Grid Fraction Problem: Calculate the Blue Shaded Square's Ratio

Fraction Operations with Grid Visual Models

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

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Step-by-step written solution

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1

Understand the problem

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

2

Step-by-step solution

The large square grid is divided into smaller squares. Let's determine how many small squares there are in total.

  • Step 1: Count the number of small squares along one side. From the SVG image, each side seems to have 10 smaller squares (since each section appears uniform and there are grids within both, rows, and columns).

  • Step 2: Calculate the total number of smaller squares in the grid. Since it's a square, the total is 10×10=100 10 \times 10 = 100 small squares.

  • Step 3: Calculate what fraction of the whole one shaded square (the blue one) represents. The shaded area is one of these squares, so it represents 1100 \frac{1}{100} of the entire grid.

Therefore, the shaded area represents 0.01 0.01 or 1100 \frac{1}{100} of the whole grid.

3

Final Answer

0.01 0.01 or 1100 \frac{1}{100}

Key Points to Remember

Essential concepts to master this topic
  • Grid Counting: Count total squares by multiplying rows × columns
  • Technique: One shaded square out of 100 total equals 1100 \frac{1}{100}
  • Check: Verify 1100=0.01 \frac{1}{100} = 0.01 by dividing 1 ÷ 100 ✓

Common Mistakes

Avoid these frequent errors
  • Counting only visible grid lines instead of squares
    Don't count the 11 lines on each side and think there are 11 × 11 = 121 squares! Grid lines create squares between them. Always count the actual square sections: 10 × 10 = 100 squares total.

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 know if it's 10×10 or 11×11 squares?

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Count the spaces between the lines, not the lines themselves! If you see 11 vertical lines, they create 10 columns of squares. Think of it like fence posts - 11 posts make 10 sections.

Why can the answer be written as both 0.01 and 1/100?

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These are just different forms of the same number! 1100 \frac{1}{100} is the fraction form, and 0.01 is the decimal form. You can convert by dividing: 1 ÷ 100 = 0.01.

What if multiple squares were shaded?

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Just count the shaded squares! If 3 squares were blue, the answer would be 3100 \frac{3}{100} or 0.03. The numerator changes but the denominator stays 100.

How do I make sure I'm counting the grid correctly?

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Count systematically: Count squares in one complete row, then count how many rows there are. Multiply these numbers together for the total.

Can I simplify 1/100 further?

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No, 1100 \frac{1}{100} is already in lowest terms because 1 and 100 share no common factors other than 1. This fraction cannot be simplified.

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