AP Board Class 8 Maths Chapter 15 Playing with Numbers Ex 15.6 Textbook Solutions PDF: Download Andhra Pradesh Board STD 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Book Answers ~ HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

AP Board Class 8 Maths Chapter 15 Playing with Numbers Ex 15.6 Textbook Solutions PDF: Download Andhra Pradesh Board STD 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Book Answers

AP Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Textbooks Solutions and answers for students are now available in pdf format. Andhra Pradesh Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Book answers and solutions are one of the most important study materials for any student. The Andhra Pradesh State Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 books are published by the Andhra Pradesh Board Publishers. These Andhra Pradesh Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 textbooks are prepared by a group of expert faculty members. Students can download these AP Board STD 8th Maths Chapter 15 Playing with Numbers Ex 15.6 book solutions pdf online from this page.

Andhra Pradesh Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Textbooks Solutions PDF

Andhra Pradesh State Board STD 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Books Solutions with Answers are prepared and published by the Andhra Pradesh Board Publishers. It is an autonomous organization to advise and assist qualitative improvements in school education. If you are in search of AP Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Books Answers Solutions, then you are in the right place. Here is a complete hub of Andhra Pradesh State Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 solutions that are available here for free PDF downloads to help students for their adequate preparation. You can find all the subjects of Andhra Pradesh Board STD 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Textbooks. These Andhra Pradesh State Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Textbooks Solutions English PDF will be helpful for effective education, and a maximum number of questions in exams are chosen from Andhra Pradesh Board.

Andhra Pradesh State Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Books Solutions

Board	AP Board
Materials	Textbook Solutions/Guide
Format	DOC/PDF
Class	8th
Subject	Maths
Chapters	Maths Chapter 15 Playing with Numbers Ex 15.6
Provider	Hsslive

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AP Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Textbooks Solutions with Answer PDF Download

Find below the list of all AP Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:

Question 1.
Find the sum of integers which are divisible by 5 from 1 to 100.
Solution:
Numbers which are divisible by 5 from 1 to 100 are 5, 10, 15, …………………95, 100.
∴ Sum of the above numbers = 5+10 + ……………..+ 95 + 100
= 5[1 + 2 + ………………….+ 20]
= 5 [ 20×(20+1)2 ]
= 5×20×212 [∵ Sum of ‘n’ natural numbers = 𝑛(𝑛+1)2 & n = 20 ]
= 1050

Question 2.
Find the sum of integers which are divisible by 2 from 11 to 50.
Solution:
. Numbers which are divisible by 2 from 11 to 50 are 12, 14,48, 50.
Sum of the numbers = 12 + 14 + ……….. + 48 + 50 ‘
= (2 + 4 + ……….. + 50) – (2 + 4 + ……….. + 10)
= 2(1 + 2 +……….. + 25) – 2 (1 + 2 + ……….. + 5)

= 25 × 26 – 5 × 6
= 650 – 30
= 620

Question 3.
Find the sum of integers which are divisible by 2 and 3 from 1 to 50.
Solution:
Numbers which are divisible by 2 and 3 i.-e., which are divisible by 6 from 1 to 50 are 6,12 …………….48.
Sum of the numbers = 6 + 12 + ……..+ 48
= 6(1 + 2 +……… + 8)
= 6 [8(8+1)2]
= 3 × 8 × 9 = 216

Question 4.
(n³ – n) is divisible by 3. Explain the reason.
Solution:

∴ If n = 4, (n³ – n) is divisible by 3.
∴ (n³ – n) is divisible by all the values of n.
Method 2:
n³ – n = n(n² – 1)
= n(n + 1)(n – 1)
∴ (n³ – n) is divisible by ‘3’ for all the values of n.
[∵ (n – 1), n, (n + 1) are three consecutive odd numbers]

Question 5.
Sum of ‘n’ odd number of consecutive numbers is divisible by ‘n’. Explain the reason.
Solution:
Sum of n’ consecutive odd numbers = n²
Since n is a factor of n², It Is divisible by ‘n’.

Question 6.
Is 1¹¹ + 2¹¹ + 3¹¹ + 4¹¹ divisible by 5? Explain.
Solution:
Sum of units digit of number 1¹¹ + 2¹¹ + 3¹¹ + 4¹¹
= 1 + 8 + 7 + 4
= 20 → 205(R = 0)
∴ 1¹¹ + 2¹¹ + 3¹¹ + 4¹¹ is divisible by 5.

Question 7.

Find the number of rectangles of the given figure?
Solution:

∴ No.of rectangles in the given figure = 1 + 2 + 3 + 4 + 5 + 6 = 21

Question 8.
Rahul’s father wants to deposit sorne amount of money every year on the day of Rahul’s birthday. On his 1st birth day Rs.100, on his 2nd birth day Rs.300, on his 3 birth day Rs.600, on his 4th birthday Rs. 1000 and so on. What is the amount deposited by his father on Rahul’s 15th birthday.
Solution:

Rahul’s father deposits on every year 200, 300, 400 more than before year.
Then he deposits ₹ 10,500 on 14th birthday.
∴ The amount deposits on 15th birthday
= 10,500 + 1,500
= ₹ 12,000/-

Question 9.
Find the sum of integers from 1 to 100 which are divisible by 2 or 5.
Solution:
Sum of the numbers which are divisible by 2 from 1 to 100
= 2 + 4 + ……….. + 100
= 2(1 + 2 + ………… +50)
= 2 × 50×(50+1)2
= 50 × 51 = 2550
Sum of the numbers which are dMsible by 5froin I to 100
= 5 + 10 + ……….. + 100
= 5(1 + 2 +……….. +20)
= 5 × 20×(20+1)2
=5 × 10 × 21
=1050

Sum of the numbers which are.divisible by both 2 and 5 = 2550 + 1050 =3600
∴ Sum ol the numbers which are divisible by 2 or 5 from 1 to 100
= 10 + 20 + ………..+ 100 ( L.C.M of 2, 5 is 10)
=10(1 + 2 + ………..+ 10)
= 10 × 10×(10+1)2
= 5 × 10 × 11 .
= 550
∴ The sum of required numbers 3600—550 3050

Question 10.
Find the sum of integers from 11 to 1000 which are divisible by 3.
Solution:
Sum ol the numbers which are divisible by 3 from lito 1000
= 12 + 15+ ……….. +099
= 3(4 + 5 + ……….. +333)
= 3(1 + 2 + ……….. + 333) – 3(1 + 2+3)

= 999 × 167 – 9 × 2
= 166833 – 18
= 166815

AP Board Textbook Solutions PDF for Class 8th Maths

Andhra Pradesh Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Textbooks for Exam Preparations

Andhra Pradesh Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 exam preparation. The AP Board STD 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 8th Maths Chapter 15 Playing with Numbers Ex 15.6 Books State Board syllabus with maximum efficiency.

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