Compare Fractions: Find the Missing Symbol Between 6/7 and 3/7

Q: Why can I ignore the denominators when they're the same?

When fractions have the same denominator, you're comparing equal-sized pieces! $ \frac{6}{7} $ means 6 pieces of size 1/7, while $ \frac{3}{7} $ means 3 pieces of the same size. More pieces = bigger fraction!

Q: What if the denominators were different?

With different denominators like $ \frac{6}{7} $ and $ \frac{3}{5} $, you'd need to find a common denominator first, then compare numerators. Same-sized pieces make comparison easy!

Q: How can I visualize this comparison?

Picture a pizza cut into 7 equal slices. $ \frac{6}{7} $ means you have 6 slices, while $ \frac{3}{7} $ means you have only 3 slices. Obviously 6 slices is more than 3 slices!

Q: Is there a quick way to double-check my answer?

Yes! Convert both fractions to decimals: $ \frac{6}{7} ≈ 0.857 $ and $ \frac{3}{7} ≈ 0.429 $. Since 0.857 > 0.429, you know $ \frac{6}{7} > \frac{3}{7} $ is correct!

Q: What if both numerators were the same?

If numerators are equal (like $ \frac{4}{7} $ and $ \frac{4}{7} $), then the fractions are equal, so you'd use the = symbol instead of > or

Fraction Comparison with Common Denominators

Fill in the missing sign:

$\frac{6}{7}☐\frac{3}{7}$

❤️ 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 correct sign

00:03 The denominator is equal

00:07 When the denominator is equal, the larger numerator is the larger 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

Understand the problem

Fill in the missing sign:

$\frac{6}{7}☐\frac{3}{7}$

Step-by-step solution

To solve this problem, follow these steps:

Identify the two fractions: $\frac{6}{7}$ and $\frac{3}{7}$ .
Since both fractions have a common denominator, compare the numerators directly: 6 and 3.
Determine that the numerator 6 is greater than 3.
Based on this comparison, the fraction $\frac{6}{7}$ is greater than $\frac{3}{7}$ .
Thus, the correct sign to fill in the blank is $>$ .

The correct answer to the problem is $>$ .

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators are equal, compare the numerators directly
Technique: Since 6 > 3, then $\frac{6}{7} > \frac{3}{7}$
Check: Convert to decimals: 6÷7 = 0.857... and 3÷7 = 0.428... ✓

Common Mistakes

Avoid these frequent errors

Comparing denominators instead of numerators
Don't look at the denominators when they're the same = wrong comparison! Both fractions have 7 in the denominator, so this doesn't help determine which is larger. Always compare the numerators when denominators are equal.

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

$\frac{5}{25}☐\frac{1}{5}$

FAQ

Everything you need to know about this question

Why can I ignore the denominators when they're the same?

When fractions have the same denominator, you're comparing equal-sized pieces! $\frac{6}{7}$ means 6 pieces of size 1/7, while $\frac{3}{7}$ means 3 pieces of the same size. More pieces = bigger fraction!

What if the denominators were different?

With different denominators like $\frac{6}{7}$ and $\frac{3}{5}$ , you'd need to find a common denominator first, then compare numerators. Same-sized pieces make comparison easy!

How can I visualize this comparison?

Picture a pizza cut into 7 equal slices. $\frac{6}{7}$ means you have 6 slices, while $\frac{3}{7}$ means you have only 3 slices. Obviously 6 slices is more than 3 slices!

Is there a quick way to double-check my answer?

Yes! Convert both fractions to decimals: $\frac{6}{7} ≈ 0.857$ and $\frac{3}{7} ≈ 0.429$ . Since 0.857 > 0.429, you know $\frac{6}{7} > \frac{3}{7}$ is correct!

What if both numerators were the same?

If numerators are equal (like $\frac{4}{7}$ and $\frac{4}{7}$ ), then the fractions are equal, so you'd use the = symbol instead of > or <.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with 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