Solve 1/2 ÷ 1/2: Step-by-Step Fraction Division

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

Division by a fraction is the same as multiplication by its reciprocal. When you flip $ \frac{1}{2} $ to get $ \frac{2}{1} $, you're finding what to multiply by instead of divide by.

Q: What's the reciprocal of a fraction?

The reciprocal is the fraction flipped upside down. For $ \frac{1}{2} $, the reciprocal is $ \frac{2}{1} $ or just 2. The numerator and denominator swap places!

Q: Why does any number divided by itself equal 1?

Think about it: How many halves fit into one half? Exactly 1! This is true for any non-zero number. $ \frac{3}{4} \div \frac{3}{4} = 1 $ too!

Q: Can I use this method for all fraction division problems?

Yes! The reciprocal method works for all fraction division. Just remember: flip the second fraction, then multiply. It's that simple!

Q: What if I get confused about which fraction to flip?

Always flip the fraction after the division sign. In $ \frac{1}{2} \div \frac{1}{2} $, flip the second $ \frac{1}{2} $ to get $ \frac{2}{1} $, then multiply.

Fraction Division with Reciprocal Method

Complete the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem together!

00:08 Remember to divide the top numbers by each other, and the bottom numbers by each other.

00:14 Now, let's find the answers.

00:17 Any number divided by itself is always one.

00:21 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following exercise:

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

Step-by-step solution

To solve the division of two fractions $\frac{1}{2} \div \frac{1}{2}$ , we follow these steps:

Step 1: Recognize that dividing by a fraction is equivalent to multiplying by its reciprocal. In this case, we replace division with multiplication by flipping the second fraction.
Step 2: Thus, $\frac{1}{2} \div \frac{1}{2}$ becomes $\frac{1}{2} \times \frac{2}{1}$ .
Step 3: Perform the multiplication: Multiply the numerators and the denominators.
Numerator: $1 \times 2 = 2$
Denominator: $2 \times 1 = 2$
Step 4: Simplify the result: The fraction $\frac{2}{2}$ simplifies to 1.

Thus, the result of the division $\frac{1}{2} \div \frac{1}{2}$ is $1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Rule: Division by fraction equals multiplication by its reciprocal
Technique: Convert $\frac{1}{2} \div \frac{1}{2}$ to $\frac{1}{2} \times \frac{2}{1}$
Check: Any number divided by itself equals 1, so $\frac{1}{2} \div \frac{1}{2} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying the fractions directly without using reciprocal
Don't multiply $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ ! This gives you multiplication, not division. Always flip the second fraction first, then 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 by a fraction is the same as multiplication by its reciprocal. When you flip $\frac{1}{2}$ to get $\frac{2}{1}$ , you're finding what to multiply by instead of divide by.

What's the reciprocal of a fraction?

The reciprocal is the fraction flipped upside down. For $\frac{1}{2}$ , the reciprocal is $\frac{2}{1}$ or just 2. The numerator and denominator swap places!

Why does any number divided by itself equal 1?

Think about it: How many halves fit into one half? Exactly 1! This is true for any non-zero number. $\frac{3}{4} \div \frac{3}{4} = 1$ too!

Can I use this method for all fraction division problems?

Yes! The reciprocal method works for all fraction division. Just remember: flip the second fraction, then multiply. It's that simple!

What if I get confused about which fraction to flip?

Always flip the fraction after the division sign. In $\frac{1}{2} \div \frac{1}{2}$ , flip the second $\frac{1}{2}$ to get $\frac{2}{1}$ , then multiply.

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Solve 1/2 ÷ 1/2: Step-by-Step Fraction Division

Fraction Division with Reciprocal Method

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I flip the second fraction when dividing?

What's the reciprocal of a fraction?

Why does any number divided by itself equal 1?

Can I use this method for all fraction division problems?

What if I get confused about which fraction to flip?

🌟 Unlock Your Math Potential

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