Calculate the Area: Finding the Value of an Orange-Shaded Grid Region

Fractional Area with Grid Counting

Determine the numerical value of the shaded area:

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Determine the numerical value of the shaded area:

2

Step-by-step solution

To solve this problem, we'll follow a few simple steps to calculate the shaded area by counting strips and converting to a decimal:

  • Step 1: Identify the total number of vertical strips in the entire rectangle. From the diagram, there are 10 strips in total.
  • Step 2: Count the number of shaded vertical strips. According to the diagram, 5 strips are shaded.
  • Step 3: Write the fraction of the shaded area relative to the total area. The fraction is 510\frac{5}{10}.
  • Step 4: Simplify the fraction, which is already simplified, and then convert it to a decimal. 510=0.5\frac{5}{10} = 0.5.

Therefore, the solution to the problem is 0.5 0.5 .

3

Final Answer

0.5

Key Points to Remember

Essential concepts to master this topic
  • Grid Method: Count shaded strips and divide by total strips
  • Technique: Convert 510 \frac{5}{10} to decimal by dividing 5 ÷ 10 = 0.5
  • Check: Verify 5 out of 10 strips are shaded visually ✓

Common Mistakes

Avoid these frequent errors
  • Counting individual grid squares instead of strips
    Don't count tiny squares within each strip = overcomplicated counting and wrong totals! This makes the problem much harder than needed. Always count the vertical strips as whole units to find the fraction.

Practice Quiz

Test your knowledge with interactive questions

Determine the numerical value of the shaded area:

FAQ

Everything you need to know about this question

Why do I count strips instead of individual squares?

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Counting strips is much simpler and more accurate! Each strip represents the same fractional part, so you just need to count how many strips are shaded versus the total.

How do I convert the fraction to a decimal?

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Divide the numerator by the denominator: 510=5÷10=0.5 \frac{5}{10} = 5 ÷ 10 = 0.5 . You can also recognize that tenths are easy decimals!

What if the shaded area doesn't line up perfectly with strips?

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In this problem, the shaded region does align perfectly with whole strips. If it didn't, you'd need to count partial strips as fractions.

Can I leave my answer as a fraction?

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The question asks for a numerical value, which typically means decimal form. However, 12 \frac{1}{2} and 0.5 represent the same value!

How do I know I counted the strips correctly?

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Look at the diagram carefully! The orange shading covers exactly half the rectangle - from the left edge to the middle vertical line. That's 5 out of 10 strips.

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