Triangle
• What is a Quadrilateral
• Parts of the Circle

Class 6 Maths Chapter 5 Understanding Elementary Shapes

• Comparison of Line Segments
• Different Types of Angles
• Measure an Angle with a Protractor
• Classification of Triangles
• Different Types of Quadrilaterals
• Different types of Three Dimensional Shapes

Class 6 Maths Chapter 6 Integers

• Integers Examples
• Operations with Integers Worksheet

Class 6 Maths Chapter 7 Fractions

• Types of fraction
• Fraction on The Number Line
• Proper Fractions
• Improper And Mixed Fractions
• Equivalent Fractions Chart
• Simplest Form Of A Fraction
• Like Fractions
• Comparing Fractions Worksheets
• Addition And Subtraction Of Fractions

Class 6 Maths Chapter 8 Decimals

• Tenths and Hundreths
• Convert Unlike Decimals to like decimals
• Using Decimals
• Addition Of Numbers With Decimals
• Subtraction Of Decimals

Class 6 Maths Chapter 9 Data Handling

• Recording Data
• Collection and Organisation of Data
• Pictograph Examples and Worksheets
• Interpretation of A Pictograph
• Drawing A Pictograph
• A Bar Graph

Class 6 Maths Chapter 10 Mensuration

• Perimeter of Closed Shapes
• Find Area of Plane Figures

Class 6 Maths Chapter 11 Algebra

• Matchstick Patterns
• The Idea Of A Variable
• More Matchstick Patterns
• More Examples Of Variables
• Use Of Variables In Common Rules
• Expressions With Variables
• Using Expressions Practically
• What Is An Equation?
• Solution Of An Equation

Class 6 Maths Chapter 12 Ratio and Proportion

• What is Ratio and Proportion
• Unitary Method

Class 6 Maths Chapter 13 Ratio and Proportion

• Making Symmetric Figures: Ink-blot Devils
• Figures with Two Lines of Symmetry
• Figures with Multiple (more than two) Lines of Symmetry
• Reflection and Symmetry

Class 6 Maths Chapter 14 Practical Geometry

• Construction of a Circle
• Construction of a Line Segment
• Construction of a Perpendicular Bisector
• Construction of Angles using compass ruler

NCERT Solutions For Class 6 Maths Solutions (Download PDF)

Clear your doubt then and there. This will help you not only to secure good marks in your Class 6 final exams, but also in other competitive exams that are conducted for students of Class 6. As you go to higher classes, it will help you to crack competitive scholarship exams, like NTSE, as well. So, make the best use of these solutions.

Remember, at this point, you cannot afford to skip any chapter even if it is not so important from the exam point of view. At this point, all the chapters are equally important so that your command over the subject gets really good. So, as you solve questions from your NCERT Maths textbook, go through the NCERT Solutions for Class 6 Maths here every time you face any difficulty with any question. Do not skip it for later.

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NCERT Solutions

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DAV Class 6 Maths Chapter 1 Worksheet 1 Solutions

The DAV Class 6 Maths Book Solutions Pdf  and DAV Class 6 Maths Chapter 1 Worksheet 1 Solutions of Natural Numbers and Whole Numbers offer comprehensive answers to textbook questions.

DAV Class 6 Maths Ch 1 WS 1 Solutions

Quotient 1. Write the Roman Numerals for each of the following. (a) 33 (b) 500 (c) 48 (d) 76 (e) 95 (f) 41 (g) 87 (h) 66 (i) 19 (j) 1000 Solution: (a) 33 = XXXIII (b) 500 = D (c) 48 = XLVIII (d) 76 = LXXVI (e) 95 = XCV (f) 41 = XLI (g) 87 = LXXXVII (h) 66 = LXVI (i) 19 = XIX (j) 1000 = M

Quotient 2. Convert the following into Hindu Arabic Numerals. (a) XXVI (b) LXXVII (c) XCI (d) LXXXV (e) D (f) XCIX (g) XCVII (h) LV (i) XLI (j) XXIX Solution: (a) XXVI = 26 (b) LXXVII = 77 (c) XCI = 91 (d) LXXXV = 85 (e) D = 500 (f) XCIX = 99 (g) XCVII = 97 (h) LV = 55 (i) XLI = 41 (j) XXIX = 29

Question 3. Solve and write the results in Roman Numerals. (a) 32 + 67 (b) 216 – 174 (c) 12 × 7 (d) 3645 ÷ 45 Solution: (a) 32 + 67 = 99 = XCIX (b) 216 – 174 = 42 = XLII (c) 12 × 7 = 84 = LXXXIV (d) 3645 ÷ 45 = 81 = LXXXI

Question 4. Which of the following is meaningless? (a) VVII (b) XLI (c) LIV (d) IC (e) LIL (f) IVC (g) XCI (h) VL Solution: (a) VVII = Meaningless (b) XLI = 41 (c) LIV = 54 (d) IC = Meaningless (e) LIL = Meaningless (f) IVC = Meaningless (g) XCI = 91 (h) VL = Meaningless

Question 5. Match the following.

Solution: DXLV = 545 MMX = 2010 CMVIII = 908 CCIII = 203 DXCI = 591

Question 6. Write the following in Roman Numerals. (a) Year in which India got Indepen-dence. (b) Year in which India became Republic. (c) Year in which you were born. (d) Present year. Solution: (a) 1947 = MCMXLVII (b) 1950 = MCML (c) __________ (d) __________

DAV Class 6 Maths Chapter 1 Worksheet 1 Notes

Natural Numbers: All positive numbers starting from 1 are called natural numbers. Example: 1, 2, 3, 4, 5, 6, 7, 8 …………..

Roman Numerals: Symbols for some Hindu Arabic Numerals are called Roman Numerals. Example:

Example 1: Convert the given Hindu Arabic Numerals into Roman Numerals.

(i) 46 Solution: 46 = XLVI

(ii) 98 Solution: 98 = XCVIII

(iii) 63 Solution: 63 = LXIII

(iv) 80 Solution: 80 = LXXX

(v) 56 Solution: 56 = LVI

Example 2: Convert the following into Hindu Arabic Numerals.

(i) XLVIII Solution: XLVIII = 50 – 10 + 8 = 48

(ii) LIX Solution: LIX = 50 + 9 = 59

(iii) XCVII Solution: XCVII = 100 – 10 + 7 = 97

(iv) XXXI Solution: XXXI = 10 + 10 + 10 + 1 = 31

(v) LXXIX Solution: LXXIX = 50 + 10 + 10 + 9 = 79

Ratio and Proportion Class 6 RS Aggarwal Exe-8B Goyal Brothers ICSE Maths Solutions

Ratio and Proportion Class 6 RS Aggarwal Exe-8B Goyal Brothers ICSE Maths Solutions Ch-8. In this article you will learn about PROPORTION . Visit official Website CISCE  for detail information about ICSE Board Class-6 Mathematics.

Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other

Proportion Formula

let us assume that, in proportion, the two ratios are a : b & c : d. The two terms ‘b’ and ‘c’ are called ‘ mean term ,’ whereas the terms ‘a’ and ‘d’ are known as ‘extremes or extreme terms .’ If  a/b = c/d  then  a : b :: c : d

Exercise- 8B

(Ratio and Proportion Class 6 RS Aggarwal Exe-8B Goyal Brothers ICSE Maths Solutions Ch-8)

Que-1: Verify that :

(i) 12:18 = 8:12    (ii) 81kg : 45kg = 18men : 10men (iii) {3*(1/3)}:{2*(1/2)} = 12:9   (iv) 6:45 ≠ 4.8 : 3.6

Sol:  (i) 12/18 = (12÷6)/(18÷6) = (2/3)×(4/4) = 8/12 Hence Proved.

(ii) 81 kg : 45 kg : : 18 men : 10 men or 81:45::18:10 Product of means = 45 × 18 = 810 Product of extremes = 81 × 10 = 810 Product of means = Product of extremes Hence, (T).

(iii) L.H.S = (3+1/3):(2+1/2) = (10/3):(5/2) = 4:3 = (4 X 3)/(3 X 3) = 12/9 = 12:9 = R.H.S(VERIFIED)

(iv) 6/45 is not equal 4.8/3.6 2/15 is not equal 2.4/1.8 2/15 is not equal 1.2/0.9 2/15 is not equal 12/10/9/10 2/15 is not equal 12/10×10/9 2/15 is not equal 4/3 then proof that is not equal

Que-2: Which of the following numbers are in proportion.

(i) 30, 42, 5, 7    (ii) 4,11,22,33   (iii) 9,13,10,14    (iv) 16,18,24,27

Sol:  (i) 30 1st term, 42 2nd term, 5 3rd term, 7 4th term therefore 1st term × 4th term = 2nd term × 3rd term = 30×7= 42×5 = 210 = 210 = L.H.S = R.H.S

(ii) 4 1st term, 11 2nd term, 22 3rd term, 33 4th term therefore 1st term × 4th term = 2nd term × 3rd term = 4×33 = 11×22 = 132 = 232 = L.H.S ≠ R.H.S

(iii) 9 1st term, 13 2nd term, 10 3rd term, 14 4th term therefore 1st term × 4th term = 2nd term × 3rd term = 9×14 = 13×10 = 126 = 130 = L.H.S ≠ R.H.S

(iv) 16 1st term, 18 2nd term, 24 3rd term, 27 4th term therefore 1st term × 4th term = 2nd term × 3rd term = 16×27 = 18×24 = 432 = 432. = L.H.S = R.H.S

Que-3: Find the value of x in each of the following proportions.

(i) 36:81 :: x:63    (ii) 27:x :: 63:84   (iii) x:92 :: 87:116   (iv) 45:x :: 25:35

Sol:    (i) 36:81 :: x:63 36/81 = x/63 x = (36×63)/81 x = 28.

(ii) 27:x :: 63:84 27/x = 63/84 x = (27×84)/63 x = 36.

(iii) x:92 :: 87:116 x/92 = 87/116 x = (87×92)/116 x = 69

(iv) 45:x :: 25:35 45/x = 25/35 x = (45×35)/25 x = 63.

Que-4: In a proportion, the 1st, 2nd and 4th terms are 32, 112 and 217 respectively. Find the 3rd terms.

Sol:  Let the third term be x Therefore, 32 : 112 :: x : 217 so, 32/112 = x/217 x = (32×217)/112 x = 62 So, the third term is 62.

Que-5: In a proportion, the 1st, 3rd and 4th terms are 51, 81 and 108 respectively. Find the 2nd term.

Sol:  Let the second term be x . Then, 51 : x : : 81   : 108 81x = 51×108 x = (51×108)/81 x = 68.

Que-6: The income of Ruchi and Rajan are in the ratio 4:7. If Ruchi earns Rs16800 per month, how much does Rajan earn per month ?

Sol:  Ruchi’s income : Rajan’s income = 4 : 7 We know Ruchi’s income is ₹16,800, so let’s represent Rajan’s income as x. We can set up the proportion: 4/7 = 16800/x To solve for x, we can cross-multiply: 4x = 7 × 16800 4x = 117600 Now, divide both sides by 4: x = 117600 ÷ 4 x = 29400

Que-7: An electric pole casts a shadow of length 20 metres at a time when a tree 6 metres high casts a shadow of length 8 metres. Find the height of the pole.

Sol:  Let the height of the pole = x m Then, we have: x : 20 :: 6 : 8 Now, we know: Product of extremes = Product of means 8x = 20​ × 6 x = 120/8 = 15 Hence, the height of the pole is 15 m.

Que-8: The ratio of copper and zinc in an alloy is 9:5. If the weight of zinc in the alloy is 9.5g, what is the weight of copper in it ?

Sol:  Ratio of copper to zinc = 9:5 Weight of zinc = 9.5 g Let the weight of copper be x g. x/9.5 = 9/5 x = (9.5×9)/5 x = 85.5/5 x = 7.1 g.

Que-9: The ratio of length and the breadth of a rectangular plot is 9:5. If its breadth is 60m, find its length.

Sol:    Ratio of length and breath of a rectangle is 9:5 breath is 60m Assume that length and breadth of rectangle are 9x  m and 5x m respectively as ratio is 9 : 5 Equate 5x breadth with given breadth 60 m and solve for x 5x = 60 => x = 12 Substitute x= 12 in length 9x and calculate the length Length = 9x Length = 9 * 12 Length = 108 m

–: Ratio and Proportion Class 6 RS Aggarwal Exe-8B Goyal Brothers ICSE Maths Solutions Ch-8 :–

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CBSE Class 12 Physics Competency-Based Questions With Answer Key 2024-25: Chapter 1 Electrostatics FREE PDF Download

Cbse class 12 physics chapter 1 practice questions 2025: the 2024-25 competency-focused questions for cbse class 12 physics electrostatics are given here. check and download the mcqs and free response questions in pdf format..

CBSE Class 12 Physics Chapter 1 Competency-Based Questions

1. The capacitance of a capacitor is Co. It is connected to a battery of voltage V   which charges the capacitor. With the capacitor still connected to the battery,   a slab of dielectric material is introduced between the plates of the capacitor.   Which  of  the  following explains  the effect  of  the  dielectric  slab in  the above   situation? 

A. The electric field between the plates of the capacitor rises. 

B. The potential difference between the plates falls. 

C. The total charge on the capacitor increases. 

D. The ability of the capacitor to store charge decreases. 

2. The image below shows two examples of electric field lines. 

Which of the following statements is true? 

A. The electric fields in both I and II arise due to a single positive point charge  located somewhere on the left. 

B. The  electric  fields  in  both  I  and  II  can  be  created  by  negative  charges  located  somewhere on  the left and positive charges  somewhere on  the  right. 

C. The electric  field  in I  is  the  same everywhere  but  the electric  field  in II  becomes stronger as we move from left to right. 

D. As you move from left to right, the electric fields in both I and II become  stronger. 

3. In a given region, electric potential varies with position as V(x) = 3 + 2x 2 . Identify which of the following statements is correct. 

A. Potential difference between the two points x = 2 and x = ‐2 is 2 V. 

B. A charge of 1 C placed at x = 2 experiences a force of 6 N. 

C. The force experienced by the above charge is along +x ‐ axis. 

D. The electric field in the given region is non‐uniform along x ‐ axis. 

4. A parallel plate capacitor is charged to a potential difference V. Two protons P   and Q are placed at the two locations inside the capacitor as shown. 

Which one of the statements is correct? 

A. The forces on the two protons are identical. 

B. The  force on proton P near  the positive plate is more  than  the force on  proton Q. 

C. The force on proton Q near the negative plate is more than the force on  proton P. 

D. The forces on both the protons are zero. 

5. In a given region of an electric field, there is no charge present. A closed container  is placed in this region of the electric field.  What is  the  requirement  for  the  total  flux  through  the closed container  to be  zero? 

A. The field must be uniform. 

B. The container must be symmetric. 

C. The container must be oriented in a particular direction. 

D. There is no such requirement. The total flux through the container is zero  no matter what

6. A uniform electric field of 5000 V/m exists in a certain region. What volume of   this space will contain energy equal to 10‐6 J? (Take ∈o = 8.8 x10‐12  SI units) 

B. 9 x 10 ‐3 m 3

C. 9 x 10 ‐6 m 3

D. 9 x 10 3 m 3

7. Given are three different square arrangements of charges. 

(a) Draw relevant vector diagrams to represent the resultant electric field ER at  the center of the square in each case. 

(b) Identify the arrangement in which the resultant electric field is the smallest  at the center of the square. 

8. The figure below shows an arrangement of four charges along with some electric   field lines drawn between the charges. 

(a) Identify three things that are incorrect in this figure. 

(b) Draw a correct diagram representing the electric field lines for this system of  charges. 

9. In  the  case  of  a  spherical  charged  conductor  of  radius  R,  hollow  or  solid,  the   electric potential is constant and maximum inside and on the surface.  On the outside, the electric potential varies as,  where r is the distance from the center of the sphere. 

(a) Represent the variation of electric potential due to a charged sphere with   distance graphically. 

(b) How  does  the  electric  field  intensity  due  to  a  charged  sphere  vary  with   distance r from the center in the above case? 

(c) Represent the variation of electric field intensity due to a charged sphere   with distance graphically. 

10. For a given charge distribution, an equipotential surface is the locus of all points 

having the same potential. 

Draw two equipotential surfaces for each of the following: 

(a) a uniform electric field 

(b) a point charge 

(c) an infinite straight line of charge 

11. Study the graph between electric field intensity E versus the distance r. 

(a) Describe the nature of variation of electric field intensity between r = 0 and  r ≤ a. 

(b) Describe the nature of variation of electric field intensity for r > a. 

(c) Give an  example  of  the  body  of  charge  distribution  that  can  exhibit  the  above studied electric field distribution. 

12. Given is a pair of parallel charged metal plates in the arrangement as shown. 

(a) Sketch the electric field lines between the plates in I and II.

(b) Mention  whether  net electric  field  intensity  is  zero  or  non‐zero  in  each  case. 

13. The  dielectric  strength of a medium is  the minimum electric  field  required  to  cause ionization of the medium. For air, this value is taken as 3 million V/m.  With this information, find out if a metal sphere of radius 1 cm, surrounded by  air, can hold a charge of 1 coulomb. 

14. (a) If electric field strength at a point is zero at a given point, then what can you   say about the electric potential at that point? Explain. 

(b) In the two instances below, state whether electric field intensity and electric   potential are zero or non zero at the mid‐point joining the two‐point charges. 

15. A metal sphere A of radius a is charged to a potential V. It is enclosed inside a  hollow metal shell B of radius b.  

What will be the potential of A if it is connected to shell B by a conducting wire?  Show the working. 

• CBSE Class 12 Maths Competency-Based Questions With Answer Key 2024-25: Chapter 1 Relations and Functions
• CBSE Class 12 Biology Competency-Based Questions With Answer Key 2024-25: Chapter 1 Biodiversity And Conservation

Tips To Prepare For Board Exam 

• Create a Study Plan: Making study plan befor exam will beneficial for students. Break your syllabus into small sections as per your comfort level and allocate time for each subject based on its difficulty and your comfort level with it.
• Understand the Syllabus: Make sure you are familiarise your exam syllabus and ensure you cover all topics. Focus on important and high-weightage topics
• Use Quality Study Materials: Rely on NCERT or prescribed textbooks as they are usually the basis for board exams. Use additional reference books and guides for more in-depth understanding if necessary.
• Practice Past Papers: Practice last year board exam sample papers to get a feel for the types of questions asked and the exam format. Take timed mock tests to improve your speed and accuracy.
• Focus on Conceptual Understanding: Ensure you understand the concepts thoroughly rather than just memorising facts.
• Regular Revision: Regularly revise what you've studied to brushup your memory. Make concise notes for quick revision of key points.
• Manage Stress: Practice stress management techniques like deep breathing, meditation, or light exercise. Take regular breaks during study sessions to avoid burnout.
• Stay Positive and Motivated: Set achievable goals and reward yourself for meeting them. Keep a positive mindset and remind yourself of your goals and progress.
• CBSE 2025 Board Exam Dates
• CBSE Class 12 Syllabus 2024-25 (ALL SUBJECT PDFS)
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NCERT Solutions for Class 7 Maths Chapter 15 - Visualising Solid Shapes

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes PDF Download

NCERT Solutions for Class 7 Maths Chapter 15 PDF is available for students on the official website of Vedantu. Chapter 15 of Visualising Solid Shapes for class 7 as per the NCERT syllabus explains the concepts of drawing 3-D figures. It also describes the methods to identify and count vertices, edges, and faces. This is the basic concept of how to visualize solid shapes and how we can use this concept in our day-to-day life. Register Online for NCERT Solutions Class 7 Science tuition on Vedantu.com to score more marks in CBSE board examination. Students can also download NCERT Solution PDF for all subjects to prepare for their forthcoming Exams. We assure you to offer the best assistance and guidance.

Access NCERT Solutions for Class 7 Maths Chapter 15 – Visualising Solid Shapes

1. Identify the nets which can be used to make cubes (cut out copies of the nets and try it): 

Ans: Cube's nets are \[\left( {ii} \right),{\text{ }}\left( {iii} \right),{\text{ }}\left( {iv} \right){\text{ and }}\left( {vi} \right).\]

2. Dice are cubes with dots on each face. Opposite faces of a die always 

have a total of seven dots on them. 

(Image will be uploaded soon)

Here are two nets to make dice (cubes); the numbers inserted in each square indicate 

the number of dots in that box.

Insert suitable numbers in the blanks, remembering that the number on the 

opposite faces should total to \[7.\]

3. Can this be a net for a die? Explain your answer.

Ans: one pair of opposite faces will have \[1{\text{ and }}4\] on them and another pair of opposite faces will have \[3{\text{ and }}6\] on them whose total is not equal to \[7.\]

Therefore, this cannot be a net for a die.

4. Here is an incomplete net for making a cube. Complete it in at least two different 

ways. Remember that a cube has six faces. How many faces are there in the net here? 

(Give two separate diagrams. If you like, you may use a squared sheet for easy 

manipulation.)

Ans: In the given net there are \[3\] faces.

It can be completed as,

5. Match the nets with appropriate solids:

Exercise 15.2

1. Use isometric dot paper and make an isometric sketch for each one of the given 

2. The dimensions of a cuboid are \[5\] cm, \[3\]cm and \[2\] cm. Draw three different isometric 

sketches of this cuboid.

Ans: The dimensions of given cuboid are $5\;{\text{cm}},\,\,3\;{\text{cm}}$ and $2\;{\text{cm}}$  

Three different isometric sketches are,

3. Three cubes each with $2\;{\text{cm}}$ edge are placed side by side to form a cuboid. Sketch an 

oblique or isometric sketch of this cuboid.

Ans: Oblique sketch is,

Isometric sketch is,

4. Make an oblique sketch for each one of the given isometric shapes:

Ans: Oblique sketches are,

5. Give (i) an oblique sketch and (ii) an isometric sketch for each of the following:

(a) A cuboid of dimensions $5\;{\text{cm}},\,\,3\;{\text{cm}}$ and $2\;{\text{cm}}$. (Is your sketch unique?)

         (i) Oblique sketch                 (ii) Isometric sketch

(Images will be uploaded soon)

(b) A cube with an edge $4\;{\text{cm}}$ long.

             (i) Oblique sketch                               (ii) Isometric sketch

(Images will be uploaded soon) 

6. An isometric sheet is attached at the end of the book. You could try to make on it 

some cubes or cuboids of dimensions specified by your friend.

Ans: Cubes and cuboids shapes on isometric sheet is,

Exercise 15.3

1. What cross-sections do you get when you give a:

(i) vertical cut (ii) horizontal cut to the following solids?

(a) A brick

(b) A round apple

(d) A circular pipe

(e) An ice-cream cone.

Exercise 15.4

1. A bulb is kept burning just right above the following solids. Name the shape of the

 shadows obtained in each case. Attempt to give a rough sketch of the shadow. (You

 may try to experiment first and then answer these questions)

2. Here are the shadows of some \[{\text{3 - D}}\] objects, when seen under the lamp of the 

overhead projector. Identify the solid (s) that match each shadow. (There may be 

multiple answers for these!)

3. Examine if the following are true statements: 

(i) The cube can cast a shadow in the shape of a rectangle. 

Ans: The statement is true.

(ii) The cube can cast a shadow in the shape of a hexagon.

Ans: The statement is false.

NCERT Solutions for Class 7 Maths Chapter 15 – Free PDF Download

Class 7 chapter 15 includes:.

Exercise 15.1 Solutions: 5 Questions (2 Short Questions and 3 Long Questions).

Exercise 15.2 Solutions: 5 Questions (1 Short question and 4 Long questions).

Exercise 15.3 Solutions: 1 question (MCQ).

Exercise 15.4 Solutions: 3 questions (1 short question and 2 long questions).

Introduction

Solid Shapes or figures are very common in our surroundings. We come across these solid shapes in the form of laptops, mobile phones, computers, ice-cream cones, tin cans, and so many other things. These solid shapes have length, breadth, and height.

Figures that are drawn on a paper are called plane figures, such as circle, triangle, square, cube, rectangle, etc.

The solid figures that occupy space are spheres, cones, cylinders, cuboids, cubes, etc.

The plane figures are 2-dimensional and solid-shapes are 3-dimensional.

The corners of a solid are called its vertices, the line segments joining its vertices are called its edges, and its surfaces are called faces.

3-D solids can be represented in 2-D  by drawing their oblique sketches or isometric sketches.

A net is a skeleton-outline of a 2-D solid which when folded results in a 3-D shape. A solid can have more than one net.

Different sections of a solid are viewed either by slicing it or by observing its 2-D shadow. It can also be viewed from the front, top, or side.

The following are examples of 2-Dimensional Shapes.

Properties of 2 - Dimensional Shapes

1. A two-dimensional solid has two dimensions length and breadth.

2. The shape of a 2-D solid will always depend on two coordinates.

The following are examples of 3-Dimensional Shapes.

Properties of 3 - Dimensional Shapes

A three-dimensional shape has length, breadth, and height. 

It has depth. 

All things that we see and touch in our environment are three-dimensional solids. 

The inside and outside of a 3-D solid are separated by a surface.

3-D solids have faces, vertices, edges, and volume. This property helps you to differentiate between 2-D and 3-D solids.

Some examples are pyramids, cones, spheres, cylinders, prisms, etc.

Faces, Edges, and Vertices

Face: The flat surface of a solid is called a face.

Edge: A line that joins two corners of a solid is an edge.

Vertices: The corners of a solid are its vertices.

Example: A cube has 8 vertices, 12 edges, and 6 faces.

Formula: If F, E, and V denote the number of faces, edges, and vertices of a cube respectively, then we have:

F – E + V = 2

Description of Some Basic Shapes

Square: It has four sides and four corners. All the sides of a square are of the same length. For example, a sandwich, napkin, chessboard, etc.

Rectangle: A rectangle has four sides and four corners. The opposite sides of a rectangle are of the same length. For example, a table, laptop, mobile phone, etc.

Triangle: A triangle has three sides and three vertices. For example, traffic lights, etc.

Cuboid: A cuboid has six flat surfaces, twelve straight edges, and eight vertices. For example, book, lunch box, cabinet, cubicles, etc.

Cube: A cube has six flat faces, eight vertices, and 12 straight edges. For example, dice, sugar cube, etc.

Cylinder: A cylinder has three faces: 1 curved face and 2 flat faces. It has two curved edges. For example, a gas cylinder, tin-can, pipes, candle, etc.

Cone: A cone has two faces, one slant face, and one flat face. For example, ice-cream cone, funnel, etc.

Solid Shape

A solid can be sketched in two ways.

An oblique sketch is drawn on a squared paper and does not indicate exact measurement but conveys all important aspects of the appearance of the solid.

An isometric sketch is drawn on a 3-D drawing paper and has proportional measurements of the solid.

Note: In the case of an isometric sketch the measurements are exact whereas it is not so for an oblique sketch. 

We can view different sections of a solid in many ways:

When we slice the shape, it results in the cross-section of the solid.

We can observe a 2-D shadow of a 3-D shape.

We can look at the shape from different angles, i.e., the front-view, the side-view, and the top-view.

Description of Some More Solid Shapes

Triangular Prism: A triangular prism resembles a kaleidoscope. It has triangular bases. There are five faces, nine edges, and six vertices in a triangular prism.

Triangular Pyramid: A triangular pyramid is also called a tetrahedron. It has a triangular base. There are four faces, six edges, and four vertices in a triangular pyramid.

Square Pyramid: A square pyramid has a square base. It has five faces, eight edges, and five vertices.

Sphere: A sphere has no flat face. It has only a spherical face. A sphere has one face, no edges, and no vertices.

Polyhedrons

A solid made up of polygon regions is called a polyhedron. For example, cubes, cuboids, prisms, and pyramids are polyhedrons. Please note that spheres, cylinders, and cones are not polyhedrons because they are not made up of polygon regions.

There are two types of polyhedrons: Convex polyhedrons and Regular polyhedrons.

Convex Polyhedrons

When a line segment joining any two points on the surface of a polygon lies inside or on the polygon, the polygon is called a convex polyhedron.

Regular Polyhedrons

Regular polygons whose faces are regular and they meet at each vertex, are called regular polyhedrons.

A prism is a polyhedron shape whose base and top are congruent and the lateral faces are parallelograms.

Types of Prism

Triangular prism

Rectangular prism

Pentagonal prism

Hexagonal prism

Triangular pyramid

Rectangular pyramid

Square pyramid

Pentagonal pyramid

Hexagonal pyramid

Nets for Building a 3 - D Shape

Geometry net is a skeleton-outline of a 2-D solid which when folded results in a 3-D shape. A net can be used in order to find the surface area of an object.

Net is a 2-D representation of a 3-D object that is unfolded along its edges. A three-dimensional shape may have different nets.

Why Should You Use Vedantu’s NCERT Solutions for Class 7 Maths?

Key Features of NCERT Solutions: These solutions are designed to help students achieve proficiency in their studies. They are crafted by experienced educators who excel in teaching Class 7 Maths. Some of the features include:

Comprehensive explanations for each exercise and questions, promoting a deeper understanding of the subject.

Clear and structured presentation for easy comprehension.

Accurate answers aligned with the curriculum, boosting students' confidence in their knowledge.

Visual aids like diagrams and illustrations to simplify complex concepts.

Additional tips and insights to enhance students' performance.

Chapter summaries for quick revision.

Online accessibility and downloadable resources for flexible study and revision.

The NCERT Solutions for Class 7 Maths Chapter 15 - Visualising Solid Shapes, provided by Vedantu, is a valuable tool for Class 7 students. It helps introduce Maths concepts in an accessible manner. The provided solutions and explanations simplify complex ideas, making it easier for Class 7 students to understand the material. By using Vedantu's resources, Students can develop a deeper understanding of NCERT concepts. These solutions are a helpful aid for grade 7 students, empowering them to excel in their studies and develop a genuine appreciation for “ Visualising Solid Shapes ”.

FAQs on NCERT Solutions for Class 7 Maths Chapter 15 - Visualising Solid Shapes

1. How many sums are there in the NCERT Solutions for Class 7 Maths Chapter 15- Visualising Solid Shapes?

There are four exercises in the NCERT Solutions for Class 7 Maths Chapter 15- Visualising Solid Shapes. In the first exercise, Ex.-15.1, there are 5 sums. In the second exercise, Ex.-15.2, there are 6 sums. In the third exercise, Ex.- 15.3, there is 1 sum that will enhance your practical knowledge of solid shapes. In the last exercise, Ex.-15.4 there are 3 sums. Most of the sums in these exercises have sub-questions.

2. Is the Class 7 NCERT Maths Chapter 15- Visualising Solid Shapes difficult to understand?

No, the Class 7 NCERT Maths Chapter 15- Visualising Solid Shapes is not difficult to understand. The basic solid shapes of geometry are explained in this chapter. The concepts of isometric shapes, cubes, cuboids, cylinders, etc are discussed in this chapter. In short, this chapter is an introduction to the basic solid shapes in geometry. So, students will be able to understand the concepts covered in this chapter easily. Also, a thorough revision will enable them to solve all the sums of this chapter correctly, in their examination.

3. Can I get reliable NCERT Solutions for Class 7 Chapter 15- Visualising Solid Shapes online?

Yes, you can get reliable NCERT Solutions for Class 7 Chapter 15- Visualising Solid Shapes on Vedantu. The solutions for this chapter are prepared by the subject matter experts at Vedantu, as per the guidelines of NCERT for Class 7. These NCERT Solutions are among the most reliable study resources available online for Visualising Solid Shapes. So, you can rely on these NCERT Solutions for your exam preparation. Every sum is solved in a stepwise manner to facilitate an easy understanding of all students. You can download the PDF of NCERT Solutions for Class 7 Maths Chapter 15- Visualising Solid Shapes from Vedantu for free, for practicing the sums offline.

4. What is the difference between a cube and a cuboid?

A cube and a cuboid both are solid shapes, that is, both the shapes have three dimensions, length, breadth, and height. For a cube, all the dimensions are of equal length, whereas, for a cuboid, the length, breadth, and height all are of different measures.

5. How is Vedantu Going to Help you Prepare for Your Exams?

Vedantu provides a comprehensive study of NCERT subjects. These studies will clarify all your doubts about the topics and develop your conceptual foundation. These concepts are self-explanatory but you can still approach the team of experts in Vedantu for further understanding.

6. Mention the topics that are covered in NCERT Solutions for Chapter 15 of Class 7 Maths?

Geometry is the study of two-dimensional and three-dimensional forms and objects in our environment, as they all have length, breadth, and height. Chapter 15 of the NCERT Solutions for Class 7 Maths Visualising Solid Shapes begins with an explanation of concepts such as 2D and 3D, as well as why they are referred to by their appropriate names. Diagrams are used to clarify terms such as vertices, edges, and faces.

7. How will this chapter help students in their daily life?

In NCERT Solutions for Chapter 15 of Class 7 Maths, certain activities will help students comprehend three-dimensional space and how objects may be formed in three dimensions. They are instructed to create frames or nets of the desired shapes and then attempt to construct those shapes using the prepared cuttings or frames. This will aid in the development of visualizing abilities required for the exercise questions and this is how this chapter will help students in their daily life.

8. What topics are covered in Chapter 15 of Class 7 Maths?

The NCERT Solutions for Chapter 15 of Class 7 Maths begins with an introduction to forms and objects in 2D and 3D space. The fundamentals of terminology like edges, faces, and vertices of shapes are reviewed in Chapter 15. The concept of perceiving solid objects and how to observe their different sections are described, as well as how to draw solids on a flat surface, oblique sketches, and isometric sketches. The chapter concludes with a discussion of shadow play as a technique of observing three-dimensional objects in two-dimensional space.

9. What are all things students should consider while studying this chapter?

10. List some important facts in Chapter 15 of Class 7 Maths.

Plane and Solid Shapes: Plane shapes have only length and breadth, such as square, rectangle, hexagon, and so on, but solid shapes have height in addition to length and breadth, such as cuboid, cube, sphere, cone, and so on.

2D representation of a 3D solid: This can be accomplished by drawing the solid's image on paper, and there are two methods for doing so. The first is an oblique drawing, and the second is an isometric drawing.

NCERT Solutions for Class 7 Maths

Ncert solutions for class 7.