Solve the equation 9 = 36b for b.

1. Identify the equation: The given equation is $9 = 36b$.
2. Isolate the variable $b$: To solve for $b$, we need to get $b$ by itself on one side of the equation. We can do this by dividing both sides of the equation by the coefficient of $b$, which is 36.
$$ \frac{9}{36} = \frac{36b}{36} $$
3. Simplify the fraction: The left side of the equation simplifies to $\frac{9}{36}$. We can simplify this fraction by finding the greatest common divisor (GCD) of 9 and 36, which is 9. Divide both the numerator and the denominator by 9:
$$ \frac{9 \div 9}{36 \div 9} = \frac{1}{4} $$
The right side of the equation simplifies to $b$ because $\frac{36b}{36} = b$.
So, the equation becomes:
$$ \frac{1}{4} = b $$
4. State the final answer: The value of $b$ is $\frac{1}{4}$.