Solve the Fraction Division: 1/4 ÷ 1/2 Step by Step

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

Division means "how many times does this fit?" When you flip $ \frac{1}{2} $ to $ \frac{2}{1} $, you're asking "how many halves fit into a quarter?" which becomes multiplication!

Q: What does reciprocal mean exactly?

A reciprocal is when you flip the numerator and denominator. For $ \frac{1}{2} $, the reciprocal is $ \frac{2}{1} $ or just 2. Remember: any number times its reciprocal equals 1!

Q: How do I multiply fractions after flipping?

Multiply straight across: numerator × numerator and denominator × denominator. So $ \frac{1}{4} \times \frac{2}{1} = \frac{1 \times 2}{4 \times 1} = \frac{2}{4} $

Q: Do I always need to simplify my answer?

Yes! Always reduce to lowest terms. $ \frac{2}{4} $ simplifies to $ \frac{1}{2} $ by dividing both top and bottom by 2.

Fraction Division with Reciprocal Method

Solve the following exercise:

$\frac{1}{4}:\frac{1}{2}=\text{?}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve the problem step by step.

00:08 First, divide the numerator by the numerator, and the denominator by the denominator.

00:14 Next, calculate the quotients. You're doing great!

00:19 And there you go! That's the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{1}{4}:\frac{1}{2}=\text{?}$

Step-by-step solution

When we approach solving such questions, we need to know the rule of dividing fractions,

When we need to divide a fraction by a fraction, we use the method of multiplying by the reciprocal.

This means we flip the numerator and denominator of the second fraction, and then perform fraction multiplication.

Instead of:

1/4 : 1/2 =

We get:

1/4 * 2/1 =

We'll remember that in fraction multiplication we multiply numerator by numerator and denominator by denominator

1*2 / 4*1 =
2/4 =

We'll reduce the fraction and get:

1/2

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: To divide fractions, multiply by the reciprocal of the divisor
Technique: Change $\frac{1}{4} \div \frac{1}{2}$ to $\frac{1}{4} \times \frac{2}{1}$
Check: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ confirms our division ✓

Common Mistakes

Avoid these frequent errors

Dividing numerators and denominators directly
Don't divide $\frac{1}{4} \div \frac{1}{2}$ as $\frac{1 \div 1}{4 \div 2} = \frac{1}{2}$ ! This accidentally gives the right answer but uses wrong logic that fails with other numbers. Always flip the second fraction and multiply.

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 means "how many times does this fit?" When you flip $\frac{1}{2}$ to $\frac{2}{1}$ , you're asking "how many halves fit into a quarter?" which becomes multiplication!

What does reciprocal mean exactly?

A reciprocal is when you flip the numerator and denominator. For $\frac{1}{2}$ , the reciprocal is $\frac{2}{1}$ or just 2. Remember: any number times its reciprocal equals 1!

How do I multiply fractions after flipping?

Multiply straight across: numerator × numerator and denominator × denominator. So $\frac{1}{4} \times \frac{2}{1} = \frac{1 \times 2}{4 \times 1} = \frac{2}{4}$

Do I always need to simplify my answer?

Yes! Always reduce to lowest terms. $\frac{2}{4}$ simplifies to $\frac{1}{2}$ by dividing both top and bottom by 2.

What if I'm dividing by a whole number?

Write the whole number as a fraction first! For example, 3 becomes $\frac{3}{1}$ , then flip it to $\frac{1}{3}$ and multiply as usual.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime