Sequential Division Problem: Tracking Position After Dividing by 3, 1/8, and 4

Question

A frog jumps on the number axis.

It starts with the digit 1. It first jumps to a value equal to the value it is set to, divided by 3-.

Then it jumps to a value equal to the value at which it is placed, divided by $+\frac{1}{8}$ .

Finally it jumps to a value equal to the value it is at, divided by 4-.

Where will you stop at the end of three jumps?

To solve this problem, we will perform each division in sequence as described:

Step 1: Initial Position

- The frog starts at $x = 1$ .

Step 2: First Jump

- Divide by $-3$ :
$x = \frac{1}{-3} = -\frac{1}{3}$ .

Step 3: Second Jump

- Divide by $+\frac{1}{8}$ :
$x = \frac{-\frac{1}{3}}{\frac{1}{8}} = -\frac{1}{3} \times 8 = -\frac{8}{3}$ .

Step 4: Third Jump

- Divide by $-4$ :
$x = \frac{-\frac{8}{3}}{-4} = \frac{8}{3} \times \frac{1}{4} = \frac{8}{3} \times \frac{1}{4} = \frac{8}{12} = \frac{2}{3}$ .

Therefore, the frog stops at the position $+\frac{2}{3}$ .

$+\frac{2}{3}$