1. The problem states that a 10x8 grid is divided vertically into two halves: the left half (5 columns) painted yellow and the right half (5 columns) painted blue. 2. Then, it says to paint $\frac{1}{5}$ of the entire grid black. 3. First, calculate the total number of squares in the grid: $10 \times 8 = 80$ squares. 4. To find how many squares correspond to $\frac{1}{5}$ of the grid, multiply total squares by $\frac{1}{5}$: $$80 \times \frac{1}{5} = 16$$ 5. So, 16 squares should be painted black. 6. Since the grid is already divided into two halves of 40 squares each (yellow and blue), painting 16 squares black means replacing some of the yellow or blue squares with black. 7. The problem does not specify which half to paint black, so the 16 black squares can be anywhere. Final answer: $16$ squares of the grid should be painted black.