What would be a simple rule to multiply a number with ∩?

Question

Homi · Accepted Answer

This problem asks us to find a rule for multiplication in a symbolic number system.

Step 1 — Understand the symbolic number system

Let us identify the numerical value of each unique symbol shown in the expressions. This system is similar to ancient Egyptian numerals, where symbols represent powers of ten.

The 'vertical stroke' (implied by '|||') represents one unit.
The '∩' symbol represents ten.
The 'curly symbol' (like a question mark with a curl) represents one hundred.
The 'hooked arrow symbol' (in expression (ii)) represents one thousand.

So, we have: $\text{vertical stroke} = 1$ $\text{∩} = 10$ $\text{curly symbol} = 100$ $\text{hooked arrow symbol} = 1000$

Step 2 — Formulate the multiplication rule

We have determined that the symbol '∩' represents the number 10. Multiplying a number by 10 in our standard decimal system means each digit shifts one place to the left. This means each unit of a certain power of ten becomes a unit of the next higher power of ten. For example, 1 becomes 10, and 10 becomes 100.

In this symbolic system, multiplying by '∩' means we replace each symbol with the symbol for the next higher power of ten. For instance, a 'vertical stroke' (1) becomes a '∩' (10). A '∩' (10) becomes a 'curly symbol' (100). A 'curly symbol' (100) becomes a 'hooked arrow symbol' (1000).

$\boxed{\text{To multiply a number by ∩, replace each symbol in the number with the symbol for the next higher power of ten.}}$

Diagram 1

Answer

(i) To multiply a number by ∩, replace each symbol in the number with the symbol for the next higher power of ten. For example, a 'vertical stroke' (1) becomes a '∩' (10), a '∩' (10) becomes a 'curly symbol' (100), and a 'curly symbol' (100) becomes a 'hooked arrow symbol' (1000). (ii) Not applicable. (iii) Not applicable.

Question 19

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