Fraction Comparison: Identifying Parts Greater Than 1/9

Q: How do I know which sections are painted in the diagram?

Look for sections with shading or color fill. In these diagrams, painted sections appear darker or filled with color, while unpainted sections are just outlined.

Q: Why do all the diagrams have 9 sections?

Having the same number of total sections makes comparison easier! When denominators are equal, you just compare the numerators to see which fraction is larger.

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

Count systematically: go left to right, top to bottom. Count painted sections first, then total sections. Write the fraction as $ \frac{\text{painted}}{\text{total}} $.

Q: How do I compare fractions with the same denominator?

When denominators are the same, the fraction with the larger numerator is bigger. For example: $ \frac{3}{9} > \frac{1}{9} $ because 3 > 1.

Q: Can I simplify the fractions before comparing?

Yes! $ \frac{3}{9} = \frac{1}{3} $ and $ \frac{1}{9} $ stays the same. Then compare: $ \frac{1}{3} $ is clearly larger than $ \frac{1}{9} $.

Fraction Comparison with Visual Models

Choose the way in which the painted part is greater than $\frac{1}{9}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the shapes where the marked part is larger than the given fraction

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

00:08 We'll compare to the given fraction and choose the shapes that are larger than the fraction

00:11 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 way in which the painted part is greater than $\frac{1}{9}$

Step-by-step solution

Let's solve the problem by following these steps:

Step 1: Identify the total and painted sections in each illustration.
Step 2: Calculate the fraction of painted sections.
Step 3: Compare each fraction to $\frac{1}{9}$ .

Now, let's analyze each choice:

Choice 1: The illustration shows one painted section out of 9 total sections, so the fraction is $\frac{1}{9}$ .

Choice 2: The illustration shows three painted sections out of 9 total sections, so the fraction is $\frac{3}{9} = \frac{1}{3}$ .

Choice 3: The illustration shows one painted section out of 9 total sections, which equals $\frac{1}{9}$ .

Choice 2's $\frac{1}{3}$ is greater than $\frac{1}{9}$ since $\frac{1}{3} = \frac{3}{9}$ .

Thus, the configuration in Choice 2 represents a painted part that is greater than $\frac{1}{9}$ .

Therefore, the option with a painted part greater than $\frac{1}{9}$ is Choice 2.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Visual Analysis: Count painted sections and total sections in each diagram
Technique: Convert to common denominators: $\frac{3}{9} = \frac{1}{3}$
Check: Compare numerators when denominators match: $\frac{3}{9} > \frac{1}{9}$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring total sections when counting
Don't just count painted sections = wrong fraction! This ignores the denominator completely. Always count both painted sections (numerator) and total sections (denominator) to form the correct fraction.

Practice Quiz

Test your knowledge with interactive questions

What is the marked part?

FAQ

Everything you need to know about this question

How do I know which sections are painted in the diagram?

Look for sections with shading or color fill. In these diagrams, painted sections appear darker or filled with color, while unpainted sections are just outlined.

Why do all the diagrams have 9 sections?

Having the same number of total sections makes comparison easier! When denominators are equal, you just compare the numerators to see which fraction is larger.

What if I can't see the visual clearly?

Count systematically: go left to right, top to bottom. Count painted sections first, then total sections. Write the fraction as $\frac{\text{painted}}{\text{total}}$ .

How do I compare fractions with the same denominator?

When denominators are the same, the fraction with the larger numerator is bigger. For example: $\frac{3}{9} > \frac{1}{9}$ because 3 > 1.

Can I simplify the fractions before comparing?

Yes! $\frac{3}{9} = \frac{1}{3}$ and $\frac{1}{9}$ stays the same. Then compare: $\frac{1}{3}$ is clearly larger than $\frac{1}{9}$ .

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