Fraction Comparison: Identifying Parts Greater Than 2/5

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

Look for the shaded or colored sections in each visual. The painted parts will be a different color (usually red or darker) than the unpainted parts.

Q: Why do all the options have 5 boxes?

Since we're comparing to $ \frac{2}{5} $, all diagrams use 5 equal parts to make comparison easier. This way, we only need to count painted parts!

Q: What if two fractions have the same denominator?

When denominators are equal, just compare the numerators! The fraction with the larger numerator is greater. For example: $ \frac{3}{5} > \frac{2}{5} $ because 3 > 2.

Q: Can I convert these to decimals to compare?

Yes, but it's not necessary here! Since all fractions have denominator 5, comparing numerators is faster: $ \frac{1}{5} = 0.2 $, $ \frac{2}{5} = 0.4 $, $ \frac{3}{5} = 0.6 $

Q: What does 'greater than' mean with fractions?

Greater than means the fraction represents a larger portion of the whole. $ \frac{3}{5} $ is greater than $ \frac{2}{5} $ because 3 painted parts is more than 2 painted parts.

Fraction Comparison with Visual Representations

Choose the way in which the painted part is greater than $\frac{2}{5}$

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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

00:06 We'll compare to the given fraction and choose the shapes larger than the 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 way in which the painted part is greater than $\frac{2}{5}$

Step-by-step solution

To solve the problem, we need to determine which option displays parts painted more than $\frac{2}{5}$ .

Step 1: Each option shows an arrangement divided into 5 boxes. We seek parts painted red exceeding $\frac{2}{5}$ .
Step 2: Analyze each visual:
-- Option 1, 1 block painted out of 5, fraction = $\frac{1}{5}$ .
-- Option 2, 2 out of 5 blocks painted, fraction = $\frac{2}{5}$ .
-- Option 3, 3 blocks painted out of 5, fraction = $\frac{3}{5}$ .
-- Option 4, 1 block painted out of 5, fraction = $\frac{1}{5}$ .
Step 3: Compare $\frac{3}{5}$ in Option 3 with $\frac{2}{5}$ .

Therefore, the only choice where the painted part is greater than $\frac{2}{5}$ is Option 3.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Count painted parts and compare to total equal parts
Technique: Convert visuals to fractions: 3 painted out of 5 = $\frac{3}{5}$
Check: Compare numerators when denominators are equal: $\frac{3}{5} > \frac{2}{5}$ because 3 > 2 ✓

Common Mistakes

Avoid these frequent errors

Counting total boxes instead of painted ones
Don't count all 5 boxes as the fraction = $\frac{5}{5}$ ! This ignores which parts are actually painted. Always count only the painted (shaded) parts as your numerator and total equal parts as denominator.

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 parts are painted in the diagram?

Look for the shaded or colored sections in each visual. The painted parts will be a different color (usually red or darker) than the unpainted parts.

Why do all the options have 5 boxes?

Since we're comparing to $\frac{2}{5}$ , all diagrams use 5 equal parts to make comparison easier. This way, we only need to count painted parts!

What if two fractions have the same denominator?

When denominators are equal, just compare the numerators! The fraction with the larger numerator is greater. For example: $\frac{3}{5} > \frac{2}{5}$ because 3 > 2.

Can I convert these to decimals to compare?

Yes, but it's not necessary here! Since all fractions have denominator 5, comparing numerators is faster: $\frac{1}{5} = 0.2$ , $\frac{2}{5} = 0.4$ , $\frac{3}{5} = 0.6$

What does 'greater than' mean with fractions?

Greater than means the fraction represents a larger portion of the whole. $\frac{3}{5}$ is greater than $\frac{2}{5}$ because 3 painted parts is more than 2 painted parts.

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