Grid Fraction Problem: Find the Ratio of Shaded Squares to Total Area

Grid Fraction Problems with Visual Area Counting

What is the marked part?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:02 First, find the part that is marked.
00:07 Next, count how much of it is colored.
00:11 Put this number on top as the numerator.
00:15 Now, count the total number of parts in the whole.
00:21 Place this number on the bottom as the denominator.
00:25 And that's how we solve the question.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the marked part?

2

Step-by-step solution

Let's solve this problem step-by-step:

First, examine the grid and count the total number of sections. Observing the grid, there is a total of 6 columns, each representing equal-sized portions along the grid, as evidenced by vertical lines.

Next, count how many of these sections are colored. The entire portion from the first column to the fourth column is colored. This means we have 4 out of 6 sections that are marked red.

We can then express the colored area as a fraction: 46 \frac{4}{6} .

3

Final Answer

46 \frac{4}{6}

Key Points to Remember

Essential concepts to master this topic
  • Grid Analysis: Count total sections by identifying all vertical and horizontal divisions
  • Shaded Counting: Count from left edge: 4 out of 6 columns are shaded
  • Fraction Check: Verify 46 \frac{4}{6} represents shaded area correctly ✓

Common Mistakes

Avoid these frequent errors
  • Miscounting grid sections by ignoring division lines
    Don't count squares instead of sections = wrong denominator! Students often see 6 squares but miss that the grid shows 6 equal columns. Always count the actual divisions shown by the grid lines to find total parts.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

FAQ

Everything you need to know about this question

How do I know if I'm counting the grid sections correctly?

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Look for the vertical lines that divide the rectangle into equal parts. Count these sections, not individual squares. In this problem, there are 6 equal columns created by the vertical divisions.

What if the shaded area doesn't start from the left edge?

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It doesn't matter where the shading starts! Just count how many sections are shaded compared to the total. The position doesn't affect the fraction value.

Should I simplify the fraction 46 \frac{4}{6} ?

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In this case, no! The answer choices are given as sixths, so 46 \frac{4}{6} is the expected form. However, knowing that 46=23 \frac{4}{6} = \frac{2}{3} can help you check your work.

What if I can't see the grid lines clearly?

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Look for the outline around the shaded area - it often shows the boundaries between sections. You can also count by estimating equal divisions across the total width.

How do I avoid confusing rows and columns?

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Focus on the direction of the shading. If the shaded area goes from left to right (like in this problem), count the vertical divisions. If it goes up and down, count horizontal divisions.

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