Compare Fractions: Find the Symbol Between 4/7 and 1/7

Q: Why can I compare numerators directly when denominators are the same?

When denominators are the same, you're comparing equal-sized pieces. Having 4 pieces out of 7 is clearly more than having 1 piece out of 7!

Q: What if the denominators were different?

If denominators are different, you'd need to find a common denominator first. But since both fractions have denominator 7, you can compare directly!

Q: How do I remember which symbol to use?

Think of the symbols as arrows pointing to the smaller number. Since 4 > 1, the arrow points from 4 toward 1, giving us $ \frac{4}{7} > \frac{1}{7} $.

Q: Can I visualize this to make sure?

Yes! Imagine a pizza cut into 7 slices. $ \frac{4}{7} $ means 4 slices, while $ \frac{1}{7} $ means 1 slice. Clearly, 4 slices is more than 1 slice!

Q: What if I accidentally use the wrong symbol?

No worries! Just remember: the bigger side of the symbol (>) points to the bigger number. So $ \frac{4}{7} > \frac{1}{7} $ is correct because 4 is bigger than 1.

Comparing Fractions with Same Denominators

Fill in the missing symbol:

$\frac{4}{7}☐\frac{1}{7}$

❤️ 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

00:09 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 symbol:

$\frac{4}{7}☐\frac{1}{7}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given fractions, $\frac{4}{7}$ and $\frac{1}{7}$ .
Step 2: Note that both fractions share the same denominator of 7.
Step 3: Compare the numerators of the fractions, 4 and 1.

Now, let's work through each step:
Step 1: The problem provides us with the fractions $\frac{4}{7}$ and $\frac{1}{7}$ .
Step 2: We can compare the numerators directly since the denominators are the same. The numerators are 4 and 1, respectively.
Step 3: Since 4 is greater than 1, $\frac{4}{7}$ is greater than $\frac{1}{7}$ .

Therefore, the correct comparison symbol to fill in the blank is $>$ .

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Same Denominators: Compare numerators directly when denominators are identical
Technique: Since 4 > 1, then $\frac{4}{7} > \frac{1}{7}$
Check: Verify by thinking: 4 parts out of 7 is more than 1 part out of 7 ✓

Common Mistakes

Avoid these frequent errors

Comparing denominators instead of numerators
Don't compare the denominators (7 = 7) and conclude the fractions are equal! This ignores the numerators completely. Always compare numerators when denominators are the same.

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 compare numerators directly when denominators are the same?

When denominators are the same, you're comparing equal-sized pieces. Having 4 pieces out of 7 is clearly more than having 1 piece out of 7!

What if the denominators were different?

If denominators are different, you'd need to find a common denominator first. But since both fractions have denominator 7, you can compare directly!

How do I remember which symbol to use?

Think of the symbols as arrows pointing to the smaller number. Since 4 > 1, the arrow points from 4 toward 1, giving us $\frac{4}{7} > \frac{1}{7}$ .

Can I visualize this to make sure?

Yes! Imagine a pizza cut into 7 slices. $\frac{4}{7}$ means 4 slices, while $\frac{1}{7}$ means 1 slice. Clearly, 4 slices is more than 1 slice!

What if I accidentally use the wrong symbol?

No worries! Just remember: the bigger side of the symbol (>) points to the bigger number. So $\frac{4}{7} > \frac{1}{7}$ is correct because 4 is bigger than 1.

🌟 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