In this chapter, we provide RD Sharma Class 6 ex 4.5 Solutions Chapter 4 Operations on Whole Numbers for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Class 6 ex 4.5 Solutions Chapter 4 Operations on Whole Numbers Maths pdf, Now you will get step by step solution to each question.

Textbook | NCERT |

Class | Class 6 |

Subject | Maths |

Chapter | Chapter 4 |

Chapter Name | Operations on Whole Numbers |

Exercise | Ex 4.5 |

**RD Sharma Solutions for Class 6 Chapter 4 ****Operations on Whole Numbers** **Ex 4.5 Download PDF**

**Operations on Whole Numbers**

**Chapter 4: Operations on Whole Numbers**** – Exercise 4.5**

**Question: 1**

Without drawing a diagram, find:

**Solution:**

(i) 10th square number:

A square number can easily be remembered by the following rule

N^{th} square number = n × n

10th square number = 10 × 10 = 100

(ii) 6th triangular number:

A triangular number can easily be remembered by the following rule

N^{th} triangular number = n × ( n + 1 )2

Therefore, 6^{th} triangular number = 6 × (6 + 1)2 = 21

**Question: 2**

(i) Can a rectangle number also be a square number?

(ii) Can a triangular number also be a square number?

**Solution:**

(i) Yes, a rectangular number can also be a square number; for example, 16 is a square number also a rectangular number.

(ii) Yes, there e×ists only one triangular number that is both a triangular number and a square number, and that number is 1.

**Question: 3**

Write the first four products of two numbers with difference 4 starting from in the following order:

1 , 2 , 3 , 4 , 5 , 6 , ………..

Identify the pattern in the products and write the next three products.

**Solution:**

1 × 5 = 5 (5 – 1 = 4)

2 × 6 = 12 (6 – 2 =4)

3 × 7 = 21 (7 – 3 = 4)

4 × 8 = 32 (8 – 4 = 4)

**Question: 4**

*Observe the pattern in the following and fill in the blanks:*

**Solution:**

9 × 9 + 7 =88

98 × 9 + 6 = 888

987 × 9 + 5 = 8888

9876 × 9 + 4 = 88888

98765 × 9 + 3 = 888888

987654 × 9 + 2 = 8888888

9876543 × 9 + 1 = 88888888

**Question: 5**

*Observe the following pattern and extend it to three more steps:*

**Solution:**

6 × 2 – 5 = 7

7 × 3 – 12 = 9

8 × 4 – 21 = 11

9 × 5 – 32 = 13

10 × 6 – 45 = 15

11 × 7 – 60 = 17

12 × 8 – 77 = 19

**Question: 6**

Study the following pattern:

1 + 3 = 2 × 2

1 + 3 + 5 = 3 × 3

1 + 3 + 5 + 7 = 4 × 4

1 + 3 + 5 + 7 + 9 = 5 × 5

By observing the above pattern, find:

**Solution:**

(i) 1 + 3 + 5 + 7 + 9 + 11

= 6 × 6

= 36

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15

= 8 × 8

= 64

(iii) 21 + 23 + 25 + … + 51

= (21 + 23 + 25 +…+ 51) can also be written as

(1 + 3 + 5 + 7 +…+ 49 + 51) – (1 + 3 + 5 +…+ 17 + 19)

(1 + 3 + 5 + 7+…+ 49 + 51) = 26 × 26 = 676

and, (1 + 3 + 5 +…+ 17 + 19 ) = 10 × 10 = 100

Now,

(21 + 23 + 25 +…+ 51 ) = 676 – 100 = 576

**Question: 7**

*Study the following pattern:*

By observing the above pattern, write next two steps.

**Solution:**

The next two steps are as follows:

1 × 1 + 2 × 2 + 3 × 3 + 4 × 4 + 5 × 5

= 5 × 6 × 116

= 55

1 × 1+ 2 × 2 + 3 × 3 + 4 × 4 + 5 × 5 + 6 × 6

= 6 × 7 × 136

= 91

**Question: 8**

*Study the following pattern:*

By observing the above pattern, find:

**Solution:**

(i) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10

= 10 × 112

= 55

(ii) 50 + 51 + 52 + …+ 100

This can also be written as

(1 + 2 + 3 + …+ 99 + 100) – (1 + 2 + 3 + 4 + …+ 47 + 49)

Now,

(1 + 2 + 3 + …+ 99 + 100 ) = 100 × 1012

and, (1 + 2 + 3 + 4 +…+ 47 + 49 ) = 49 × 502

So, (50 + 51 + 52 + …+ 100 ) = 100 × 1012 – 49 × 502

= 5050 – 1225

= 3825

(iii) 2 + 4 + 6 + 8 + 10 +…+ 100

This can also be written as 2 × (1 + 2 + 3 + 4 + …+ 49 + 50)

Now,

(1 + 2 + 3 + 4 + …+ 49 + 50 ) = 50 × 512

= 1275

Therefore, (2 + 4 + 6 + 8 + 10 + …+ 100) = 2 × 1275 = 2550

**All Chapter RD Sharma Solutions For Class 6 Maths**

I think you got complete solutions for this chapter. If You have any queries regarding this chapter, please comment on the below section our subject teacher will answer you. We tried our best to give complete solutions so you got good