1. The problem is to paint \(\frac{1}{4}\) of a grid consisting of 100 equal square cells arranged in 10 rows and 10 columns.\n\n2. To find how many cells to paint, we use the formula for a fraction of a whole: \n$$\text{Number of cells to paint} = \text{Total cells} \times \text{Fraction}$$\n\n3. Here, the total number of cells is 100 and the fraction is \(\frac{1}{4}\). So, \n$$\text{Number of cells to paint} = 100 \times \frac{1}{4}$$\n\n4. Multiply 100 by \(\frac{1}{4}\): \n$$100 \times \frac{1}{4} = \frac{100}{4} = 25$$\n\n5. Therefore, you need to paint 25 cells out of the 100 cells in the grid to cover \(\frac{1}{4}\) of the grid.\n\n6. You can choose any 25 cells to paint, but a common way is to paint 2 full rows and half of the third row (since each row has 10 cells, 2 rows = 20 cells, plus 5 cells in the next row = 25 cells).