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

Q: Why do I flip the second fraction?

When dividing by a fraction, you're asking 'how many groups of this size fit?' Flipping $ \frac{1}{4} $ to $ \frac{4}{1} $ changes division into multiplication, which is much easier to calculate!

Q: What does 'reciprocal' actually mean?

A reciprocal is when you flip a fraction upside down. The reciprocal of $ \frac{1}{4} $ is $ \frac{4}{1} $. Think of it as the 'opposite' fraction that helps turn division into multiplication.

Q: How can I check if my answer makes sense?

Think about it logically: How many quarters fit in a half? Since a quarter is smaller than a half, the answer should be greater than 1. Our answer of 2 makes perfect sense!

Q: Can I use this method for any fraction division problem?

Yes! The reciprocal method works for all fraction division problems. Just remember: Keep the first fraction the sameChange ÷ to ×Flip the second fractionMultiply and simplify

Fraction Division with Reciprocal Method

Complete the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Instead of division, we'll use multiplication by the reciprocal

00:08 We'll swap the numerator and denominator of the fraction

00:13 Make sure to multiply numerator by numerator and denominator by denominator

00:18 Calculate the multiplications

00:21 Calculate the quotient

00:23 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

Complete the following exercise:

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

Step-by-step solution

To solve the division of two fractions $\frac{1}{2} : \frac{1}{4}$ , follow these steps:

Step 1: Identify the operation: The problem involves dividing $\frac{1}{2}$ by $\frac{1}{4}$ .
Step 2: Use the reciprocal: In fraction division, multiply by the reciprocal of the second fraction. Thus, $\frac{1}{2} : \frac{1}{4} = \frac{1}{2} \times \frac{4}{1}$ .
Step 3: Perform the multiplication: Now compute the multiplication by multiplying the numerators and the denominators: $\frac{1 \times 4}{2 \times 1} = \frac{4}{2}$ .
Step 4: Simplify the fraction: The fraction $\frac{4}{2}$ simplifies to $2$ .

Thus, the solution to the division $\frac{1}{2} : \frac{1}{4}$ is $2$ . Therefore, the correct answer choice is $2$ (Choice 1).

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Rule: To divide fractions, multiply by the reciprocal of the divisor
Technique: $\frac{1}{2} ÷ \frac{1}{4} = \frac{1}{2} × \frac{4}{1} = \frac{4}{2}$
Check: Think 'how many quarters fit in a half?' Answer: 2 quarters ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting fractions instead of dividing
Don't change $\frac{1}{2} ÷ \frac{1}{4}$ into $\frac{1}{2} - \frac{1}{4} = \frac{1}{4}$ ! Division means 'how many times does the second fraction fit into the first,' not subtraction. Always flip the second fraction and multiply.

Practice Quiz

Test your knowledge with interactive questions

$\frac{1}{3}+\frac{1}{4}=$

FAQ

Everything you need to know about this question

Why do I flip the second fraction?

When dividing by a fraction, you're asking 'how many groups of this size fit?' Flipping $\frac{1}{4}$ to $\frac{4}{1}$ changes division into multiplication, which is much easier to calculate!

What does 'reciprocal' actually mean?

A reciprocal is when you flip a fraction upside down. The reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$ . Think of it as the 'opposite' fraction that helps turn division into multiplication.

How can I check if my answer makes sense?

Think about it logically: How many quarters fit in a half? Since a quarter is smaller than a half, the answer should be greater than 1. Our answer of 2 makes perfect sense!

What if I get a fraction that doesn't simplify to a whole number?

That's completely normal! Many fraction divisions result in fractions. Just make sure to simplify your final answer by dividing both numerator and denominator by their greatest common factor.

Can I use this method for any fraction division problem?

Yes! The reciprocal method works for all fraction division problems. Just remember:

Keep the first fraction the same
Change ÷ to ×
Flip the second fraction
Multiply and simplify

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

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?

What does 'reciprocal' actually mean?

How can I check if my answer makes sense?

What if I get a fraction that doesn't simplify to a whole number?

Can I use this method for any fraction division problem?

🌟 Unlock Your Math Potential

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