Reduce the Fraction 3/12 to Its Simplest Form: Step-by-Step Solution

Q: How do I find the greatest common factor of 3 and 12?

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

Q: What does 'simplest form' actually mean?

Simplest form means the numerator and denominator have no common factors except 1. The fraction $ \frac{1}{4} $ is in simplest form because 1 and 4 share no common factors.

Q: Can I reduce fractions by canceling individual digits?

Never cancel individual digits! You can only divide the entire numerator and denominator by the same number. Canceling digits like the '2' in 12 is mathematically incorrect.

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

Then the fraction is already in simplest form! For example, $ \frac{5}{8} $ cannot be reduced further because 5 and 8 share no common factors except 1.

Q: Is there a faster way than listing all factors?

Yes! You can use the prime factorization method: $ 3 = 3 $ and $ 12 = 2^2 × 3 $. The GCF is the product of common prime factors, which is 3.

Fraction Simplification with Greatest Common Factor

Reduce the given fraction into its simplest form:

$\frac{3}{12}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce as much as possible

00:03 Divide by the greatest common factor

00:07 Make sure to divide both numerator and denominator

00:10 Calculate the quotients

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

Reduce the given fraction into its simplest form:

$\frac{3}{12}=$

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 3, therefore:

$\frac{3:3}{12:3}=\frac{1}{4}$

Final Answer

$\frac{1}{4}$

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: $\frac{3÷3}{12÷3} = \frac{1}{4}$
Check: Verify GCF is correct by ensuring 1 and 4 share no common factors ✓

Common Mistakes

Avoid these frequent errors

Using a factor that isn't the greatest common factor
Don't divide by just any common factor like 1 = $\frac{3}{12}$ stays the same! This leaves the fraction unreduced. Always find the greatest common factor (GCF = 3) to get the 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 3 and 12?

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

What does 'simplest form' actually mean?

Simplest form means the numerator and denominator have no common factors except 1. The fraction $\frac{1}{4}$ is in simplest form because 1 and 4 share no common factors.

Can I reduce fractions by canceling individual digits?

Never cancel individual digits! You can only divide the entire numerator and denominator by the same number. Canceling digits like the '2' in 12 is mathematically incorrect.

What if the numerator and denominator have no common factors?

Then the fraction is already in simplest form! For example, $\frac{5}{8}$ cannot be reduced further because 5 and 8 share no common factors except 1.

Is there a faster way than listing all factors?

Yes! You can use the prime factorization method: $3 = 3$ and $12 = 2^2 × 3$ . The GCF is the product of common prime factors, which is 3.

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