Figure it Out :
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.
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!
3. Try making your own number system.
SOLUTIONS:
1️⃣ Using Sticks for Arithmetic (Method 1)
Let one stick = one unit (or “one thing”).
➕ Addition:
Put all the sticks together in one pile.
👉 Example: 3 sticks + 2 sticks = 5 sticks in total.
➖ Subtraction:
Take away the smaller pile from the bigger one.
👉 Example: 5 sticks − 2 sticks = 3 sticks left.
✖ Multiplication:
Make equal groups of sticks.
👉 Example: 3 × 4 → make 4 groups of 3 sticks each → all together 12 sticks.
➗ Division:
Share the sticks equally into groups.
👉 Example: 12 ÷ 3 → make 3 equal groups → each group gets 4 sticks.
That’s how you can add, subtract, multiply, or divide using only collections of sticks—no need for written numbers!
2️⃣ Extending the Letter System (Method 2)
Let each letter stand for one number:
a = 1, b = 2, c = 3, … z = 26
After z (26), start again with two letters:
aa = 27, ab = 28, ac = 29 … az = 52 ba = 53, bb = 54, and so on.
You can keep adding more letters to the left for bigger numbers, just like how we add more digits in 100, 1000, etc.
👉 So this becomes like a base-26 system using letters instead of digits!
3️⃣ Make Your Own Number System
Let’s be creative 😊
Here’s one example you can easily understand:
💠 Base-4 System
Use different shapes (like emoji or symbols):
| Value | Symbol |
|---|---|
| 0 | ⚪ |
| 1 | 🔹 |
| 2 | 🔸 |
| 3 | 🔺 |
Each new place is worth 4 times the one next to it (just like in our decimal system).
Example:
Write 9 in this system:
9 = (2 × 4) + 1 → 🔸🔹
Write 15 in this system:
15 = (3 × 4) + 3 → 🔺🔺
You just made your own number system! 🎉
🌟 Summary
| Operation | What to Do |
|---|---|
| Add | Combine objects |
| Subtract | Remove objects |
| Multiply | Make equal groups |
| Divide | Share equally |
| Letter System | Use combinations like aa, ab, ac… |
| Your Own System | Pick symbols and a rule (like base-4) |
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