Grid Fraction Problem: Identifying the 3/7 Shaded Region

Q: How do I know which direction to count the sections?

Look at the shaded region - it shows you the pattern! In this problem, the shading covers complete vertical strips, so count the vertical divisions.

Q: What if the shaded area doesn't cover complete sections?

The shaded area should cover whole sections for basic fraction problems. If it covers partial sections, you'll need to break those down into smaller equal parts first.

Q: Why is my answer different when I count rows?

Because there's only 1 row in this grid! The equal divisions are vertical columns. Always identify the direction of equal divisions before counting.

Q: How can I double-check my fraction answer?

Add up all sections: shaded + unshaded = total. For $ \frac{3}{7} $, check that 3 + 4 = 7 sections total!

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

Look for the boundary lines around the shaded area - they show you where sections begin and end. Count carefully by following each vertical line from top to bottom.

Visual Fractions with Grid Counting

What is the marked part?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the marked part

00:03 Let's count the colored amount

00:06 Let's put this amount in the numerator

00:10 Now let's count the number of parts that divide the whole

00:15 Let's put this number in the denominator

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the marked part?

Step-by-step solution

To solve this problem, we will count the total number of equal sections in the grid and the number of these sections that the marked area covers.

Step 1: Determine Total Sections. The grid is divided into several vertical sections. By examining the grid lines, we see that the total number of vertical sections is 7.
Step 2: Determine Marked Sections. The marked (colored) part spans 3 of these vertical sections within the total grid.
Step 3: Compute Fraction. The fraction of the total area covered by the marked part is calculated as the number of marked sections divided by the total number of sections: $\frac{3}{7}$ .

Therefore, the fraction of the area that is marked is $\frac{3}{7}$ .

Final Answer

$\frac{3}{7}$

Key Points to Remember

Essential concepts to master this topic

Total Sections: Count all equal divisions in the entire grid
Technique: Count shaded sections: 3 out of 7 total sections
Check: Verify shaded sections plus unshaded sections equal total: 3 + 4 = 7 ✓

Common Mistakes

Avoid these frequent errors

Counting rows instead of the correct divisions
Don't count horizontal rows when the problem shows vertical divisions = wrong denominator! The grid has 1 row but 7 vertical sections. Always identify which direction the equal divisions run before counting.

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 which direction to count the sections?

Look at the shaded region - it shows you the pattern! In this problem, the shading covers complete vertical strips, so count the vertical divisions.

What if the shaded area doesn't cover complete sections?

The shaded area should cover whole sections for basic fraction problems. If it covers partial sections, you'll need to break those down into smaller equal parts first.

Why is my answer different when I count rows?

Because there's only 1 row in this grid! The equal divisions are vertical columns. Always identify the direction of equal divisions before counting.

How can I double-check my fraction answer?

Add up all sections: shaded + unshaded = total. For $\frac{3}{7}$ , check that 3 + 4 = 7 sections total!

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

Look for the boundary lines around the shaded area - they show you where sections begin and end. Count carefully by following each vertical line from top to bottom.

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