What fraction of the flag shown below is shaded? Use the squares to help you and give your answer in its simplest form.

Steps to Solve

1. Identify Total Area of the Flag

The flag is represented in a grid format. Count the total number of squares in the flag to find the total area.

In this case, the flag is a $6$ by $4$ grid:

$$ \text{Total Area} = 6 \times 4 = 24 \text{ squares} $$

2. Identify Shaded Area

Count the number of shaded squares in the flag. The red cross consists of:

• 2 shaded squares vertically in the center column.
• 2 shaded squares horizontally in the middle row.

Thus, the total shaded area is:

$$ \text{Shaded Area} = 2 + 2 = 4 \text{ squares} $$

3. Calculate the Fraction of the Shaded Area

To find the fraction of the shaded area, use the following formula:

$$ \text{Fraction} = \frac{\text{Shaded Area}}{\text{Total Area}} $$

Substituting the values:

$$ \text{Fraction} = \frac{4}{24} $$

4. Simplify the Fraction

Now, simplify the fraction:

To reduce $\frac{4}{24}$, divide both the numerator and the denominator by their greatest common divisor, which is $4$:

$$ \frac{4 \div 4}{24 \div 4} = \frac{1}{6} $$