NCERT Solutions for Class 9 – Complete Chapter-wise Study Material
Exploring Sequences and Progressions is one of the most important chapters in the Class 9 Mathematics Ganita Manjari English NCERT Solutions curriculum. This chapter plays a significant role in helping students build a strong conceptual foundation while preparing for school examinations, class tests, unit tests, half-yearly examinations, annual examinations, and CBSE board assessments. The chapter has been carefully designed according to the latest NCERT syllabus, making it an essential part of every student's study plan.
The Exploring Sequences and Progressions - Class 9 Mathematics Ganita Manjari English NCERT Solutions available on ATP Education explain every question in a simple, accurate, and step-by-step manner. Each answer is prepared according to the latest CBSE guidelines so that students can understand the concepts clearly without confusion. Whether you are completing your homework, revising before examinations, or strengthening your understanding of the subject, these solutions provide reliable academic support throughout your learning journey.
One of the biggest advantages of studying Exploring Sequences and Progressions is that it helps students understand important concepts, definitions, examples, and textbook exercises in an organized way. Instead of memorizing answers, students learn how to develop logical thinking, improve analytical skills, and write well-structured answers in examinations. This chapter also helps improve problem-solving ability and encourages conceptual learning, which is essential for scoring higher marks in school and competitive examinations.
Our Class 9 Mathematics Ganita Manjari NCERT Solutions cover all textbook questions, important exercise questions, and chapter-wise explanations in English Medium. Every solution is written in easy-to-understand language, allowing students to revise the chapter quickly before examinations. Regular practice of these solutions improves confidence, strengthens subject knowledge, and reduces examination stress.
Students preparing for school assessments should carefully study Exploring Sequences and Progressions because questions from this chapter are frequently asked in objective questions, short answer questions, long answer questions, competency-based questions, and case-study questions. Understanding the concepts explained in this chapter also helps students connect related topics from other chapters, making overall learning more effective and meaningful.
At ATP Education, we continuously update our Class 9 Mathematics Ganita Manjari English NCERT Solutions according to the latest NCERT textbooks and CBSE curriculum. Students can confidently use these chapter-wise solutions for daily study, homework assistance, quick revision, examination preparation, and self-learning. By studying Exploring Sequences and Progressions thoroughly and practising every question regularly, students can strengthen their concepts, improve writing skills, and achieve better academic performance in both school and board examinations.
Exploring Sequences and Progressions - Class 9 Mathematics Ganita Manjari English NCERT Solutions
Exploring Sequences and Progressions
EXERCISE SET 3.3 (SOLVED)
-
Prove that the following rational numbers are equal:
(i) 2/3 and 4/6
4/6 = 2÷2 / 6÷2 = 2/3
Hence equal.
(ii) 5/4 and 10/8
10/8 = 10÷2 / 8÷2 = 5/4
Hence equal.
(iii) -3/5 and -6/10
-6/10 = -6÷2 / 10÷2 = -3/5
Hence equal.
(iv) 9/3 and 3
9/3 = 3
Hence equal.
-
Find the sum:
(i) 2/5 + 3/10
= 4/10 + 3/10
= 7/10
(ii) 7/12 + 5/8
LCM = 24
= 14/24 + 15/24
= 29/24
(iii) -4/7 + 3/14
= -8/14 + 3/14
= -5/14
-
Find the difference:
(i) 5/6 - 1/4
LCM = 12
= 10/12 - 3/12
= 7/12
(ii) 11/8 - 3/4
= 11/8 - 6/8
= 5/8
(iii) -7/9 - (-2/3)
= -7/9 + 2/3
= -7/9 + 6/9
= -1/9
-
Find the product:
(i) 2/3 × 3/10
= 6/30
= 1/5
(ii) 7/11 × 5/8
= 35/88
(iii) -4/7 × 5/14
= -20/98
= -10/49
-
Find the quotient:
(i) 2/3 ÷ 3/10
= 2/3 × 10/3
= 20/9
(ii) 7/11 ÷ 5/8
= 7/11 × 8/5
= 56/55
(iii) -4/7 ÷ 5/14
= -4/7 × 14/5
= -8/5
-
Show that:
(1/2 + 3/4) × 8/3 = 1/2 × 8/3 + 3/4 × 8/3
LHS:
= (2/4 + 3/4) × 8/3
= 5/4 × 8/3
= 10/3
RHS:
= 4/3 + 2
= 10/3
Hence LHS = RHS.
-
Simplify using distributive property:
7/9 (6/7 - 3/4)
= 7/9 × 6/7 - 7/9 × 3/4
= 2/3 - 7/12
= 8/12 - 7/12
= 1/12
-
Find the rational number x:
5/6 (x + 3/5) = 5/6 x + 1/2
LHS:
= 5x/6 + 5/6 × 3/5
= 5x/6 + 1/2
Hence proved.
Source File: turn0file0
Exploring Sequences and Progressions
EXERCISE SET 3.3 (SOLVED)
-
Prove that the following rational numbers are equal:
(i) 2/3 and 4/6
4/6 = 2÷2 / 6÷2 = 2/3
Hence equal.
(ii) 5/4 and 10/8
10/8 = 10÷2 / 8÷2 = 5/4
Hence equal.
(iii) -3/5 and -6/10
-6/10 = -6÷2 / 10÷2 = -3/5
Hence equal.
(iv) 9/3 and 3
9/3 = 3
Hence equal.
-
Find the sum:
(i) 2/5 + 3/10
= 4/10 + 3/10
= 7/10
(ii) 7/12 + 5/8
LCM = 24
= 14/24 + 15/24
= 29/24
(iii) -4/7 + 3/14
= -8/14 + 3/14
= -5/14
-
Find the difference:
(i) 5/6 - 1/4
LCM = 12
= 10/12 - 3/12
= 7/12
(ii) 11/8 - 3/4
= 11/8 - 6/8
= 5/8
(iii) -7/9 - (-2/3)
= -7/9 + 2/3
= -7/9 + 6/9
= -1/9
-
Find the product:
(i) 2/3 × 3/10
= 6/30
= 1/5
(ii) 7/11 × 5/8
= 35/88
(iii) -4/7 × 5/14
= -20/98
= -10/49
-
Find the quotient:
(i) 2/3 ÷ 3/10
= 2/3 × 10/3
= 20/9
(ii) 7/11 ÷ 5/8
= 7/11 × 8/5
= 56/55
(iii) -4/7 ÷ 5/14
= -4/7 × 14/5
= -8/5
-
Show that:
(1/2 + 3/4) × 8/3 = 1/2 × 8/3 + 3/4 × 8/3
LHS:
= (2/4 + 3/4) × 8/3
= 5/4 × 8/3
= 10/3
RHS:
= 4/3 + 2
= 10/3
Hence LHS = RHS.
-
Simplify using distributive property:
7/9 (6/7 - 3/4)
= 7/9 × 6/7 - 7/9 × 3/4
= 2/3 - 7/12
= 8/12 - 7/12
= 1/12
-
Find the rational number x:
5/6 (x + 3/5) = 5/6 x + 1/2
LHS:
= 5x/6 + 5/6 × 3/5
= 5x/6 + 1/2
Hence proved.
Source File: turn0file0
Exploring Sequences and Progressions
EXERCISE SET 3.3 (SOLVED)
-
Prove that the following rational numbers are equal:
(i) 2/3 and 4/6
4/6 = 2÷2 / 6÷2 = 2/3
Hence equal.
(ii) 5/4 and 10/8
10/8 = 10÷2 / 8÷2 = 5/4
Hence equal.
(iii) -3/5 and -6/10
-6/10 = -6÷2 / 10÷2 = -3/5
Hence equal.
(iv) 9/3 and 3
9/3 = 3
Hence equal.
-
Find the sum:
(i) 2/5 + 3/10
= 4/10 + 3/10
= 7/10
(ii) 7/12 + 5/8
LCM = 24
= 14/24 + 15/24
= 29/24
(iii) -4/7 + 3/14
= -8/14 + 3/14
= -5/14
-
Find the difference:
(i) 5/6 - 1/4
LCM = 12
= 10/12 - 3/12
= 7/12
(ii) 11/8 - 3/4
= 11/8 - 6/8
= 5/8
(iii) -7/9 - (-2/3)
= -7/9 + 2/3
= -7/9 + 6/9
= -1/9
-
Find the product:
(i) 2/3 × 3/10
= 6/30
= 1/5
(ii) 7/11 × 5/8
= 35/88
(iii) -4/7 × 5/14
= -20/98
= -10/49
-
Find the quotient:
(i) 2/3 ÷ 3/10
= 2/3 × 10/3
= 20/9
(ii) 7/11 ÷ 5/8
= 7/11 × 8/5
= 56/55
(iii) -4/7 ÷ 5/14
= -4/7 × 14/5
= -8/5
-
Show that:
(1/2 + 3/4) × 8/3 = 1/2 × 8/3 + 3/4 × 8/3
LHS:
= (2/4 + 3/4) × 8/3
= 5/4 × 8/3
= 10/3
RHS:
= 4/3 + 2
= 10/3
Hence LHS = RHS.
-
Simplify using distributive property:
7/9 (6/7 - 3/4)
= 7/9 × 6/7 - 7/9 × 3/4
= 2/3 - 7/12
= 8/12 - 7/12
= 1/12
-
Find the rational number x:
5/6 (x + 3/5) = 5/6 x + 1/2
LHS:
= 5x/6 + 5/6 × 3/5
= 5x/6 + 1/2
Hence proved.
Source File: turn0file0
Exploring Sequences and Progressions
EXERCISE SET 3.3 (SOLVED)
-
Prove that the following rational numbers are equal:
(i) 2/3 and 4/6
4/6 = 2÷2 / 6÷2 = 2/3
Hence equal.
(ii) 5/4 and 10/8
10/8 = 10÷2 / 8÷2 = 5/4
Hence equal.
(iii) -3/5 and -6/10
-6/10 = -6÷2 / 10÷2 = -3/5
Hence equal.
(iv) 9/3 and 3
9/3 = 3
Hence equal.
-
Find the sum:
(i) 2/5 + 3/10
= 4/10 + 3/10
= 7/10
(ii) 7/12 + 5/8
LCM = 24
= 14/24 + 15/24
= 29/24
(iii) -4/7 + 3/14
= -8/14 + 3/14
= -5/14
-
Find the difference:
(i) 5/6 - 1/4
LCM = 12
= 10/12 - 3/12
= 7/12
(ii) 11/8 - 3/4
= 11/8 - 6/8
= 5/8
(iii) -7/9 - (-2/3)
= -7/9 + 2/3
= -7/9 + 6/9
= -1/9
-
Find the product:
(i) 2/3 × 3/10
= 6/30
= 1/5
(ii) 7/11 × 5/8
= 35/88
(iii) -4/7 × 5/14
= -20/98
= -10/49
-
Find the quotient:
(i) 2/3 ÷ 3/10
= 2/3 × 10/3
= 20/9
(ii) 7/11 ÷ 5/8
= 7/11 × 8/5
= 56/55
(iii) -4/7 ÷ 5/14
= -4/7 × 14/5
= -8/5
-
Show that:
(1/2 + 3/4) × 8/3 = 1/2 × 8/3 + 3/4 × 8/3
LHS:
= (2/4 + 3/4) × 8/3
= 5/4 × 8/3
= 10/3
RHS:
= 4/3 + 2
= 10/3
Hence LHS = RHS.
-
Simplify using distributive property:
7/9 (6/7 - 3/4)
= 7/9 × 6/7 - 7/9 × 3/4
= 2/3 - 7/12
= 8/12 - 7/12
= 1/12
-
Find the rational number x:
5/6 (x + 3/5) = 5/6 x + 1/2
LHS:
= 5x/6 + 5/6 × 3/5
= 5x/6 + 1/2
Hence proved.
Source File: turn0file0
NCERT Book Solutions
Chapter-wise NCERT Solutions for Class 6 to 12 prepared according to the latest CBSE syllabus.
HINDI MEDIUM
NCERT Solutions Class 9
Chapter Orienting Yourself: The Use of Coordinates Solutions
Orienting Yourself: The Use of Coordinates Open Chapters
Explore Now →
NCERT Solutions Class 9
Chapter Introduction to Linear Polynomials Solutions
Introduction to Linear Polynomials Open Chapters
Explore Now →
NCERT Solutions Class 9
Chapter The World of Numbers Solutions
The World of Numbers Open Chapters
Explore Now →
NCERT Solutions Class 9
Chapter Exploring Algebraic Identities Solutions
Exploring Algebraic Identities Open Chapters
Explore Now →
NCERT Solutions Class 9
Chapter I’m Up and Down, and Round and Round Solutions
I’m Up and Down, and Round and Round Open Chapters
Explore Now →
NCERT Solutions Class 9
Chapter Measuring Space: Perimeter and Area Solutions
Measuring Space: Perimeter and Area Open Chapters
Explore Now →
NCERT Solutions Class 9
Chapter Introduction to Probability Solutions
Introduction to Probability Open Chapters
Explore Now →
NCERT Solutions Class 9
Chapter Exploring Sequences and Progressions Solutions
Exploring Sequences and Progressions Open Chapters
Explore Now →
NCERT Book Solutions
Chapter-wise NCERT Solutions for Class 6 to 12 prepared according to the latest CBSE syllabus.
ENGLISH MEDIUM
NCERT Solutions Class 9 Mathematics
Class 9 Mathematics Book Solutions
Mathematics Open Book
Explore Now →
NCERT Solutions Class 9 Beehive (English)
Class 9 Beehive (English) Book Solutions
Open Book
Explore Now →
NCERT Solutions Class 9 Mathematics Ganita Manjari
Class 9 Mathematics Ganita Manjari Book Solutions
GANITA MANJARI Open Book
Explore Now →Benefits of Studying NCERT Solutions
Studying from NCERT Solutions helps students build strong conceptual understanding and improve problem-solving skills. These solutions are especially useful for revision because every answer is written according to the marking scheme followed by CBSE.
- Improve conceptual understanding.
- Learn correct answer-writing techniques.
- Prepare effectively for school examinations.
- Complete syllabus revision in less time.
- Practice important textbook questions.
- Build confidence before examinations.
Prepared According to the Latest CBSE Syllabus
All NCERT Book Solutions for Class 9 available on ATP Education are updated according to the latest CBSE curriculum. Whenever NCERT introduces changes in textbooks or syllabus, our study materials are revised accordingly so that students always receive accurate and updated content.
Helpful for Competitive Examinations
NCERT textbooks form the foundation of many competitive examinations. Students preparing for Olympiads, NTSE, CUET, UPSC Foundation, SSC and several entrance examinations can strengthen their basics through these chapter-wise solutions. Understanding NCERT concepts also improves analytical thinking and logical reasoning.
Simple and Student-Friendly Explanations
Our experts prepare every answer in a simple, clear and student-friendly format. Difficult concepts are explained step by step with proper reasoning so that students of every learning level can understand them easily. This approach helps students remember concepts for a longer period and perform confidently during examinations.
Start Learning with ATP Education
Explore the complete collection of NCERT Solutions for Class 9 and begin your preparation with confidence. Every chapter is available online for free and can be accessed anytime. Whether you want to complete homework, revise important chapters or prepare for examinations, ATP Education provides reliable and high-quality study resources to help you achieve academic success.
