Calculate the Area: Finding the Value of One Orange Shaded Unit Square

Fraction Areas with Grid Visualization

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 these steps:

  • Step 1: Identify the total number of divisions in the grid.
  • Step 2: Count the number of shaded divisions.
  • Step 3: Calculate the fraction of the shaded area relative to the total.

Now, let's work through each step:
Step 1: The grid is divided into 10 equal vertical columns.
Step 2: Of these columns, 1 column is shaded.
Step 3: Since there are 10 columns in total, the shaded area represents 110\frac{1}{10} of the total area.

Finally, the fraction 110\frac{1}{10} can be expressed as the decimal 0.10.1.

Therefore, the numerical value of the shaded area is 0.10.1.

3

Final Answer

0.1

Key Points to Remember

Essential concepts to master this topic
  • Grid Analysis: Count total divisions and shaded divisions first
  • Technique: Express as fraction then convert: 110=0.1 \frac{1}{10} = 0.1
  • Check: Verify decimal makes sense: 1 out of 10 equals 0.1 ✓

Common Mistakes

Avoid these frequent errors
  • Counting squares instead of the actual shaded portion
    Don't count individual grid squares when only part of the area is shaded = wrong fraction! This leads to answers like 1 instead of 0.1. Always identify what fraction of the total area is actually shaded.

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 is the answer 0.1 and not just 1?

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The answer represents the fraction of the total area that is shaded, not the number of shaded sections. Since 1 out of 10 columns is shaded, that's 110=0.1 \frac{1}{10} = 0.1 of the whole area.

How do I convert fractions to decimals quickly?

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Divide the numerator by the denominator! For 110 \frac{1}{10} , divide 1 ÷ 10 = 0.1. Remember: tenths become one decimal place, hundredths become two decimal places.

What if the grid had different divisions?

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The same process applies! Count the total divisions, count the shaded divisions, then write as a fraction and convert to decimal.

Can I leave my answer as a fraction?

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While 110 \frac{1}{10} is mathematically correct, the question asks for the numerical value, which typically means decimal form: 0.1.

How do I know I'm reading the grid correctly?

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Look for the colored/shaded region and count how many equal parts it covers. Then count the total number of equal parts in the entire grid.

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