What fraction of the flag is shaded?
Understand the Problem
The question is asking to find the fraction of a flag that is shaded versus the total area of the flag. This involves calculating the number of shaded sections and the total sections within the grid.
Answer
The fraction of the flag that is shaded is $\frac{13}{48}$.
Answer for screen readers
The fraction of the flag that is shaded is $\frac{13}{48}$.
Steps to Solve
- Count the total sections in the flag
Count the total number of sections (grid squares) in the flag. The flag consists of a grid of 6 rows and 8 columns.
Total sections:
$$ 6 \times 8 = 48 $$
- Count the shaded sections
Count the number of shaded sections in the flag. The shaded parts form a cross:
- For the horizontal part, there are 8 shaded sections in the middle row.
- For the vertical part, there are 6 shaded sections in the middle column, but the middle section overlaps with the horizontal part.
So, the total shaded sections:
$$ 8 + (6 - 1) = 8 + 5 = 13 $$
- Calculate the fraction shaded
To find the fraction of the flag that is shaded, divide the number of shaded sections by the total sections.
$$ \text{Fraction shaded} = \frac{\text{Shaded sections}}{\text{Total sections}} = \frac{13}{48} $$
The fraction of the flag that is shaded is $\frac{13}{48}$.
More Information
The flag's shading shows a typical cross pattern, often used in various flags around the world, reflecting historical and cultural significance.
Tips
- One common mistake is to double-count overlapping sections. When counting shaded areas that overlap, ensure to avoid including them more than once.
- Another mistake could be miscounting the total numbers in a grid; it’s essential to carefully count both rows and columns.
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