Solve the Fraction Problem: Converting 7 Books ÷ 10 Students to 7/10

Q: Why is it 7/10 and not 10/7?

Think about it logically: you have 7 books for 10 students. Each student gets less than one book, so the fraction must be less than 1. Since $ \frac{7}{10} = 0.7 $ is less than 1, it makes sense!

Q: What does 7/10 actually mean in this problem?

$ \frac{7}{10} $ means each student receives seven-tenths of a book. In decimal form, that's 0.7 books per student.

Q: What if I had 10 books and 7 students instead?

Then each student would get $ \frac{10}{7} $ books, which is more than 1 book per student. Always put the total items as the numerator and number of people as the denominator.

Q: How do I remember which number goes where?

Use this memory trick: "Items over People" - the number of items goes on top (numerator), and the number of people goes on bottom (denominator).

Fraction Division with Real-World Distribution

Match the following description with the corresponding fraction:

7 books are distributed equally among 10 students.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Match the following description with the corresponding fraction:

7 books are distributed equally among 10 students.

Step-by-step solution

In this problem, we need to determine how to represent the description "7 books are distributed equally among 10 students" as a fraction.

To find out how many books each student receives, we'll take the following steps:

Step 1: Identify the quantities given. We have 7 books to distribute.
Step 2: Recognize that there are 10 students among whom these books need to be distributed equally.
Step 3: Formulate the fraction. Each student receives a fraction of the books described by the number of books divided by the number of students. This is represented by the fraction $\frac{7}{10}$ .

This fraction $\frac{7}{10}$ accurately represents the share of books each student would get if 7 books are distributed equally among 10 students.

Therefore, the correct answer to this problem is $\frac{7}{10}$ .

Final Answer

$\frac{7}{10}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Items divided among people equals fraction representation
Technique: 7 books ÷ 10 students = 7/10 books per student
Check: Multiply back: 7/10 × 10 students = 7 books total ✓

Common Mistakes

Avoid these frequent errors

Flipping the numerator and denominator
Don't write 10/7 when dividing 7 books among 10 students = each student gets more than one book! This is impossible when you have fewer items than people. Always put the total amount as numerator and number of people as denominator.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction shown in the picture, in words:

FAQ

Everything you need to know about this question

Why is it 7/10 and not 10/7?

Think about it logically: you have 7 books for 10 students. Each student gets less than one book, so the fraction must be less than 1. Since $\frac{7}{10} = 0.7$ is less than 1, it makes sense!

What does 7/10 actually mean in this problem?

$\frac{7}{10}$ means each student receives seven-tenths of a book. In decimal form, that's 0.7 books per student.

How can you split books among students?

In real life, you might photocopy pages, share books, or take turns reading. In math problems, we assume items can be divided equally to find each person's share.

What if I had 10 books and 7 students instead?

Then each student would get $\frac{10}{7}$ books, which is more than 1 book per student. Always put the total items as the numerator and number of people as the denominator.

How do I remember which number goes where?

Use this memory trick: "Items over People" - the number of items goes on top (numerator), and the number of people goes on bottom (denominator).

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Simple 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