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NCERT Solutions for Class 6 Maths Chapter 1: Knowing our Numbers - Exercise 1.2

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NCERT Solutions for Class 6 Maths Chapter 1 (Ex 1.2)

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Class:

NCERT Solutions for Class 6

Subject:

Class 6 Maths

Chapter Name:

Chapter 1 - Knowing Our Numbers

Exercise:

Exercise - 1.2

Content-Type:

Text, Videos, Images and PDF Format

Academic Year:

2023-24

Medium:

English and Hindi

Available Materials:

  • Chapter Wise

  • Exercise Wise

Other Materials

  • Important Questions

  • Revision Notes



Important Topics under NCERT Solutions for Class 6 Math Chapter 1 Knowing our Numbers (Ex 1.2) Exercise 1.2

NCERT Class 6 Math Chapter 1 is Knowing Your Numbers. It is one of the fundamental chapters that is covered in Class 6 and is divided into 9 major topics. Students are advised to learn from and practice the solved questions time and again to be able to get a good grasp on numbers and their uses. 


The following is a list of the important topics that have been covered in the chapter on Knowing Your Numbers. We recommend that students go through each topic very carefully to be able to understand the concepts clearly and be able to score well in exams. 

  • Introduction

  • Comparing Numbers

  • How Many Numbers Can You Make?

  • Shifting Digits

  • Introducing 10000

  • Revisiting Place Value

  • Introducing 100000

  • Large Numbers

  • Large Numbers in Practice

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

Exercise: 1.2

1. 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.

Ans: Tickets sold on first day \[ = 1094\] 

Tickets sold on second day \[ = 1812\] 

Tickets sold on third day \[ = 2050\] 

Tickets sold on fourth day \[ = 2751\]

Total tickets sold \[ = 1094 + 1812 + 2050 + 2751\]\[ = 7707\]


2. Shekhar is a famous cricket player. He has so far scored \[6980\] runs in test matches. He wishes to complete \[10000\] runs. How many more runs does he need?

Ans: Number of runs scored by Shekhar \[ = 6980\]

Total number of runs he needs \[ = 10000 - 6980 = 3020\].


3. 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?

Ans: Successful candidate secured votes \[ = {\text{ }}5,77,500\]

Rival candidate secured votes \[ = {\text{  }}3,48,700\] 

Margin of votes \[ = {\text{ }}5,77,500{\text{ }}--{\text{ }}3,48,700{\text{ }} = {\text{ }}2,28,800\]


4. Kirti Bookstore sold books worth \[2,85,891\] in the first week of June and books worth ` \[4,00,768\] in the second week o the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?

Ans: Books sold in week one \[ = {\text{ }}2,85,891\]
Books sold in week second \[ = {\text{ }}4,00,768\]
Total sale \[ = {\text{ }}4,00,768{\text{ }} + {\text{ }}2,85,891{\text{ }} = 6,86,659\]

Clearly, second week sale is more than the first week sale

Difference\[\; = {\text{ }}4,00,768{\text{ }}--{\text{ }}2,85,891{\text{ }} = {\text{ }}1,14,877\]

5. Find the difference between the greatest and the least number that can be written using the digits \[{\mathbf{6}},{\text{ }}{\mathbf{2}},{\text{ }}{\mathbf{7}},{\text{ }}{\mathbf{4}},{\text{ }}{\mathbf{3}}\] each only once.

Ans: Largest five digit number \[ = {\text{ }}76432\]
Smallest five-digit number \[ = 23467{\text{ }}\]
Therefore, the difference between then \[ = {\text{ }}76432{\text{ }}--{\text{ }}23467{\text{ }} = {\text{ }}52965\]

6. A machine, on an average, manufactures \[2,825\] screws a day. How many screws did it produce in the month of January \[2006?\]
Ans: Screws produced in one day \[ = 2,825\] 

Total Screws produced in \[31\] days \[ = 2,825{\text{ }} \times 31{\text{ }} = {\text{ }}87,575\]

Hence, the machine produced \[87,575\] screws in month of January


7. A merchant had \[Rs.{\text{ }}78,592\] with her. She placed an order for purchasing \[40\] radio sets at \[Rs.1200\]each. How much money will remain with her after the purchase?

Ans: Total money merchant had \[ = {\text{ }}Rs.{\text{ }}78,592\]
Cost of one radio \[ = Rs.1200\] 

Cost of \[40\] radios \[ = {\text{ }}1200{\text{ }} \times {\text{ }}40{\text{ }} = {\text{ }}Rs.{\text{ }}48,000\]

Money left \[ = {\text{ }}78,592{\text{ }}--{\text{ }}48,000{\text{ }} = {\text{ }}30,592\]


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

Ans: Wrong answer = 7236 x 65 = 470340

Correct answer = 7236 x 56 = 405216
Difference in answers = 470340 – 405216 = 65,124

9. To stitch a shirt \[{\mathbf{2}}{\text{ }}{\mathbf{m}}{\text{ }}{\mathbf{15}}{\text{ }}{\mathbf{cm}}\] cloth is needed. Out of \[{\mathbf{40}}{\text{ }}{\mathbf{m}}\] cloth, how many shirts can be stitched and how much cloth will remain?

Ans: Cloth required for stitch one shirt $=2 \mathrm{~m} 15    \mathrm{~cm}$       

$=2 \times 100 \mathrm{~cm}+15 \mathrm{~cm}$

$=215 \mathrm{~cm}$

Total length of cloth $=40 \mathrm{~m}=40 \times 100 \mathrm{~cm}=4000 \mathrm{~cm}$

Number of shirts that can be stitched

$\quad \,18$

$215{\overline{)\,\,{4000}\quad\quad}}$

$\quad\underline{\,-125\,\,}  $

$\quad{\,\, 1850 \,\,}$ 

$\quad\underline{\,\,-1720\,\,}$

$\quad \underline{\quad 130\,\,}$

Hence, 18 shirts can be stitched and $130 \mathrm{~cm}(1 \mathrm{~m} 30 \mathrm{~cm})$ cloth will be left.


10. Medicine is packed in boxes, each weighing \[4{\text{ }}kg{\text{ }}500{\text{ }}g\]. How many such boxes can be loaded in a can which cannot carry beyond \[800kg\]?

Ans:Weight of a box \[ = {\text{ }}4{\text{ }}kg{\text{ }}500{\text{ }}g{\text{ }} = {\text{ }}4500{\text{ }}g\]

Number of boxes = 

$\quad \,177$

$4500{\overline{)\,\,{800000}\quad\quad}}$

$\quad\underline{\,-4500\,\,}  $

$\quad{\,\, 35000 \,\,}$ 

$\quad\underline{\,\,-31500\,\,}$

$\quad \underline{\quad 3500\,\,}$

 Hence, \[177\] boxes can be loaded in the Van


11. The distance between the school and the house of a student’s house is\[{\mathbf{1}}{\text{ }}{\mathbf{km}}{\text{ }}{\mathbf{875}}{\text{ }}{\mathbf{m}}\]. Everyday she walks both ways. Find the total distance covered by her in six days.

Ans: Distance between school and her house \[ = {\text{ }}1875\]

Total distance covered \[ = {\text{ }}2{\text{ }} \times {\text{ }}1875{\text{ }} = {\text{ }}3750\]

Distance covered in \[6\] days \[ = {\text{ }}6{\text{ }} \times {\text{ }}3750{\text{ }} = {\text{ }}22500\] m

Thus, she covers \[22{\text{ }}km{\text{ }}500{\text{ }}m\] distance in \[6\] days

12. A vessel has \[4{\text{ }}liters{\text{ }}500{\text{ }}ml\] of curd. In how many glasses each of \[25{\text{ }}ml\] capacity, can it be filled?

Ans:Capacity of vessel $=4$ liters $500 \mathrm{ml}=4500 \mathrm{ml}$    

Capacity of a glass $=25 \mathrm{ml}$

Number of glasses can be filled

$\quad \,180$

$25{\overline{)\,\,{4500}\quad\quad}}$

$\quad\underline{\,-25\,\,}  $

$\quad{\,\, 200 \,\,}$ 

$\quad\underline{\,\,200\,\,}$

$\quad \underline{\quad 0\,\,}$

Therefore, 180 glasses are required.


NCERT Class 6 Maths Chapter 1 – Exercise 1.2

Chapters 1 - Knowing Our Numbers

Maths Class 6-Chapters 1 exercise 1.2 Solutions teaches about the following topics:

  1. Introduction

  2. Comparing number 

  3. How many numbers can you make?

  4. Shifting digits

  5. Introducing 10,000

  6. Revisiting place value

  7. Introducing 100000

  8. Larger numbers

  9. An aid in reading and writing large numbers

  10. Large Numbers in Practice


Introduction

Understanding the concept of numbers is the most crucial part of laying a strong foundation for the enormous subject of mathematics. This Chapters of Class 6 Maths exercise 1.2 tells of a time when there were very few numbers known to mankind and makes the student understand the history of the creation of numbers. Class 6 Maths Chapters 1 explains to the student that the task was a tough one, and the people struggled on the way but were only possible collective efforts of everybody across the world.


This Chapters also reflects upon factors leading to the development of mathematics as a whole for the development of the society demanded more complex mathematics Solutions. From this section, the students get an overview of what they will be studying in this Chapter. They will also learn about subtractions, additions, divisions, and multiplications at a high level. Students can learn about number sequences and patterns when they are studying this Chapter. Whenever they are given a collection of objects or numbers that are bigger, they will have to arrange it in ascending or descending order. The students will have to learn about this by studying the Chapters thoroughly.


Comparing Number 

Class 6 Maths Chapters 1 exercise 1.2 in this segment teaches the students to understand and calculate the values of numbers to learn how to compare two sets of numbers or more and understand various aspects of comparisons such as the higher number or, the smaller number. It teaches the student to simple tricks to understanding very quickly, such as counting and calculating whether the number is in the tens, hundreds, thousands, or its multiples. This Chapters further teaches how to compare numbers when the number of digits is the same. 

 

Comparing numbers is a difficult task for all the students who are learning about this for the first time. Therefore, they need to go through the section carefully. It might be tough for you in the initial stages; however, as you keep practicing, it becomes easier for you to find numbers and compare them as asked in the questions. The students will also learn more about the digits and comparing the digits when they are present in the hundreds or thousands of places. You can also play with your friends and learn from the game of comparing numbers, understanding which one is the smallest and largest number in a given equation.


Exercise 1.2 

Once you have studied the sections, you will be assessed and will be asked to answer 12 questions correctly. Based on your understanding, you will have to solve the problems. Therefore, you need to go through the sections mentioned above so that you can answer these questions correctly and get good scores. Also, there will be some questions asked in the section ‘International System of Numeration’ that is mentioned in the Chapters. Students need to learn everything before solving these questions.


How Many Numbers Can You Make?

This part of the Chapters from ex 1.2 Class 6 teaches the student the most important things, which are the formation of numbers. It shows the students to make new numbers when they are provided with a set of different units of numbers. It makes the students understand how using various techniques and protocols like using an ascending or descending order for the creation of new numbers; they can make the greatest or the smallest numbers using the same set of units.


In the Chapters, you will also come across a ‘Try These’ sections that will help you in assessing the things that you would have understood from the sections described above. You can solve these try these questions and get an idea about what you have learned is correct or not. The best part of these questions that it has a hint that will help you in solving the answers correctly as you are learning this Chapter for the first time. 


Many questions are asked from this section as it includes writing down the procedure and understanding the arrangement of the digits. Therefore, you must read through the section carefully, understand the concept, and then solve the questions thoroughly. You will also come across a section that has an example of standing in proper order and finding who’s the tallest or shortest amongst the children. In this section, you will learn to identify the height of the children and sort it out based on your understanding, who’s the tallest and the shortest amongst all.


The section will also teach you about ascending order and descending order by making you learn about the definitions and concepts behind it.


Shifting Digits

This part of Chapters exercise 1.2 Class 6 Maths gives an essential aspect of numbers to the students. It talks about what happens when you take a unit of number and play with the position of the groups in that number. This Chapter makes you learn a variety of ways of creating new numbers by various methods, such as shifting the individual units of numbers in the given set. This section makes the student understand new protocols of creating a number by techniques such as changing the positions of the individual units in ascending ways or descending way. 

 

When the students are learning this section, they will learn to determine and compare the numbers in the form of ascending and descending order. Also, they will learn about exchanging the numbers correctly so that they can find out the right numbers that are required. Make sure that you go through the section carefully; otherwise, it will be difficult for you to solve the questions asked in the examinations related to this field.


Introducing 10,000

This Chapters of Class 6 ex 1.2 makes the crucial breakthrough of teaching students about more significant numbers. Whatever the student may spire to grow up and become, there would be several things that the student should have an aptitude for is such as accounting, especially personal accounting. If the student would become a man of business, his concept of the higher number, especially numbers greater than 10000, is essential for his success.

 

In this section, students are required to learn addition or multiplication that comes after 99. They will be introduced not only to the numbers that are greater 10000 but also will learn how to reach that number when they are asked to equate smaller numbers. Therefore, keeping their concept when reading this Chapter becomes essential for the students to a certain extent.


Revisiting Place Value

This chapter takes us back to the part where the students were taught about pace value. That time the students were primarily working with two digits. With the recent development in the lessons, now this Chapter aims to make the student learn the concepts of place value surrounding a greater number of digits. 


The students will learn more about one’s place, ten’s place, a hundred’s place, thousand’s place, and ten thousand’s place in this section. This will help them in building their foundation so that they can quickly grasp that is being taught to them as they move forward to the upper classes in the future.


Introducing 100000

After teaching making the students revise the lessons on place value and utilizing that knowledge to create greater numbers. This section of Class 6 exercise 1.2 teaches the students, even more, greater numbers. With the place value, it explains to the students how the number 1,00,000 can be achieved.


Larger Numbers

Once the students understand the concepts and techniques of place value to make such numbers, these Chapters enable the student to run free and creates a greater number. This segment is crucial because it helps students with the essential understanding of Maths, which he will use when he grows up. An aid in reading and writing large numbers.


This art of the Chapters advises students on protocols to make reading and writing numbers more transparent. It makes the student learn that the use of commas can be of great help, especially when writing large numbers. If the numbers are large enough to be in crores or even more or even less, suing a comma is a great help to distinguish the value of the number.


Large Numbers in Practice

In this section, you will learn about measuring the length, thickness, and height of any object that is given to you. You will carefully read and understand the question that is related to large numbers before answering them.


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