Identify the Shape with Exactly 2/5 Shaded Area

Q: How do I know if all segments are equal?

Look at the grid lines or divisions in the shape. Equal segments will have the same size and spacing. If the shape is divided into squares or rectangles of identical dimensions, then they're equal parts!

Q: What if I count wrong and get the wrong fraction?

Double-check by counting slowly: first count all segments (this becomes your denominator), then count only the painted ones (this becomes your numerator). Write as painted/total.

Q: Can a shape have more than one correct fraction representation?

No! Each visual model represents exactly one fraction. However, equivalent fractions like $ \frac{2}{5} $ and $ \frac{4}{10} $ would look different because they need different total segments.

Q: Why does the painted area need to be exactly 2/5?

The question asks for a specific fraction, so you need to find the shape where painted parts ÷ total parts equals exactly $ \frac{2}{5} $. Other fractions like $ \frac{1}{5} $ or $ \frac{3}{5} $ won't match!

Fraction Representation with Visual Models

Choose the shape in which the painted part is $\frac{2}{5}$

❤️ 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 Choose the figure where the colored part equals the given fraction

00:03 In each figure, we'll count the colored amount and divide by the number of parts

00:09 We'll compare to the given fraction and choose the figure that equals the given fraction

00:13 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

Choose the shape in which the painted part is $\frac{2}{5}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: For each shape, count the total number of equal segments.
Step 2: Count the number of segments that are painted.
Step 3: Calculate the fraction of the painted area by dividing the number of painted segments by the total number of segments.
Step 4: Identify the shape where the fraction of painted area is $\frac{2}{5}$ .

Now, let's work through each step:

Step 1: Let's examine the shapes given in the choices.

Step 2: For choice 3, the shape has 5 equal segments. Two of these segments are painted.

Step 3: Calculate the fraction for choice 3:

$\frac{\text{Number of painted parts}}{\text{Total number of parts}} = \frac{2}{5}$

Step 4: Therefore, choice 3 is the correct shape with $\frac{2}{5}$ of the area painted.

Therefore, the solution to the problem is the shape from choice 3, where $\frac{2}{5}$ of the area is painted.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Count painted parts over total equal parts to find fraction
Technique: For $\frac{2}{5}$ , find shape with 2 painted out of 5 total
Check: Verify painted segments equal 2 and total segments equal 5 ✓

Common Mistakes

Avoid these frequent errors

Counting unequal segments as equal parts
Don't count segments of different sizes as equal parts = wrong fraction! This creates incorrect denominators because fractions require equal-sized parts. Always ensure all segments are identical in size 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 if all segments are equal?

Look at the grid lines or divisions in the shape. Equal segments will have the same size and spacing. If the shape is divided into squares or rectangles of identical dimensions, then they're equal parts!

What if I count wrong and get the wrong fraction?

Double-check by counting slowly: first count all segments (this becomes your denominator), then count only the painted ones (this becomes your numerator). Write as painted/total.

Can a shape have more than one correct fraction representation?

No! Each visual model represents exactly one fraction. However, equivalent fractions like $\frac{2}{5}$ and $\frac{4}{10}$ would look different because they need different total segments.

Why does the painted area need to be exactly 2/5?

The question asks for a specific fraction, so you need to find the shape where painted parts ÷ total parts equals exactly $\frac{2}{5}$ . Other fractions like $\frac{1}{5}$ or $\frac{3}{5}$ won't match!

What if none of the shapes look like they have 2/5 painted?

Count carefully for each option! Sometimes the painted sections might be separated (like 1 painted + 1 painted = 2 total painted). Focus on the total count, not whether painted parts are connected.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Simple 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