We have a paint that can cover $\frac{7}{12}$ $m^2$ of board with $\frac{7}{9}$ dL. We want to find out how much area (in $m^2$) can be covered by 1 dL of the paint.

1. Problem Description

We have a paint that can cover $\frac{7}{12}$ $m^2$ of board with $\frac{7}{9}$ dL. We want to find out how much area (in $m^2$) can be covered by 1 dL of the paint.

2. Solution Steps

To find the area covered by 1 dL, we need to divide the area covered by $\frac{7}{9}$ dL by $\frac{7}{9}$. This can be expressed as:

$Area = \frac{7}{12} \div \frac{7}{9}$

To divide by a fraction, we multiply by its reciprocal:

$Area = \frac{7}{12} \times \frac{9}{7}$

We can simplify before multiplying:

$Area = \frac{1}{4} \times \frac{3}{1}$

$Area = \frac{3}{4}$

The equation written on the page is incorrect, instead it should have been:

$\frac{7}{12} \div \frac{7}{9} = \frac{7}{12} \times \frac{9}{7}$

After simplification it yields:

$\frac{1}{4} \times \frac{3}{1} = \frac{3}{4}$

The final answer written on the page is $\frac{4}{3}$, but it should be $\frac{3}{4}$

3. Final Answer

The area that can be covered by 1 dL of paint is $\frac{3}{4}$ $m^2$.