Convert Grid Representation to Fraction: Shaded Squares Problem

Q: How do I count the squares without making mistakes?

Go systematically! Count row by row: first row has 4 squares, second row has 4 squares. Total = 8 squares. Then identify how many are shaded (just 1).

Q: Why is the answer not 1/4 since only one square is shaded?

The denominator must be the total number of equal parts, not just the number of rows or columns. Since there are 8 total squares, the answer is $ \frac{1}{8} $, not $ \frac{1}{4} $.

Q: How do I know which part is the numerator and denominator?

Numerator = number of shaded parts (1). Denominator = total number of equal parts (8). Remember: part over whole!

Q: Can fractions from grids be simplified?

Yes! Always check if you can simplify. In this case, $ \frac{1}{8} $ is already in simplest form because 1 and 8 share no common factors other than 1.

Visual Fractions with Grid Models

Write the fraction shown in the drawing:

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Write the mathematical representation of the given fraction

00:03 In black, the number of parts into which the whole is divided (denominator)

00:12 In red, the given number of parts (numerator)

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

Write the fraction shown in the drawing:

Step-by-step solution

To solve this problem, let's analyze the drawing:

The drawing shows a large rectangle divided into 8 smaller squares of equal size, arranged in 2 rows and 4 columns.
One of the squares in the first row is shaded.
Count the total number of equal small squares: 8.
Identify the shaded portion: 1 square is shaded.

Thus, the fraction representing the shaded part of the drawing is:

$\frac{\text{Number of shaded parts}}{\text{Total number of equal parts}} = \frac{1}{8}$

The solution is therefore $\frac{1}{8}$ , which matches choice 2.

Therefore, the solution to the problem is $\frac{1}{8}$ .

Final Answer

$\frac{1}{8}$

Key Points to Remember

Essential concepts to master this topic

Rule: Count total parts and shaded parts in the grid
Technique: Identify 8 total squares with 1 shaded square
Check: Verify by counting each square individually: 1 out of 8 ✓

Common Mistakes

Avoid these frequent errors

Miscounting the total number of parts in the grid
Don't assume the grid has 10 parts because it's arranged in rows = $\frac{1}{10}$ ! This ignores the actual layout of 2 rows × 4 columns. Always count each individual square systematically to get the correct denominator of 8.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction as a mixed number:

$\frac{10}{7}=$

FAQ

Everything you need to know about this question

How do I count the squares without making mistakes?

Go systematically! Count row by row: first row has 4 squares, second row has 4 squares. Total = 8 squares. Then identify how many are shaded (just 1).

Why is the answer not 1/4 since only one square is shaded?

The denominator must be the total number of equal parts, not just the number of rows or columns. Since there are 8 total squares, the answer is $\frac{1}{8}$ , not $\frac{1}{4}$ .

What if the grid was arranged differently?

The fraction would change! If the same 8 squares were arranged as 1 row × 8 columns or 8 rows × 1 column, you'd still get $\frac{1}{8}$ because the total parts remain the same.

How do I know which part is the numerator and denominator?

Numerator = number of shaded parts (1). Denominator = total number of equal parts (8). Remember: part over whole!

Can fractions from grids be simplified?

Yes! Always check if you can simplify. In this case, $\frac{1}{8}$ is already in simplest form because 1 and 8 share no common factors other than 1.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Mixed Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime