Simplify the Fraction 5/10: Step-by-Step Reduction

Q: How do I find the greatest common factor of 5 and 10?

List the factors of each number: 5 has factors 1, 5 and 10 has factors 1, 2, 5, 10. The largest number that appears in both lists is 5, so that's your GCF!

Q: How do I know when a fraction is fully simplified?

A fraction is in simplest form when the numerator and denominator share no common factors except 1. For $ \frac{1}{2} $, the only common factor of 1 and 2 is 1!

Fraction Simplification with Common Factors

Simplify the given fraction to its simplest form:

$\frac{5}{10}=$

❤️ 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

00:05 Let's simplify this as much as we can.

00:08 Find and divide by the greatest common factor.

00:12 Remember, divide both the top number and the bottom number.

00:17 Now, work out the results from your division.

00:20 And that's how we find the answer to this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Simplify the given fraction to its simplest form:

$\frac{5}{10}=$

Step-by-step solution

We need to identify the highest common factor (HCF): The largest number that both the numerator and the denominator can be divided by.

In this case, the number is 5, therefore:

$\frac{5:5}{10:5}=\frac{1}{2}$

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor (GCF) of numerator and denominator
Technique: Divide both 5 and 10 by their GCF of 5: $\frac{5÷5}{10÷5} = \frac{1}{2}$
Check: Verify that 1 and 2 have no common factors except 1 ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the greatest one
Don't just divide by any number that works like 2 or 3! This leaves the fraction partially simplified like $\frac{2.5}{5}$ or doesn't work at all. Always find the greatest common factor (GCF) first, then divide both parts by that number.

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 find the greatest common factor of 5 and 10?

List the factors of each number: 5 has factors 1, 5 and 10 has factors 1, 2, 5, 10. The largest number that appears in both lists is 5, so that's your GCF!

What if I can't see the GCF right away?

Try listing all factors of the smaller number first, then check which ones also divide the larger number. Or use prime factorization: 5 = 5, 10 = 2 × 5, so GCF = 5.

How do I know when a fraction is fully simplified?

A fraction is in simplest form when the numerator and denominator share no common factors except 1. For $\frac{1}{2}$ , the only common factor of 1 and 2 is 1!

Can I simplify before I find the GCF?

It's better to find the GCF first! If you simplify step-by-step with smaller factors, you might need multiple steps. Using the GCF gets you to the answer in one step.

What if the numerator is bigger than the denominator?

The same rules apply! Find the GCF of both numbers and divide. You'll get an improper fraction or mixed number in simplest form.

🌟 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