Fraction Reduction Challenge: Converting 18/36 to Lowest Terms

Q: Why isn't 3/6 the final answer?

Because $ \frac{3}{6} $ can still be simplified! Both 3 and 6 share a common factor of 3, so divide again: $ \frac{3÷3}{6÷3} = \frac{1}{2} $.

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

Start by dividing by any common factor you can see, then keep going! For example: $ \frac{18}{36} → \frac{9}{18} → \frac{3}{6} → \frac{1}{2} $. You'll reach the same answer!

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

A fraction is in lowest terms when the GCF of the numerator and denominator equals 1. This means they share no common factors except 1.

Q: Is there a shortcut for finding the GCF?

Use prime factorization: 18 = 2×3² and 36 = 2²×3²Take the lowest power of each common prime: 2¹×3² = 18

Fraction Simplification with Greatest Common Factor

Simplify the fraction below and specify the highest common factor:

$\frac{18}{36}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction to denominator - 6

00:03 Divide the fraction by the appropriate factor

00:07 Make sure to divide both numerator and denominator

00:10 Calculate the portions

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

Simplify the fraction below and specify the highest common factor:

$\frac{18}{36}$

Step-by-step solution

Let's look at the denominator of the fraction. We'll try to find a number that, when divided by 36, gives us a result of 6:

$\frac{18:6}{36:6}=\frac{3}{6}$

Final Answer

$\frac{3}{6}$ , 6

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor of numerator and denominator
Technique: Divide both parts by GCF: 18÷18 = 1, 36÷18 = 2
Check: Verify $\frac{1}{2}$ cannot be reduced further since GCF(1,2) = 1 ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the greatest one
Don't divide 18/36 by 6 to get 3/6 and stop there = incomplete simplification! While 6 is a common factor, it's not the greatest. Always find the GCF (which is 18) to get the fully simplified fraction 1/2.

Practice Quiz

Test your knowledge with interactive questions

Simplify the following fraction by a factor of 4:

$\frac{4}{8}=$

FAQ

Everything you need to know about this question

How do I find the greatest common factor quickly?

List the factors of both numbers! For 18: 1, 2, 3, 6, 9, 18. For 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest number that appears in both lists is your GCF.

Why isn't 3/6 the final answer?

Because $\frac{3}{6}$ can still be simplified! Both 3 and 6 share a common factor of 3, so divide again: $\frac{3÷3}{6÷3} = \frac{1}{2}$ .

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

Start by dividing by any common factor you can see, then keep going! For example: $\frac{18}{36} → \frac{9}{18} → \frac{3}{6} → \frac{1}{2}$ . You'll reach the same answer!

How do I know when a fraction is fully simplified?

A fraction is in lowest terms when the GCF of the numerator and denominator equals 1. This means they share no common factors except 1.

Is there a shortcut for finding the GCF?

Use prime factorization: 18 = 2×3² and 36 = 2²×3²
Take the lowest power of each common prime: 2¹×3² = 18

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