Simplify the Fraction 8/12: Step-by-Step Reduction

Q: How do I find the greatest common factor of 8 and 12?

List the factors of each number: 8: 1, 2, 4, 8 and 12: 1, 2, 3, 4, 6, 12. The largest number that appears in both lists is 4, so GCF = 4.

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

A fraction is in simplest form when the numerator and denominator have no common factors except 1. Check: do 2 and 3 share any factors? Only 1, so $ \frac{2}{3} $ is fully simplified!

Q: Can I use division to check my answer?

Yes! Convert to decimals: $ \frac{8}{12} = 0.667... $ and $ \frac{2}{3} = 0.667... $. If they're equal, your simplification is correct!

Fraction Reduction with Greatest Common Factor

Simplify the given fraction into its simplest form:

$\frac{8}{12}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction as much as possible

00:03 Divide by the greatest common factor

00:07 Make sure to divide both numerator and denominator

00:11 Calculate the quotients

00:16 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 given fraction into its simplest form:

$\frac{8}{12}=$

Step-by-step solution

We must 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 4, therefore:

$\frac{8:4}{12:4}=\frac{2}{3}$

Final Answer

$\frac{2}{3}$

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: 8÷4 = 2, 12÷4 = 3
Check: Verify $\frac{2}{3}$ cannot be reduced further ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the greatest one
Don't divide 8/12 by 2 to get 4/6 = still not simplest! This leaves the fraction partially reduced and requires more steps. Always find the greatest common factor (GCF = 4) to reach simplest form in one step.

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 8 and 12?

List the factors of each number: 8: 1, 2, 4, 8 and 12: 1, 2, 3, 4, 6, 12. The largest number that appears in both lists is 4, so GCF = 4.

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

Start by dividing by small common factors like 2 or 3, then keep going! For example: $\frac{8}{12} = \frac{4}{6} = \frac{2}{3}$ . You'll reach the same answer, just in more steps.

How do I know when a fraction is fully simplified?

A fraction is in simplest form when the numerator and denominator have no common factors except 1. Check: do 2 and 3 share any factors? Only 1, so $\frac{2}{3}$ is fully simplified!

Why is 2/3 the correct answer and not 1/5 or 3/4?

When we divide 8 by 4, we get 2 (not 1 or 3). When we divide 12 by 4, we get 3 (not 5 or 4). So $\frac{8÷4}{12÷4} = \frac{2}{3}$ .

Can I use division to check my answer?

Yes! Convert to decimals: $\frac{8}{12} = 0.667...$ and $\frac{2}{3} = 0.667...$ . If they're equal, your simplification is correct!

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