Simplify the Fraction 12/4: Step-by-Step Solution

Q: Why is 3/1 the same as just 3?

Any number divided by 1 equals itself! So $ \frac{3}{1} = 3 $. Both answers are correct, but 3 is the simplest form since we don't usually write the denominator when it's 1.

Q: What if the GCD is 1?

If the GCD is 1, the fraction is already in simplest form! You can't simplify it further because the numerator and denominator share no common factors.

Q: Can I simplify 12/4 in steps instead?

Yes! You could do $ \frac{12}{4} = \frac{6}{2} = \frac{3}{1} $ by dividing by 2, then by 2 again. But dividing by the GCD (4) in one step is faster!

Fraction Simplification with Division Method

Simplify the following fraction:

$\frac{12}{4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction by 4

00:03 Divide the fraction by the given factor

00:06 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

Simplify the following fraction:

$\frac{12}{4}=$

Step-by-step solution

Let's reduce as follows, divide the numerator by 4 and the denominator by 4:

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

Final Answer

$\frac{3}{1}$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide both numerator and denominator by their GCD
Technique: Find GCD(12,4) = 4, then 12÷4 = 3, 4÷4 = 1
Check: Verify 3/1 = 3 equals original 12÷4 = 3 ✓

Common Mistakes

Avoid these frequent errors

Dividing numerator and denominator by different numbers
Don't divide 12 by 4 but 4 by 2 = wrong fraction 3/2! This breaks the fraction's value and gives an incorrect result. Always divide both parts by the same number (the GCD).

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

Why is 3/1 the same as just 3?

Any number divided by 1 equals itself! So $\frac{3}{1} = 3$ . Both answers are correct, but 3 is the simplest form since we don't usually write the denominator when it's 1.

How do I find the GCD of 12 and 4?

List the factors: 12 has factors 1, 2, 3, 4, 6, 12 and 4 has factors 1, 2, 4. The greatest common factor they share is 4!

What if the GCD is 1?

If the GCD is 1, the fraction is already in simplest form! You can't simplify it further because the numerator and denominator share no common factors.

Can I simplify 12/4 in steps instead?

Yes! You could do $\frac{12}{4} = \frac{6}{2} = \frac{3}{1}$ by dividing by 2, then by 2 again. But dividing by the GCD (4) in one step is faster!

How do I check if my simplified fraction is correct?

Convert both fractions to decimals or cross-multiply! For example: $\frac{12}{4} = 3$ and $\frac{3}{1} = 3$ , so they're equal ✓

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