NCERT Solutions

Chapter 3 - A story of Numbers

NCERT Solutions for Class 8 Maths Chapter 3 – A Story of Numbers

Chapter 3 – A Story of Numbers from Class 8 Maths ais designed to help students understand how numbers are represented, compared, and used in different forms. This chapter builds on earlier number concepts and introduces students to rational thinking, number representation, and numerical relationships in a structured and engaging manner. The chapter also plays a vital role in strengthening numerical literacy and logical reasoning.

The NCERT Solutions for Class 8 Maths for this chapter is prepared by ALLEN experts and it enables students to understand how numbers evolve, how they are expressed in different formats, and how mathematical rules apply to various types of numbers. Each concept is explained step by step to ensure clarity, ease of learning, and effective exam preparation.

1.0Downlaod NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers : Free PDF

Students can download the A Story of Numbers Class 8 PDF with answers from the table below. The NCERT Solutions for Class 8 Maths Chapter 3 – A Story of Numbers PDF are meticulously prepared by ALLEN’s expert faculty members, who have strong subject knowledge and a deep understanding of the CBSE curriculum. These solutions are structured to help students grasp numerical concepts clearly, practice effectively, and perform confidently in school examinations.

Class 8 Maths Chapter 3 - A Story of Numbers

2.0Key Topics Covered in Class 8 Maths Chapter 3

Chapter 3 of NCERT Class 8 Maths, titled "A Story of Numbers", concentrates on improving students' comprehension of numbers and their usage. These are the main principles covered in this chapter:

Definition of a Number - A number is a representation of the amount for something.

Classification of Numbers -

A. Variety of Numbers: Different types of numbers are used for performing conversions from one type of condition to another.

B. Representation of a Number: Show representation using a number line and other forms (e.g., fractions).

C. Comparison/Organising Numbers: Comparison and arrangement of numbers according to mathematical principles.

D. Number Patterns/Relationships: Identify patterns and relationships between numbers.

E. Applying Concepts of Numbers: Numbers can be used to solve real and theoretical numerical problems through property and logical reasoning.

3.0NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers : All Exercises

Chapter 3 A Story of Numbers - Exercise 3.1

Chapter 3 A Story of Numbers - Exercise 3.2

Chapter 3 A Story of Numbers - Exercise 3.3

Chapter 3 A Story of Numbers - Exercise 3.4

Chapter 3 A Story of Numbers - Exercise 3.5

Chapter 3 A Story of Numbers - Exercise 3.6

Chapter 3 A Story of Numbers - Exercise 3.7

Chapter 3 A Story of Numbers - Exercise 3.8

Chapter 3 A Story of Numbers - Exercise 3.9

Exercise 3.1

This exercise introduces number systems and their representation, helping students understand how numbers are structured and classified. It builds foundational knowledge by exploring types of numbers and their basic properties through simple identification and classification tasks.

Key Topics Covered:

Number classification: Understanding types like natural numbers and integers.
Basic properties: Identifying characteristics of numbers.
Representation of numbers: Learning how numbers are structured.

Exercise 3.2

Students explore relationships between numbers and operations, focusing on how numbers behave under addition, subtraction, and multiplication. The exercise strengthens conceptual understanding and builds confidence in handling different numerical operations effectively.

Key Topics Covered:

Number operations: Applying addition, subtraction, and multiplication.
Properties of numbers: Understanding behavior under operations.
Logical reasoning: Analyzing relationships between numbers.

Exercise 3.3

This exercise focuses on identifying patterns and sequences in numbers. Students learn to observe changes and apply rules to extend patterns logically. It enhances analytical thinking and builds a strong base for algebraic reasoning.

Key Topics Covered:

Number patterns: Recognizing sequences and trends.
Pattern extension: Applying rules to continue sequences.
Analytical skills: Developing logical reasoning abilities.

Exercise 3.4

This section emphasizes applying number concepts to solve structured problems. Students interpret relationships and use mathematical rules to arrive at solutions, improving both accuracy and logical thinking.

Key Topics Covered:

Problem-solving techniques: Applying concepts to real problems.
Numerical relationships: Understanding connections between numbers.
Logical application: Using rules in practical scenarios.

Exercise 3.5

This exercise includes multi-step numerical problems that require careful calculation and reasoning. It helps students improve accuracy while applying previously learned concepts in more complex situations.

Key Topics Covered:

Multi-step calculations: Solving layered numerical problems.
Concept application: Using earlier concepts effectively.
Accuracy in computation: Avoiding calculation errors.

Exercise 3.6

Students work on advanced number relationships and logical reasoning questions. The exercise encourages deeper understanding of how numbers interact and strengthens problem-solving strategies.

Key Topics Covered:

Advanced number reasoning: Exploring deeper relationships.
Logical thinking: Applying reasoning in problem-solving.
Concept integration: Combining multiple ideas.

Exercise 3.7

This exercise further develops pattern recognition and application skills. Students analyze number structures and apply mathematical rules to solve complex pattern-based questions.

Key Topics Covered:

Complex patterns: Understanding advanced sequences.
Application skills: Solving pattern-based problems.
Mathematical reasoning: Applying logical rules effectively.

Exercise 3.8

This section focuses on interpreting and solving number-based problems using learned concepts. Students strengthen their understanding by applying knowledge in varied scenarios.

Key Topics Covered:

Concept application: Using knowledge in different contexts.
Problem interpretation: Understanding question requirements.
Numerical analysis: Breaking down problems logically.

Exercise 3.9

The final exercise consolidates all concepts from the chapter through mixed problems. It tests understanding, accuracy, and reasoning, ensuring a strong grasp of number systems and operations.

Key Topics Covered:

Concept revision: Reinforcing all chapter topics.
Mixed problem-solving: Handling varied question types.
Comprehensive understanding: Building strong foundations.

4.0NCERT Class 8 Maths Chapter 3 - A Story of Numbers - Detailed Solutions

FIGURE IT OUT-01

Suppose you are using the number system that uses sticks to represent numbers, as in Method 1. Without using either the number names or the numerals of the Hindu number system, give a method for adding, subtracting, multiplying and dividing two numbers or two collections of sticks.
Sol.
Addition (Join the sticks): Just put both collections of sticks together. You have: || (2 sticks) and||| (3 sticks) Join them: $∥ + ∣∣∣ \to ∣∣∣ ∣$ You now have 5 sticks.
Subtraction (Remove sticks): Remove sticks from a collection. You have: |||||(6 sticks) and||(3 sticks) Take away 3 sticks from 6: $∥∥∥∥ - ∥∥ \to ∥$ You are left with 3 sticks.
Multiplication (Make equal groups): Repeated addition - make that many groups of sticks and combine. You want: $∥$ | ( 2 sticks) $\times ∥$ || ( 3 sticks) That means: 3 groups of 2 sticks Group 1: || Group 2: || Group 3: || Put all sticks together: $∣∣ + ∣∣ + ∣∣ \to ∣∣∣∣ ∣$ (You have 6 sticks.)
Division (Make equal groups from a set): Divide sticks into equal groups. You have: |||||| (6 sticks) and||| (3 sticks) Take away 3 sticks from 6: |||||| $\div ∥∣∣ \to ∣∣$ (group size = 2) How many groups of 2 can you make? Group 1: || Group 2: || Group 3: || You made 3 groups of 2 sticks. So, $6 \div 2 = 3$ (but again, we don't say " 3 "we just show 3 groups of sticks.)
One way of extending the number system in Method 2 is by using strings with more than one letter - for example, we could use 'aa' for 27. How can you extend this system to represent all the numbers? There are many ways of doing it! Sol.
a, b, c, ..., z are 26 numbers $aa, bb, \dots, zz$ are 26 more numbers. i.e., $aa = 27$ ; $bb = 28$ aaa, bbb, ……zzz are 26 more numbers i.e., $aaa = 53, bbb = 54$
Try making your own number system. Sol.
Let base be 3 Then $3^{0} = 1 = A, 3^{1} = 3 = B, 3^{2} = 9 = C \dots .$ ,

1	A	$3^{0} = 1$
2	AA	$1 + 1$
3	B	$3^{1} = 3$
4	BA	$3 + 1$
5	BAA	$3 + 1 + 1$
6	BB	$3 + 3$
7	BBA	$3 + 3 + 1$
8	BBAA	$3 + 3 + 1 + 1$
9	C	$3^{2} = 9$
10	CA	$9 + 1$
11	CAA	$9 + 1 + 1$
12	CB	$9 + 3$

FIGURE IT OUT-02

Represent the following numbers in the Roman system. (i) 1222 (ii) 2999 (iii) 302 (iv) 715 Sol.
(i) $1222 = 1000 + 100 + 100 + 10 + 10 + 1 + 1 =$ MCCXXII (ii) $2999 = 1000 + 1000 + (1000 - 100) + (100 - 10) + (10 - 1) =$ MMCMXCIX (iii) $302 = 100 + 100 + 100 + 1 + 1 =$ CCCII (iv) $715 = 500 + 100 + 100 + 10 + 5$ = DCCXV

FIGURE IT OUT-03

A group of indigenous people in a Pacific island use different sequences of number names to count different objects. Why do you think they do this? Sol.
Counting in twos is more efficient in representing numbers than, for example, a tally system.
Consider the extension of the Gumulgal number system beyond 6 in the same way of counting by 2 s. Come up with ways of performing the different arithmetic operations (,, $+ - \times, \div$ ) for numbers occurring in this system, without using Hindu numerals. Use this to evaluate the following: (i) (ukasar-ukasar-ukasar-ukasarurapon) + (ukasar-ukasar-ukasarurapon) (ii) (ukasar-ukasar-ukasar-ukasarurapon) - (ukasar-ukasar-ukasar) (iii) (ukasar-ukasar-ukasar-ukasarurapon) × (ukasar-ukasar) (iv) (ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar) ÷ (ukasar-ukasar) Sol. (i) uk - uk - uk - uk - ur

5.0Key Features and Benefits of Class 8 Maths Chapter 3

This chapter provides clear insight into the concept of numbers and their practical use in mathematics learned at school and beyond.

Improves Number Awareness: Understanding how numbers relate, compare, and are arranged enhances a student’s overall numerical understanding.
Builds Logical Reasoning Skills: Studying number patterns and relationships helps students develop the ability to reason logically and reach correct mathematical conclusions.
Ensures Conceptual Understanding: The chapter focuses on explaining the logic behind numerical operations, helping students move beyond rote memorisation.
Prepares for Higher-Level Mathematics: A strong grasp of number concepts supports learning advanced topics such as Algebra, Rational Numbers, and Data Handling.
Enhances Application Skills: Practice with application-based and reasoning questions allows students to apply number concepts in various problem-solving situations.
Supports Effective Exam Preparation: Since number-based questions are commonly asked in exams, mastering this chapter improves accuracy, confidence, and performance.

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