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

Q: How do I count the grid squares accurately?

Count the vertical lines and horizontal lines carefully. If there are 11 vertical lines, that creates 10 columns. If there are 11 horizontal lines, that creates 10 rows. So you have 10 × 10 = 100 total squares.

Q: Why is the answer both a fraction AND a decimal?

They're just different ways to express the same value! $ \frac{8}{100} $ and 0.08 both mean 8 out of 100 parts. Fractions show the exact relationship, while decimals are useful for calculations.

Q: What if I counted the shaded area wrong?

Look carefully at the blue shaded region. Count each individual square that's completely filled with color. In this grid, there's one complete row of 8 shaded squares at the top.

Q: Do I need to simplify the fraction 8/100?

While $ \frac{8}{100} $ can simplify to $ \frac{2}{25} $, the question asks for the fraction of the whole. Since the grid has 100 squares, 8/100 is actually the clearest answer as it directly shows the relationship.

Fraction Representation with Visual Grid Analysis

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

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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 $5 \times 10$ 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 $\frac{\text{number of shaded squares}}{\text{total number of squares}} = \frac{8}{100}$ .
Step 4: Convert Fraction to Decimal.
The fractional representation $\frac{8}{100}$ can also be expressed as a decimal, $0.08$ .

Therefore, the shaded area represents $\frac{8}{100}$ or $0.08$ of the whole grid.

Final Answer

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

Key Points to Remember

Essential concepts to master this topic

Grid Analysis: Count total squares first, then identify shaded squares
Fraction Setup: Write as shaded squares over total squares: $\frac{8}{100}$
Verification: Convert to decimal 0.08 and check it matches visual proportion ✓

Common Mistakes

Avoid these frequent errors

Miscounting the grid dimensions
Don't assume the grid is 5×10 without careful counting = wrong denominator! Students often miscount rows or columns, leading to fractions like 8/50 instead of 8/100. Always count both dimensions systematically and multiply to find total squares.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{5}{100}=$

FAQ

Everything you need to know about this question

How do I count the grid squares accurately?

Count the vertical lines and horizontal lines carefully. If there are 11 vertical lines, that creates 10 columns. If there are 11 horizontal lines, that creates 10 rows. So you have 10 × 10 = 100 total squares.

Why is the answer both a fraction AND a decimal?

They're just different ways to express the same value! $\frac{8}{100}$ and 0.08 both mean 8 out of 100 parts. Fractions show the exact relationship, while decimals are useful for calculations.

What if I counted the shaded area wrong?

Look carefully at the blue shaded region. Count each individual square that's completely filled with color. In this grid, there's one complete row of 8 shaded squares at the top.

Do I need to simplify the fraction 8/100?

While $\frac{8}{100}$ can simplify to $\frac{2}{25}$ , the question asks for the fraction of the whole. Since the grid has 100 squares, 8/100 is actually the clearest answer as it directly shows the relationship.

How can I check if my visual counting is correct?

Use the decimal form! 0.08 means 8%, which should look like a very small portion of the whole grid. If your shaded area looks like much more than 8%, recount your squares.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime