Solve the Fraction Division: 4/12 ÷ 2/4 Step-by-Step

Q: Why do I flip the second fraction when dividing?

Division by a fraction is the same as multiplication by its reciprocal. Think of it this way: dividing by $ \frac{2}{4} $ means "how many $ \frac{2}{4} $ pieces fit into $ \frac{4}{12} $?"

Q: What's the reciprocal of a fraction?

The reciprocal is simply the fraction flipped upside down. So the reciprocal of $ \frac{2}{4} $ is $ \frac{4}{2} $. The numerator and denominator switch places!

Q: Do I need to simplify the fractions before dividing?

It's helpful but not required. You can simplify before or after the calculation. In this problem, $ \frac{4}{12} = \frac{1}{3} $ and $ \frac{2}{4} = \frac{1}{2} $, giving us $ \frac{1}{3} \div \frac{1}{2} = \frac{2}{3} $.

Q: How do I know when my answer is fully simplified?

Your fraction is simplified when the numerator and denominator have no common factors other than 1. For $ \frac{16}{24} $, both are divisible by 8, so $ \frac{16 \div 8}{24 \div 8} = \frac{2}{3} $.

Q: Can I convert to decimals instead?

Yes! $ \frac{4}{12} = 0.333... $ and $ \frac{2}{4} = 0.5 $, so $ 0.333... \div 0.5 = 0.666... = \frac{2}{3} $. But working with fractions is usually more precise.

Fraction Division with Reciprocal Multiplication

Solve the following exercise:

$\frac{4}{12}:\frac{2}{4}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Okay, let's solve this math problem together.

00:11 First, divide the numerator by the numerator. Then pause. And divide the denominator by the denominator.

00:20 Now, let's calculate the quotients together. Ready? Let's go!

00:26 Great job! And there you have it. This is the solution to our question. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{4}{12}:\frac{2}{4}=\text{?}$

Step-by-step solution

To solve the division problem $\frac{4}{12}:\frac{2}{4}$ , we will follow these steps:

Step 1: Identify the fractions involved: $\frac{4}{12}$ and $\frac{2}{4}$ .
Step 2: Convert the division into multiplication by the reciprocal of the divisor. The reciprocal of $\frac{2}{4}$ is $\frac{4}{2}$ .
Step 3: Multiply the first fraction by this reciprocal:

$\frac{4}{12} \times \frac{4}{2} = \frac{4 \times 4}{12 \times 2}$

$= \frac{16}{24}$

Step 4: Simplify the resulting fraction. The greatest common divisor of 16 and 24 is 8.

$\frac{16 \div 8}{24 \div 8} = \frac{2}{3}$

Thus, the solution to the problem is $\frac{2}{3}$ .

Final Answer

$\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Division by a fraction equals multiplication by its reciprocal
Technique: Convert $\frac{4}{12} \div \frac{2}{4}$ to $\frac{4}{12} \times \frac{4}{2}$
Check: Simplify final answer to lowest terms: $\frac{16}{24} = \frac{2}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing numerators and denominators directly
Don't divide $\frac{4}{12} \div \frac{2}{4}$ as $\frac{4 \div 2}{12 \div 4} = \frac{2}{3}$ ! This only works by coincidence and gives wrong answers for most problems. Always flip the second fraction and multiply instead.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

$\frac{1}{2}:\frac{1}{2}=\text{?}$

FAQ

Everything you need to know about this question

Why do I flip the second fraction when dividing?

Division by a fraction is the same as multiplication by its reciprocal. Think of it this way: dividing by $\frac{2}{4}$ means "how many $\frac{2}{4}$ pieces fit into $\frac{4}{12}$ ?"

What's the reciprocal of a fraction?

The reciprocal is simply the fraction flipped upside down. So the reciprocal of $\frac{2}{4}$ is $\frac{4}{2}$ . The numerator and denominator switch places!

Do I need to simplify the fractions before dividing?

It's helpful but not required. You can simplify before or after the calculation. In this problem, $\frac{4}{12} = \frac{1}{3}$ and $\frac{2}{4} = \frac{1}{2}$ , giving us $\frac{1}{3} \div \frac{1}{2} = \frac{2}{3}$ .

How do I know when my answer is fully simplified?

Your fraction is simplified when the numerator and denominator have no common factors other than 1. For $\frac{16}{24}$ , both are divisible by 8, so $\frac{16 \div 8}{24 \div 8} = \frac{2}{3}$ .

Can I convert to decimals instead?

Yes! $\frac{4}{12} = 0.333...$ and $\frac{2}{4} = 0.5$ , so $0.333... \div 0.5 = 0.666... = \frac{2}{3}$ . But working with fractions is usually more precise.

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