CBSE Class 6 Maths Chapter 2 Important Questions with Solutions - Whole Numbers

Chapter 2 - Whole Numbers of Class 6 Maths is an important one as it forms the base of students for higher concepts of Maths. Therefore, students should know what they’ll be learning in the chapter before solving the questions. So, here are the important topics included in Chapter 2 of Class 6 Maths.

1. Introduction to Predecessor and successor

2. Whole Numbers

3. The Number Line

• Addition on the number line

• Subtraction on the number line 

• Multiplication on the number line

4. Properties of Whole Numbers

• Closure

• Commutative

• Associative

• Distributive

5. Patterns in Whole Numbers

• Patterns Observation

Study Important Questions for Class 6 Maths Chapter 2 – Whole Numbers

Questions:                                                                                   (1 Mark)

1. Write the successor and predecessor of \[\mathrm{2006399}\]

Ans: Successor

\[2006399+1=2006400\].

Predecessor

\[2006399-1=2006398\].

2. Zero is the smallest natural number say True or False

Ans: False, 0 is not a natural number it’s a whole number.

3. The smallest whole number is 

Ans: The smallest whole number is 0.

4. The smallest even whole number is 

(a) 0

(b) 2

(c) 4

(d) None

Ans: (a) 0

5. Division by ___ is not defined.

Ans: Division by zero is not defined.

6. Commutative and associative property hold good only for subtraction and division only. Say true/ false

Ans: False, its hold good only for addition and multiplication.

7. The additive identity is _____ ?

Ans: The additive identity is 0.

8. The multiplicative identity is ______?

Ans: The multiplicative identity is 1.

9. Fill up the blanks: \[\mathrm{a }\!\!\times\!\!\text{ =0 }\!\!\times\!\!\text{ =0}\]

Ans: \[a\times 0=0\times a=0\].

10. \[\mathrm{a+(b+c)}\ne \left( \mathrm{a+b} \right)\mathrm{+c}\] say true or false?

Ans: False, as the above statement is associative property for addition.

Questions:                                                                                                                (2 Mark)

1. Find the sum of \[\mathrm{745, 387, and 613}\].

Ans:

\[\begin{align} & 745 \ + \ 387 \ + \ 613 \ = \ 745 \ + \ 1000 \\ & 745 \ + \ 387 \ + \ 613 \ = \ 1745 \\ \end{align}\] (By using associative property)

2. Add and subtract the below numbers on number line \[\mathrm{5 and 3}\].

Ans: Addition on Number line \[=5+3=8\].

(Image will be uploaded soon)

Subtraction on Number line \[=5-3=2\].

(Image will be uploaded soon)

3. Multiply using number line \[\mathrm{4 }\!\!\times\!\!\text{ 3}\]

Ans: Multiplication on number line \[4\times 3=12\].

(Image will be uploaded soon)

Questions: (3 Mark)

1. Find the sum by suitable rearrangement: \[\mathrm{2852 + 553 + 2648 + 647}\]

Ans: 

\[\begin{align} & 2852+553+2648+647=553+647+2648+647 \\ & 2852+553+2648+647=1200+550\:\:\left( By\text{ }associative\text{ }property \right) \\ & 2852+553+2648+647=6700 \\ \end{align}\]

2. Find the product \[\mathrm{885 }\!\!\times\!\!\text{ 94}\]

Ans:

\[\begin{align} & 885\times 94=885\times \left( 100-6 \right)\:\left ( By\text{ }distributive\text{ }property\text{ }over\text{ }subtractive,\text{ }multiplicative \right) \\ & 885\times 94=885\times 100-885\times 6 \\ & 885\times 94=88500-5310 \\ & 885\times 94=83190 \\ \end{align}\]

3. Find the value of \[\mathrm{768 }\!\!\times\!\!\text{ 73+768 }\!\!\times\!\!\text{ 27}\]

Ans: \[768\times 73+768\times 27\] The above property looks similar to \[a\times b+a\times c\] which distributive property of multiplication after addition hence, \[a\times b+a\times c=a\left( b+c \right)\]. \[\begin{align} & 768\times 73+768\times 27=768\left( 73+27 \right). \\ & 768\times 73+768\times 27=768\times 100. \\ & 768\times 73+768\times 27=76800. \\ \end{align}\]

4. Find the value of \[\mathrm{1123 }\!\!\times\!\!\text{ 648+1123 }\!\!\times\!\!\text{ 122+1123 }\!\!\times\!\!\text{ 230}\]

Ans: By using distributive property of multiplication over addition, \[a\times b+a\times c=a\left( b+c \right)\]

\[\begin{align} & 1123\times 648+1123\times 122+1123\times 230=1123\left( 648+122+230 \right). \\ & 1123\times 648+1123\times 122+1123\times 230=1123\left( 1000 \right). \\ & 1123\times 648+1123\times 122+1123\times 230=1123000. \\ \end{align}\]

5. Find the product of \[\mathrm{4 }\!\!\times\!\!\text{ 250 }\!\!\times\!\!\text{ 3890}\]

Ans:

\[\begin{align} & 4\times 250\times 3890=1000\times 3860\left( By\text{ grouping} \right) \\ & 4\times 250\times 3890=3860000 \\ \end{align}\]

6. Find the product of \[\mathrm{3568 }\!\!\times\!\!\text{ 99}\]

Ans: We know that\[a\times b+a\times c=a\left( b+c \right)\]

\[\begin{align} & 3568\times 99=3568\times \left( 100-1 \right)\:\text{(By using distribution property of multiplication over subtraction)}. \\ & 3568\times 99=3568\times 100-3568\times 1. \\ & 3568\times 99=353232. \\ \end{align}\]

7. Find the number which when divided by \[\mathbf{53}\]gives \[\mathbf{8}\]as a quotient and \[\mathbf{4}\]as a remainder

Ans: Given divisor \[=53\], quotient \[=8\], Remainder \[=4\]

By division algorithm,

\[Dividend\text{ }=\text{ }(divisor\text{ }\times quotient)\text{ }+\text{ }\operatorname{Re}mainder\] \[\begin{align} & =\left( 53\times 8 \right)+4 \\ & =424+4 \\ & \text{Required number}=428 \\ \end{align}\]

Questions:                                                                                                     (5 Mark)

1. Find the product of largest \[\mathbf{4}\] digit number and largest \[\mathbf{3}\] digit number using distributive law.

Ans: Largest \[4\] digit number \[=9999\]

Largest \[3\] digit number \[=999\]

We know that distractive law,

\[\begin{align} & a\left( b+c \right)=a\times b+a\times c\ldots (i) \\ & a\left( b-c \right)=a\times b-a\times c\ldots (ii) \\ \end{align}\]

Product of largest \[4\] digit number and largest \[3\] digit number,

\[9999\times 999\]

Using (ii), we can write as \[9999\times \left( 1000-1 \right)\]

\[\begin{align} & 9999\times \left( 1000-1 \right)=9999\times 1000-9999\times 1 \\ & 9999\times \left( 1000-1 \right)=9999000-9999 \\ & 9999\times \left( 1000-1 \right)=9,989,001 \\ \end{align}\]

2. Show that \[\mathrm{36 }\!\!\times\!\!\text{ }\left( \mathrm{10 }\!\!\times\!\!\text{ 20} \right)\mathrm{=}\left( \mathrm{36 }\!\!\times\!\!\text{ 10} \right)\mathrm{ }\!\!\times\!\!\text{ 20}\]

Ans: \[36\times \left( 10\times 20 \right)=\left( 36\times 10 \right)\times 20\ldots (1)\]

LHS of equation (1), \[36\times \left( 10\times 20 \right)\]

\[=36\times 200=6400\ldots \ldots (2)\]

RHS of equation (1), \[\left( 36\times 10 \right)\times 20\]

\[=360\times 20=6400\ldots \ldots (3)\]

From (2) and (3), LHS = RHS

Hence, \[36\times \left( 10\times 20 \right)=\left( 36\times 10 \right)\times 20\].

Important Questions on Whole Numbers for Class 6- Free PDF Download

Whole Numbers is a chapter that deals with both theoretical and practical aspects. This chapter presents the definition, properties, numerical, and diagrammatic representations which may be difficult for students to comprehend. Lack of a well-structured course plan, regular practice, and a solid course curriculum may barricade students, preventing you from securing good marks.

To get a thorough comprehension of all the formulas, theories, concepts, and topics under the chapter-Whole Numbers, students must indulge in continuous practice curated by a well structured and formatted approach. This will help you improve your knowledge of the concepts and topics and be efficient during the preparation or revision process. 

Students must implement the crucial questions to strengthen and better your preparation or revision process in their preparation schedule. Students can download the Important Questions For Class 6 Maths Chapter 2 PDF for free and achieve their study objectives. 

Class 6 Whole Numbers Important Questions

Class 6 Maths Chapter 2 Important Questions will help students gain a comprehensive understanding and acquire fundamentals of the formulas, concepts, topics, and theories under the chapter- Whole Numbers. Regular and continuous practice of the essential questions on class 6 Mathematics Chapter 2 will help you solve the numerical, identify the true and false statements, and fill the missing blanks. A comprehensive brief of the chapter for students to understand and acquire are as follows:

Whole Numbers

The numbers that start from one and go on as 1,2, 3,4,5... are called natural numbers or counting numbers. The number group that adds a zero to the collection of natural numbers and goes on as 0,1,2,3,4, 5… are called Whole Numbers. Whole numbers consist of zero and natural numbers, and except zero all the whole numbers are composed of natural numbers. 

Facts About Whole Numbers

• The number zero is the first and the smallest whole number.

• All the natural numbers are also whole numbers.

• The smallest natural number is one.

• All whole numbers are not natural numbers. For instance, zero is a whole number but is not considered as a natural number.

• There are several infinite or uncountable numbers of whole numbers.

Properties of Whole Numbers

Closure Property

• Closure property can be applicable on the addition for Whole Numbers. For instance, 0 + 2 = 2; so Whole Numbers are closed on addition.

• Closure property can be applicable on the multiplication for the Whole Number. For instance, 0 x 2 = 0; so Whole Numbers are closed on multiplication.

• Closure property can be applicable on the subtraction of the Whole Number. For instance, 5 - 0 = 5; so Whole Numbers are not closed on subtraction.

• Closure property can apply to the division of the Whole Number. For instance, 2/1 = 2; however, division by zero is undefined. So, Whole Numbers are not closed on division.

Commutative Property

• Commutative property can be applicable on the addition for Whole Numbers. For instance, 0 + 2 = 2 = 0 = 2; so Whole Numbers are commutative on addition.

• Commutative property can be applicable to the multiplication of Whole Numbers. For instance, 0 x 2 = 0 or 2 x 0 = 0; so Whole Numbers are commutative on multiplication.

• Commutative property can be applied to the subtraction of the Whole Number. For instance, 5 - 0 = 5 but 0 - 5 = ?; so Whole Numbers are not commutative on subtraction.

• Commutative property can be applied to the division of the Whole Number. For instance, 4/1 = 4 but 1/4 = ?; so Whole Numbers are not commutative on division. 

Associative Property

• Associativity property can be applicable on the addition for Whole Numbers. For instance, 0 + (2 + 3) = (0 + 2) + 3 = 5; so Whole Numbers are associative on addition.

• Associativity property can be applicable on the multiplication for Whole Number. For instance, 0 x (2 x 3) = 0 or (0 x 2) x 3 = 0; so Whole Numbers are associative on multiplication.

• Associativity property can be applied to the subtraction of the Whole Number. For instance, 10 - (2 - 1) = 9 but (10 - 2) - 1 = 7; so Whole Numbers are not associative on subtraction.

• Associativity property can be applied to the division of the Whole Number. For instance, 16 ÷ (4 ÷ 2) = 8 but (16 ÷ 4) ÷ 2 = 2; so Whole Numbers are not associative on division. 

Distributive Property

If p, q, and r are any two whole numbers, then p (q + r) = p x  q + p x  r

Additive Identity

If p is any whole number, then p + 0 = p = 0 + p

Example: 2 + 0 = 2

Multiplication Identity

If p is any whole number, then p x 1 = p = 1 x p

Example: 1 x 1 = 1

Multiplication By Zero

If p is any whole number, then p x 0 = 0 = 0 x p

Example: 1 x 0 = 0

Division By Zero

If p is any whole number, then p ÷ 0 = not defined

Important Questions for Class 6 Maths Chapter 2

To get a better review of the Important Questions of Mathematics Class 6 Chapter 2- Whole Numbers, we have enumerated a few potential questions that are most likely to appear in the annual examination:

1. State whether the statement is True or False- Zero is the smallest natural number

2. Fill in the blanks- Division by _____ is not defined

3. Find the summation of 613, 745, and 387

4. Find the product of 995 multiplied by 94

5. State whether the statement is True or False- Associative and commutative property holds good only for division and subtraction

6. Complete the sentence- The smallest whole number is _____

7. Write the predecessor and successor for the number- 2006399

8. Using the properties, find the values of the equation- 8165 multiplied by 169 subtracted by 8165 multiplied by 69 (8165 x 169 – 8165 x 69)

9. Enlist any three whole numbers that can be arranged as perfect squares

10. Using distributive property, solve the equation- 1123 multiplied by 648 added to 1123 multiplied by 122 added to 1123 multiplied by 230 (1123 x 648 + 1123 x 122 + 1123 x 230)

Benefits of Class 6 Maths Chapter 2 Important Questions

The Important Questions on Whole Numbers help students secure a good average with a thorough understanding of the chapter's fundamentals. With elementary knowledge on the topics, concepts, formulas, and theories, you can secure a better percentage in your tests or annual examinations with regular practice. A few benefits of the Important Questions for Class 6 Mathematics Chapter 2 are as follows:

• Class 6 Mathematics Chapter 2 helps students manage time efficiently through the rapid assessment of the mathematical numerical, thus honing and improving their problem-solving skills.

• Class 6 Whole Numbers Important Questions will be different from that of the Textbooks to help students overcome the challenges, boost confidence level during examinations, and make self-assessment better.

• Mathematics Chapter 2 for class 6 is an introductory chapter that will help students get a brief comprehension and elementary knowledge of the subject matter and clear your doubts about all sorts.

• Students will be able to face the biggest hurdle of managing their solving time. The continuous practice will help you develop a strategy to tackle and solve the numerical and question is a constraint period.

• The Class 6 Chapter 2 Mathematics Important Questions are curated by Vedantu experts with thorough research and knowledge, keeping in mind the highest probability of its chance in the annual examination.

Key Features of Vedantu’s Important Questions for CBSE Class 6 Maths Chapter 2

Chapter 2 Whole Numbers Important Questions free PDF by Vedantu is very beneficial for the students because:

• The questions are framed and selected by Maths experts and proficient academicians. 

• They are designed in an easy-to-understand format with step-by-step detailed solutions to all the questions.

• These important questions are provided in PDF format, allowing the students to download and access them anytime and anywhere. 

• Along with important questions, we have also provided a brief summary of all the formulas and concepts included in the chapter to ensure students get all the information required for preparing this chapter.

Important Related Links for CBSE Class 6 Maths 

Conclusion

Vedantu's CBSE Class 6 Maths Chapter 2 Important Questions with Solutions is a valuable and comprehensive resource for students seeking to enhance their understanding of mathematical concepts. With well-structured and meticulously designed questions, the platform ensures a strong grasp of fundamental topics. The inclusion of step-by-step solutions empowers students to tackle challenges independently, fostering critical thinking and problem-solving skills. Vedantu's commitment to the CBSE curriculum ensures alignment with academic requirements, making it an ideal supplement to classroom learning. By providing accessible and engaging content, Vedantu facilitates a conducive learning environment, promoting academic excellence and confidence among students in their mathematical journey.