Find the Fraction: Calculating Shaded Region in a 10x10 Grid

Question

How much of the whole does the shaded area (blue) represent?

Step-by-Step Solution

To solve this problem, we will determine the fraction of the grid that is shaded by following these steps:

  • Step 1: Determine the Layout of the Grid.
    The grid is divided into 5×105 \times 10 smaller squares (5 rows and 10 columns), resulting in a total of 50 squares.

  • Step 2: Count the Shaded Squares.
    The top row, which is fully shaded, consists of 8 shaded squares.

  • Step 3: Calculate the Fraction of the Shaded Area.
    The fraction that represents the shaded area is number of shaded squarestotal number of squares=8100\frac{\text{number of shaded squares}}{\text{total number of squares}} = \frac{8}{100}.

  • Step 4: Convert Fraction to Decimal.
    The fractional representation 8100\frac{8}{100} can also be expressed as a decimal, 0.080.08.

Therefore, the shaded area represents 8100\frac{8}{100} or 0.080.08 of the whole grid.

Answer

8100 \frac{8}{100} or 0.08 0.08