Question 1

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.

Accepted Answer

Suppose there are two groups of sheep.
The first group has 6 sheep and the second has 4 sheep.
We have counted using pebbles.
To add, put all pebbles in the same pouch.
To subtract, take out as many pebbles as in the pouch having fewer pebbles from the pouch having more pebbles.
Now, suppose we wish to know how many sheep will be twice the number in the first group.
For this, we count twice using pebbles and put all the pebbles in the same pouch.
Suppose we have 12 pebbles and want to divide them into three equal groups.
We put them one by one in three bowls till we exhaust all. The number of pebbles in each bowl gives the quotient.

Question 2

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!

Accepted Answer

a, b, c, …, z are 26 numbers
aa, bb, …, zz are 26 more numbers.

Source: This question is from A Story of Numbers, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter A Story of Numbers: Way, Extending, Number, System, Method, Strings. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from A Story of NumbersQ1: Suppose you are using the number system that uses sticks to represent numbers, as in Method 1....
Q3: Try making your own number system.
Q4: Using the ideas discussed in this section, try refining the number system you might have made...
Practice more questions from A Story of Numbers &mdash; Mathematics, Class 8 CBSE

Question 3

Try making your own number system.

Accepted Answer

Let base be 3
Then 3
0
= 1 = A, 3
1
= 3 = B, 3
2
= 9 = C….,
3.2 Some Early Number Systems
Figure It Out (Pages 59)

Source: This question is from A Story of Numbers, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter A Story of Numbers: Try, Making, Own, Number, System, A Story of Numbers. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from A Story of NumbersQ1: Suppose you are using the number system that uses sticks to represent numbers, as in Method 1....
Q4: Using the ideas discussed in this section, try refining the number system you might have made...
Practice more questions from A Story of Numbers &mdash; Mathematics, Class 8 CBSE

Question 4

Using the ideas discussed in this section, try refining the number system you might have made earlier.

Accepted Answer

Try it yourself.
3.3 The Idea of a Base
Figure It Out (Page 62)

Source: This question is from A Story of Numbers, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter A Story of Numbers: Ideas, Discussed, Section, Try, Refining, Number. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from A Story of NumbersQ1: Suppose you are using the number system that uses sticks to represent numbers, as in Method 1....
Q3: Try making your own number system.
Practice more questions from A Story of Numbers &mdash; Mathematics, Class 8 CBSE