RD Sharma Solutions for Class 6 Maths Chapter 4 Exercise 4.4 PDF

RD Sharma Solutions for Class 6 Maths Chapter 4 Exercise 4.4 focuses on the operation of division using whole numbers.

This exercise helps students understand how to divide numbers accurately and how to apply the division algorithm: Dividend = Divisor × Quotient + Remainder. It includes a variety of questions such as simple division, verifying results, and solving real-life word problems. Students also get to test their conceptual understanding through true or false questions and logical reasoning.

These solutions are created according to the latest CBSE syllabus and help build a strong foundation in number operations.

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RD Sharma Solutions for Class 6 Maths Chapter 4 Exercise 4.4 Overview

Exercise 4.4 of RD Sharma Class 6 Maths Chapter 4, titled Operations on Whole Numbers, mainly deals with the concept of division of whole numbers and its properties. The exercise begins with simple questions that help students understand when division results in the same number, and gradually moves to more complex problems involving the use of the division algorithm.

Students solve various types of problems including:

• Basic division of whole numbers

• Use of brackets in expressions to understand the correct order of operations

• True or false questions based on properties of division

• Word problems involving the division algorithm

• Finding missing values such as the dividend, divisor, quotient, or remainder using the relation: Dividend = Divisor × Quotient + Remainder

RD Sharma Solutions for Class 6 Maths Operations on Whole Numbers Chapter 4 Exercise 4.4

Here are the detailed solutions for RD Sharma Class 6 Maths Chapter 4 Exercise 4.4 on Operations on Whole Numbers. 

1. Does there exist a whole number a such that a ÷ a = a?

Solution:

Yes. There exists a whole number ‘a’ such that a ÷ a = a.

We know that the whole number is 1 where 1 ÷ 1 = 1.

2. Find the value of:

(i) 23457 ÷ 1

(ii) 0 ÷ 97

(iii) 476 + (840 ÷ 84)

(iv) 964 – (425 ÷ 425)

(v) (2758 ÷ 2758) – (2758 ÷ 2758)

(vi) 72450 ÷ (583 – 58)

Solution:

(i) 23457 ÷ 1

By division

23457 ÷ 1 = 23457

(ii) 0 ÷ 97

By division

0 ÷ 97 = 0

(iii) 476 + (840 ÷ 84)

On further calculation

476 + (840 ÷ 84) = 476 + 10

= 486

(iv) 964 – (425 ÷ 425)

On further calculation

964 – (425 ÷ 425) = 964 – 1

= 963

(v) (2758 ÷ 2758) – (2758 ÷ 2758)

On further calculation

(2758 ÷ 2758) – (2758 ÷ 2758) = 1 – 1

= 0

(vi) 72450 ÷ (583 – 58)

On further calculation

72450 ÷ (583 – 58) = 72450 ÷ 525

= 138

3. Which of the following statements are true:

(i) 10 ÷ (5 × 2) = (10 ÷ 5) × (10 ÷ 2)

(ii) (35 – 14) ÷ 7 = 35 ÷ 7 – 14 ÷ 7

(iii) 35 – 14 ÷ 7 = 35 ÷ 7 – 14 ÷ 7

(iv) (20 – 5) ÷ 5 = 20 ÷ 5 – 5

(v) 12 × (14 ÷ 7) = (12 × 14) ÷ (12 × 7)

(vi) (20 ÷ 5) ÷ 2 = (20 ÷ 2) ÷ 5

Solution:

(i) False.

We know that

LHS = 10 ÷ (5 × 2)

So we get

= 10 ÷ 10

= 1

RHS = (10 ÷ 5) × (10 ÷ 2)

So we get

= 2 × 5

= 10

(ii) True.

We know that

LHS = (35 – 14) ÷ 7

So we get

= 21 ÷ 7

= 3

RHS = 35 ÷ 7 – 14 ÷ 7

So we get

= 5 – 2

= 3

(iii) False.

We know that

LHS = 35 – 14 ÷ 7

So we get

= 35 – 2

= 33

RHS = 35 ÷ 7 – 14 ÷ 7

So we get

= 5 – 2

= 3

(iv) False.

We know that

LHS = (20 – 5) ÷ 5

So we get

= 15 ÷ 5

= 3

RHS = 20 ÷ 5 – 5

So we get

= 4 – 5

= – 1

(v) False.

We know that

LHS = 12 × (14 ÷ 7)

So we get

= 12 × 2

= 24

RHS = (12 × 14) ÷ (12 × 7)

So we get

= 168 ÷ 84

= 2

(vi) True.

We know that

LHS = (20 ÷ 5) ÷ 2

So we get

= 4 ÷ 2

= 2

RHS = (20 ÷ 2) ÷ 5

So we get

= 10 ÷ 5

= 2

4. Divide and check the quotient and remainder:

(i) 7772 ÷ 58

(ii) 6906 ÷ 35

(iii) 16135 ÷ 875

(iv) 16025 ÷ 1000

Solution:

(i) 7772 ÷ 58

So we get 7772 ÷ 58 = 134

By verifying

We know that

Dividend = Divisor × Quotient + Remainder

By substituting values

7772 = 58 × 134 + 0

So we get

7772 = 7772

LHS = RHS

(ii) 6906 ÷ 35

So we get quotient = 197 and remainder = 11

By verifying

We know that

Dividend = Divisor × Quotient + Remainder

By substituting values

6906 = 35 × 197 + 11

On further calculation

6906 = 6895 + 11

We get

6906 = 6906

LHS = RHS

(iii) 16135 ÷ 875

So we get quotient = 18 and remainder = 385

By verifying

We know that

Dividend = Divisor × Quotient + Remainder

By substituting values

16135 = 875 × 18 + 385

On further calculation

16135 = 15750 + 385

We get

16135 = 16135

LHS = RHS

(iv) 16025 ÷ 1000

So we get quotient = 16 and remainder = 25

By verifying

We know that

Dividend = Divisor × Quotient + Remainder

By substituting values

16025 = 1000 × 16 + 25

On further calculation

16025 = 16000 + 25

We get

16025 = 16025

LHS = RHS

5. Find a number which when divided by 35 gives the quotient 20 and remainder 18.

Solution:

We know that

Dividend = Divisor × Quotient + Remainder

By substituting values

Dividend = 35 × 20 + 18

On further calculation

Dividend = 700 + 18

So we get

Dividend = 718

6. Find the number which when divided by 58 gives a quotient 40 and remainder 31.

Solution:

We know that

Dividend = Divisor × Quotient + Remainder

By substituting values

Dividend = 58 × 40 + 31

On further calculation

Dividend = 2320 + 31

So we get

Dividend = 2351

7. The product of two numbers is 504347. If one of the numbers is 1591, find the other.

Solution:

The product of two numbers = 504347

One of the numbers = 1591

Consider A as the number

A × 1591 = 504347

So by division

A = 317

8. On dividing 59761 by a certain number, the quotient is 189 and the remainder is 37. Find the divisor.

Solution:

It is given that

Dividend = 59761

Quotient = 189

Remainder = 37

Consider Divisor = A

We know that

Dividend = Divisor × Quotient + Remainder

By substituting values

59761 = A × 189 + 37

On further calculation

59761 – 37 = A × 189

So we get

59724 = A × 189

By division

A = 316

9. On dividing 55390 by 299, the remainder is 75. Find the quotient.

Solution:

It is given that

Dividend = 55390

Divisor = 299

Remainder = 75

Consider Quotient = A

We know that

Dividend = Divisor × Quotient + Remainder

By substituting values

55390 = 299 × A + 75

On further calculation

55390 – 75 = A × 299

So we get

55315 = A × 299

By division

A = 185

RD Sharma Solutions for Class 6 Maths Chapter 4 Exercise 4.4 PDF

Students can download the RD Sharma Solutions for Class 6 Maths Chapter 4 Exercise 4.4 in PDF format from the link below. This resource provides comprehensive solutions to all the problems in Exercise 4.4, helping students understand division operations on whole numbers effectively. By practicing these solutions, students can strengthen their problem-solving skills and perform better in their examinations.

Key Features of RD Sharma Solutions for Class 6 Maths Chapter 4 Operations on Whole Numbers Exercise 4.4

• Provides clear and detailed solutions that strengthen the understanding of operations like division and properties of whole numbers.

• Each problem is solved using a simple and logical step-by-step method, making it easier for self-study.

•  Enhances accuracy and speed through a wide variety of problems ranging from basic to challenging levels.

• All solutions follow the latest CBSE guidelines and syllabus for Class 6.