Compare Painted Regions: Finding Areas Greater Than 1/3

Q: How do I know which sections are painted?

Look for the shaded or colored regions - they're usually filled with red, blue, or another color. The painted sections stand out from the white or unshaded areas.

Q: What if the figure is divided into different numbers of sections?

Count carefully! Each choice might have different total sections. Always write your fraction as painted sections ÷ total sections for each figure separately.

Q: How do I compare fractions like 2/3 and 1/3?

When fractions have the same denominator, just compare the numerators! Since 2 > 1, we know $ \frac{2}{3} > \frac{1}{3} $.

Q: What if I need to compare fractions with different denominators?

Convert them to have the same denominator first, or change both to decimals. For example: $ \frac{1}{2} = 0.5 $ and $ \frac{1}{3} ≈ 0.33 $.

Q: Can the painted area equal exactly 1/3?

Yes, but the question asks for areas greater than $ \frac{1}{3} $. If a figure shows exactly $ \frac{1}{3} $ painted, it doesn't meet the "greater than" requirement.

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

00:12 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

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Understand the problem

Choose the way in which the painted part is greater than $\frac{1}{3}$

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Step-by-step solution

To solve this problem, we'll visually evaluate the proportion of the painted area relative to the entire space for each choice and compare it with $\frac{1}{3}$ .

First, observe each provided choice, ensuring painted portions are clearly defined.
Count how many sections each graphic is divided into. The total sections represent the whole area.
Determine the number of sections painted in red. This represents the painted area.
Calculate the fraction of the painted area by dividing the number of painted sections by the total number of sections.
Compare these fractions with $\frac{1}{3}$ :

Choice 1: 1 section painted out of 3 total sections, $\frac{1}{3}$
Choice 2: 1 section painted out of 3 total sections, $\frac{1}{3}$
Choice 3: 2 sections painted out of 3 total sections, $\frac{2}{3}$

According to the calculations, Choice 3 results in a painted fraction of $\frac{2}{3}$ , which is greater than $\frac{1}{3}$ . Therefore, Choice 3 has the painted part greater than $\frac{1}{3}$ .

Hence, the way in which the painted part is greater than $\frac{1}{3}$ is represented by Choice 3.

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Final Answer

Key Points to Remember

Essential concepts to master this topic

Visual Analysis: Count painted sections versus total sections in each figure
Technique: Convert to fractions: 2 painted out of 3 total = $\frac{2}{3}$
Check: Compare fractions: $\frac{2}{3} > \frac{1}{3}$ since 2 > 1 ✓

Common Mistakes

Avoid these frequent errors

Confusing painted area with unpainted area
Don't count the white (unpainted) sections as the painted area = wrong fraction! Students often focus on what's NOT painted instead of what IS painted. Always identify and count only the shaded/colored sections.

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 sections are painted?

+

Look for the shaded or colored regions - they're usually filled with red, blue, or another color. The painted sections stand out from the white or unshaded areas.

What if the figure is divided into different numbers of sections?

+

Count carefully! Each choice might have different total sections. Always write your fraction as painted sections ÷ total sections for each figure separately.

How do I compare fractions like 2/3 and 1/3?

+

When fractions have the same denominator, just compare the numerators! Since 2 > 1, we know $\frac{2}{3} > \frac{1}{3}$ .

What if I need to compare fractions with different denominators?

+

Convert them to have the same denominator first, or change both to decimals. For example: $\frac{1}{2} = 0.5$ and $\frac{1}{3} ≈ 0.33$ .

Can the painted area equal exactly 1/3?

+

Yes, but the question asks for areas greater than $\frac{1}{3}$ . If a figure shows exactly $\frac{1}{3}$ painted, it doesn't meet the "greater than" requirement.

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Compare Painted Regions: Finding Areas Greater Than 1/3

Fraction Comparison with Visual Models

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