Compare Fractions: Find the Symbol Between 2/5 and 6/5

Q: Why can I just compare the numerators?

When fractions have the same denominator, they're divided into equal-sized pieces. So $ \frac{2}{5} $ means 2 pieces and $ \frac{6}{5} $ means 6 pieces of the same size. More pieces = bigger fraction!

Q: What if the denominators were different?

If denominators are different, you need to find a common denominator first. Convert both fractions so they have the same denominator, then compare numerators.

Q: Can a fraction be greater than 1?

Yes! When the numerator is larger than the denominator, the fraction is greater than 1. Here, $ \frac{6}{5} = 1\frac{1}{5} $, which equals 1.2.

Q: How do I remember which symbol to use?

Think of the symbol as a hungry mouth that always wants to eat the bigger number! The open side points to the larger fraction: \( \frac{2}{5} .

Q: Should I convert to decimals to check?

Converting to decimals is a great way to double-check your work! $ \frac{2}{5} = 0.4 $ and $ \frac{6}{5} = 1.2 $, so 0.4

Fraction Comparison with Same Denominators

Fill in the missing sign:

$\frac{2}{5}☐\frac{6}{5}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:03 The denominators are equal

00:09 When the denominator is equal, the larger numerator is the larger 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

Fill in the missing sign:

$\frac{2}{5}☐\frac{6}{5}$

Step-by-step solution

To solve this problem, we need to compare two fractions with the same denominator and determine the appropriate comparison sign:

Step 1: Notice that both fractions, $\frac{2}{5}$ and $\frac{6}{5}$ , have the same denominator, $5$ .
Step 2: Focus on comparing the numerators of both fractions: $2$ and $6$ .
Step 3: Since $2$ is less than $6$ , it follows that the fraction $\frac{2}{5}$ is less than $\frac{6}{5}$ .

Therefore, the correct comparison sign to fill in the blank is $<$ .

The missing sign is $<$ .

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare numerators when denominators are equal
Technique: Since 2 < 6, then $\frac{2}{5} < \frac{6}{5}$
Check: Convert to decimals: 0.4 < 1.2 confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Comparing denominators instead of numerators
Don't focus on the denominators when they're the same = ignoring the actual size difference! The denominators tell you the pieces are the same size, but the numerators tell you how many pieces you have. Always compare the numerators when denominators are equal.

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

$\frac{5}{9}☐\frac{3}{9}$

FAQ

Everything you need to know about this question

Why can I just compare the numerators?

When fractions have the same denominator, they're divided into equal-sized pieces. So $\frac{2}{5}$ means 2 pieces and $\frac{6}{5}$ means 6 pieces of the same size. More pieces = bigger fraction!

What if the denominators were different?

If denominators are different, you need to find a common denominator first. Convert both fractions so they have the same denominator, then compare numerators.

Can a fraction be greater than 1?

Yes! When the numerator is larger than the denominator, the fraction is greater than 1. Here, $\frac{6}{5} = 1\frac{1}{5}$ , which equals 1.2.

How do I remember which symbol to use?

Think of the symbol as a hungry mouth that always wants to eat the bigger number! The open side points to the larger fraction: $\frac{2}{5} < \frac{6}{5}$ .

Should I convert to decimals to check?

Converting to decimals is a great way to double-check your work! $\frac{2}{5} = 0.4$ and $\frac{6}{5} = 1.2$ , so 0.4 < 1.2 confirms our answer.

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