Simplify the Fraction: Converting 2/18 to Lowest Terms

Q: What if I can't see the GCD right away?

Try the prime factorization method: 2 = 2 and 18 = 2 × 3². The common prime factor is 2, so GCD = 2.

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

A fraction is in lowest terms when the GCD of the numerator and denominator is 1. For $ \frac{1}{9} $, the only common factor of 1 and 9 is 1!

Q: Can I simplify by dividing by different numbers?

No! You must divide both the numerator and denominator by the same number. This keeps the fraction's value unchanged while simplifying it.

Q: What if the numerator and denominator have no common factors?

Then the fraction is already in lowest terms! For example, $ \frac{3}{7} $ cannot be simplified further because 3 and 7 share no common factors except 1.

Fraction Simplification with Common Factor Division

Solve the following expression:

$\frac{2}{18}=$

❤️ 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

Solve the following expression:

$\frac{2}{18}=$

Step-by-step solution

First we will divide the numerator and denominator by the highest number that both are divisible by.

In this case, the number is 2

Then we will divide the fraction as follows:

$\frac{2:2}{18:2}=\frac{1}{9}$

Final Answer

$\frac{1}{9}$

Key Points to Remember

Essential concepts to master this topic

GCD Rule: Find the greatest common divisor of numerator and denominator
Division Method: Divide both 2 and 18 by their GCD of 2
Verify: Check that $\frac{1}{9}$ cannot be reduced further ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the greatest one
Don't just divide by 1 or skip finding the GCD = fraction not in lowest terms! This leaves the fraction partially simplified like $\frac{2}{18}$ instead of $\frac{1}{9}$ . Always find the greatest common divisor first.

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

How do I find the greatest common divisor (GCD)?

List the factors of both numbers: 2 has factors 1, 2 and 18 has factors 1, 2, 3, 6, 9, 18. The greatest common factor they share is 2!

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

Try the prime factorization method: 2 = 2 and 18 = 2 × 3². The common prime factor is 2, so GCD = 2.

How do I know when a fraction is fully simplified?

A fraction is in lowest terms when the GCD of the numerator and denominator is 1. For $\frac{1}{9}$ , the only common factor of 1 and 9 is 1!

Can I simplify by dividing by different numbers?

No! You must divide both the numerator and denominator by the same number. This keeps the fraction's value unchanged while simplifying it.

What if the numerator and denominator have no common factors?

Then the fraction is already in lowest terms! For example, $\frac{3}{7}$ cannot be simplified further because 3 and 7 share no common factors except 1.

🌟 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