NCERT Solutions for Class 8 Maths – Ganita Prakash
Chapter: A Story of Numbers
Exercise 3.1 (Figure it Out)
1. Method using sticks to perform operations:
Addition:
Take two collections of sticks and join them together.
The total number of sticks gives the sum.
Subtraction:
From one collection, remove sticks equal to the second collection.
The remaining sticks give the result.
Multiplication:
Arrange sticks in equal groups (repeated addition).
For example, make several groups with the same number of sticks and count all sticks.
Division:
Distribute sticks into equal groups.
The number of groups formed gives the result.
2. Extending the letter-based number system:
We can represent numbers using letters like:
- a = 1, b = 2, c = 3, …, z = 26
After z, we can continue as:
- aa = 27, ab = 28, ac = 29, …
- az = 52, ba = 53, bb = 54, …
This system works similar to place value (like base-26 system).
General Method:
Each position represents a power of 26.
So, any number can be written using combinations of letters.
3. Making your own number system:
Example System:
- Use symbols: ●, ▲, ■
- Let ● = 1, ▲ = 5, ■ = 10
Then numbers can be formed as:
- ●● = 2
- ▲● = 6
- ■▲● = 16
You can also create a place value system:
- Use base-5 system
- Digits: 0,1,2,3,4
Example:
- 10 (base 5) = 5 (in decimal)
- 21 (base 5) = 11 (in decimal)
Conclusion:
A number system can be created using symbols or letters, and rules can be defined for place values and operations.