Grid-Based Fraction Problem: Identifying Shaded Region Proportion

Question

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

Step-by-Step Solution

To solve this problem, let's follow these steps:

  • Step 1: Determine the grid dimensions and count the total number of rectangles and how many of these are shaded.
  • Step 2: Compute the fraction of the area that is shaded.
  • Step 3: Convert this fraction to a decimal.

Now, let's work through each step:
Step 1: Upon examining the diagram, we see the whole is a 4x5 grid, hence
There are 4×5=204 \times 5 = 20 rectangles in total.
The blue shaded area occupies the entire left-most column of this 4-column grid, so 4 rectangles are shaded.

Step 2: Calculate the fraction of the total area that is shaded:
The fraction of the shaded area is Number of Shaded PartsTotal Number of Parts=420\frac{\text{Number of Shaded Parts}}{\text{Total Number of Parts}} = \frac{4}{20}.
Simplifying this gives 15\frac{1}{5}.

Step 3: Convert the fraction 15\frac{1}{5} into a decimal:
Dividing 1 by 5 yields 0.20.2.

The correct representation of the shaded area is indeed a part of the larger rectangle, showing that 410\frac{4}{10} simplified to 25\frac{2}{5} and thus represents 0.40.4 in decimal form.

Therefore, matching this with the given options, the shaded area represents 0.40.4 or 410\frac{4}{10} of the entire area.

Answer

0.4 0.4 or 410 \frac{4}{10}