![](https://cdn.mathpix.com/cropped/2024_05_06_2fa7aeee8bd02a6bd1bfg-01.jpg?height=37&width=254&top_left_y=382&top_left_x=16)

Little Karlson wrote the fraction $10 / 97$. Little Boy can:

1) add any natural number to both the numerator and the denominator simultaneously,
2) multiply the numerator and the denominator by the same natural number. Can Little Boy, using these actions, obtain a fraction,

a) equal to $1 / 2$? b) equal to 1?
a) Multiplying the numerator and the denominator by the same number does not affect the value of the fraction. Therefore, the problem reduces to the equation $2(10+x)=97+x$, from which

$x=77$.

b) A fraction equals one if its numerator and denominator are equal. And Little Bear cannot make equal numbers from unequal ones.

## Answer

a) Can; b) cannot.

## Problem