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NCERT Solutions for Class 6 Maths Chapter 2: Whole Numbers - Exercise 2.3

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NCERT Solutions for Class 6 Maths Chapter 2 (Ex 2.3)

NCERT Solutions for Class 6 Maths Chapter 2 is accessible on Vedantu site in the easiest structure. The entire study material is explained in basic language. You can be certain that the substance observes the definite standards of CBSE guidelines. We have a group of subject matter experts to finetuning the solutions so that you can memorise the chapter perfectly till the examination. You can download the PDF files of Class 6 Maths Chapter 2 Solutions from Vedantu site. Every NCERT Solution is provided to make the study simple and interesting on Vedantu. Subjects like Science, Maths, English,Hindi will become easy to study if you have access to NCERT Solution for Class 6 Science , Maths solutions and solutions of other subjects.


Class:

NCERT Solutions for Class 6

Subject:

Class 6 Maths

Chapter Name:

Chapter 2 - Whole Numbers

Exercise:

Exercise - 2.3

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

Access NCERT Solutions for Class 6 Maths Chapter 2 – Whole Numbers

Exercise – 2.3

1. Which of the following will not represent zero:

(a) $\mathbf{1}+\mathbf{0}$

(b) $\mathbf{0}\times \mathbf{0}$

(c) $\dfrac{\mathbf{0}}{\mathbf{2}}$

(d) $\dfrac{\mathbf{10}-\mathbf{10}}{\mathbf{2}}$

Ans.

Note that, product of two zero is zero, so

$0\times 0=0$.

Zero divided by any nonzero number is zero, so

$\dfrac{0}{2}=0$, and

$\dfrac{10-10}{2}=\dfrac{0}{2}=0$, but

$1+0=1$.

Thus, option (a) is the correct answer.


2. If the product of two whole numbers is zero, can we say that one or both of them will be zero? Justify through examples.

Ans.

Yes, the statement described in the question is appropriate, because if any nonzero number is multiplied by zero, then the resultant product is zero. For example: 

$1\times 0=0,$ $2\times 0=0$, $3\times 0=0$, $10\times 0=0$, etc.

Again, if zero is multiplied by zero, then the resultant product is also zero, that is, $0\times 0=0$.


3. If the product of two whole numbers is $\mathbf{1}$, can we say that one or both of them will be $\mathbf{1}$ ? Justify through examples.

Ans.

No, the statement described in the question is not correct, because if any whole number other than $1$ is multiplied with $1$, then the resultant product cannot be $1$. For example:

$0\times 1=0$, $2\times 1=2$, $3\times 1=3$, $5\times 1=5$.

Now, if $1$ is multiplied by $1$, then the resultant is also $1$, that is $1\times 1=1$.

Thus, if the resultant of the product of two whole numbers is $1$, then both the numbers are needed to be $1$.


4. Find using distributive property :

(i) $\mathbf{728}\times \mathbf{101}$

Ans.

By the distributive property, if $a,b,c$ are three whole numbers, then

$a\times \left( b + c \right)=a\times b+a\times c$.

The given product is

$728\times 101$

$=728\times \left( 100+1 \right)$

$=728\times 100+728\times 1$, using the distributive property.

$=72800+728$, multiplying the numbers.

$=73528$.

(ii) $\mathbf{5437}\times \mathbf{1001}$

Ans.

The given product is

$5437\times 1001$

$=5437\times \left( 1000+1 \right)$

$=5437\times 1000+5437\times 1$, using the distributive property.

$=5437000+5437$, multiplying the numbers.

$=5442437$.

(iii) $\mathbf{824}\times \mathbf{25}$

Ans.

The given product is

$824\times 25$

$=824\times \left( 20+5 \right)$

$=824\times 20+824\times 5$, using the distributive property.

$=16480+4120$, multiplying the numbers.

$=20600$.

(iv) $\mathbf{4275}\times \mathbf{125}$

Ans.

The given product is

$4275\times 125$

$=4275\times \left( 100+20+5 \right)$,

$=4275\times 100+4275\times 20+4275\times 5$, using the distributive property.

$=427500+85500+21375$, multiplying the numbers.

$=534375$.

(v) $\mathbf{504}\times \mathbf{35}$

Ans.

The given product is

$504\times 35$

$=\left( 500+4 \right)\times 35$

$=500\times 35+4\times 35$, applying the distributive property.

$=17500+140$, multiplying the numbers.

$=17640$.


5. Study the pattern :

$\mathbf{1\times 8+1=9}$;                      $\mathbf{12}\times \mathbf{8}+\mathbf{2}=\mathbf{98}$;                 $\mathbf{123}\times \mathbf{8}+\mathbf{3}=\mathbf{987}$;

$\mathbf{1234}\times \mathbf{8}+\mathbf{4}=\mathbf{9876}$;          $\mathbf{12345\times 8+5=98765}$        

Write the next two steps. Can you say how the pattern works? (Hint: $\mathbf{12345=11111+1111+111+11+1}$).

Ans.

The next two steps will be

$123456\times 8+6=987654$;

$1234567\times 8+7=9876543$.

The pattern described in the question will be like the following way:

 $ \left( 1 \right)\times 8+1=9 $

 $ \left( 12 \right)\times 8+2=\left( 11+1 \right)\times 8+2=98 $

 $ \left( 123 \right)\times 8+3=\left( 111+11+1 \right)\times 8+3=987 $

$ \left( 1234 \right)\times 8+4=\left( 1111+111+11+1 \right)\times 8+4=9876 $

$ \left( 12345 \right)\times 8+5=\left( 11111+1111+111+11+1 \right)\times 8+5=98765 $

 $ \left( 123456 \right)\times 8+6=\left( 111111+11111+1111+111+11+1 \right)\times 8+6=987654 $

  $\left(1234567\right)\times8+7=\left(1111111+111111+11111+1111+111+11+1 \right)\times 8+7=9876543 $


Class 6 Maths Exercise 2.3

Vedantu Class 6 NCERT solutions are ideal for students who are looking for question wise solutions for Integers. Our solutions are ideal for last-minute revisions before examinations to ensure a detailed knowledge of the chapter. The ease of usage and download has proved us to be a better student-related guide. With our app easily available from play store, many students now prefer our solutions as their study partner. 


Maths Chapter 2 Whole Numbers:

The numbers like 1,2,3 etc are known as natural numbers. If zero is included with these, they become whole numbers. 


So now the whole numbers are natural numbers along with zero.


If you add 1 to a whole number, the solution becomes a successor. Similarly, if you remove 1 from a whole number, you get a predecessor. 


Example 16 + 1= 17 is successor 

16 - 1= 15 is a predecessor 


Earlier in natural numbers that starts from 1, the number 1 had no predecessor, so including zero as the predecessor of 1 we get whole numbers. 


Similarly, if you include negative and positive numbers along with zero are known as integers. 


Representation of Whole Numbers on a Number Line

The numbers are represented on a number line with zero at the start. The distance between numbers zero and 1 is called unit distance. 


Order of Numbers 

The numbers towards the right are greater numbers. Whereas the numbers towards the left are smaller numbers. 


8>4. 


8 is towards right and 4 is placed towards left on the number line. 


Addition on the Number Line

For addition of numbers on the number line, we need to move the indicated steps towards right. 


Example if we have to add 3 to 7, we shift 3 places towards right from 7.


Subtraction on the Number Line 

Similarly, for subtraction of numbers on the number line, we need to move the indicated steps towards the left. 


Example if we have to subtract 3 from 7, we shift 3 places towards left from 7.


Multiplication on the Number Line

Now for multiplication we need to move the same number of steps, for the indicated number of times starting from zero.


Example 4 ☓ 3


Starting from zero we shift 3 units at the same time 4 times. Now we will reach 12.


This is how multiplication can be done on the number line. 


Exercise 2.1 has questions based on the above explanation. For the solutions, refer to our pdf for Whole numbers. 


Properties of Whole Numbers 

While numbers are closed under addition as well as under multiplication. 


That is the product of addition or multiplication of a whole number is also a whole number.


In other words, there is a commutative property. 


Patterns in Whole Numbers

The numbers can be arranged in a particular sequence that forms a square or rectangular shape. 


Exercise 2.2 deals with such questions. Solutions to these questions are available in our NCERT solutions for Class 6.


The Role of Zero

Zero when added to any whole numbers, the result is the same number. 


Similarly, zero when multiplied by any number results in zero. This is the special property of zero.


Exercise 2.3 is based on the properties discussed above. The solutions of all the 5 questions inscribed in the NCERT textbook of Class 6 can be available in our pdf solutions. 


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FAQs on NCERT Solutions for Class 6 Maths Chapter 2: Whole Numbers - Exercise 2.3

1. If the product of two numbers is zero, then one or both of the numbers are 0. Is the statement appropriate?

Yes, the statement described in the question is appropriate because if any non-zero number is multiplied by zero, the resultant product is 0. For instance 


1×0=0, 2×0=0, 3×0=0, 4×0=0, 10×0=0, etc.


Again, if zero is multiplied by zero, the resultant product is also zero, i.e.


0×0=0

2. If the product of two whole numbers is 1, then one or both of the numbers are 1. Is this statement correct and justified by some illustrations?

No, the statement describing the question is not right, because if any whole number other than one is multiplied by one, then the consequently produced number cannot be one. For instance


0×1=0, 2×1=2, 3×1=3, 5×1=5


If one is multiplied by one, then the result is also one, so 1 X 1 is equal to 1. Hence, if the consequence of the product of two whole numbers is one, then both numbers are needed to be

3. Compute the values of 728 x 101 by using the distributive property.

a(bc)=ab+ac. (By the distributive property, if a, b, and c are 3 whole numbers, then


The given product is


728×101


=728×(100+1)


= 728×100+728×1


=72800+728


=73528.


For the best answer, you may download the pdf from the Vedantu.com website.

4. Which website will be helpful for finding NCERT solutions for class 6 math, chapter 2, whole number exercise 2.3?

There are many websites where you can find NCERT solutions for class 6 math, chapter 2, and whole number exercise 2.3, but according to me, the answer is available on the best website that provides the best study material for all subjects. It explains the question in detail and helps students understand it easily. For the best answer, you may download the pdf from the Vedantu.com website.

5. What is the importance of the syllabus?

The syllabus is very essential, as it works as a skeleton and gives a framework to both the pupils and the teachers. It also helps the student develop effective learning strategies. Besides this, it also helps the teachers organize their upcoming classes and plan accordingly. For the best answer, you may download the pdf from the Vedantu.com website.