Grid-Based Fraction Problem: Identifying Shaded Region Proportion

Fraction Visualization with Grid Models

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
1

Understand the problem

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

2

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.

3

Final Answer

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

Key Points to Remember

Essential concepts to master this topic
  • Grid Analysis: Count shaded parts and total parts systematically
  • Fraction Formation: Write as 410 \frac{4}{10} then simplify to 25 \frac{2}{5}
  • Decimal Check: Convert 25=0.4 \frac{2}{5} = 0.4 by division ✓

Common Mistakes

Avoid these frequent errors
  • Miscounting grid sections or confusing rows with columns
    Don't count 5 shaded parts when there are clearly 4 = 510=0.5 \frac{5}{10} = 0.5 ! This happens when students rush or misidentify the shaded region. Always count methodically: identify the shaded column first, then count how many rectangles it contains.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

How do I know which parts are shaded in the grid?

+

Look for the blue-colored rectangles! In this problem, the entire leftmost column is shaded blue, which means 4 out of 10 total rectangles are shaded.

Why does the answer have two forms: fraction and decimal?

+

Both 410 \frac{4}{10} and 0.4 represent the same value! Fractions show the part-to-whole relationship clearly, while decimals are useful for calculations and comparisons.

Do I need to simplify the fraction?

+

While 410 \frac{4}{10} is correct, simplifying to 25 \frac{2}{5} shows you understand equivalent fractions. Both forms are acceptable answers!

What if the grid looks different or more complex?

+

The same method works: count total parts, count shaded parts, write the fraction. Whether it's a 3×4 grid or 5×6 grid, always use shaded partstotal parts \frac{\text{shaded parts}}{\text{total parts}} .

How can I double-check my counting?

+

Try counting in different ways: count by rows, then by columns, or number each rectangle 1, 2, 3... This helps catch counting mistakes and builds confidence!

🌟 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

More Questions

Click on any question to see the complete solution with step-by-step explanations