Solve Fraction Division: 1/6 ÷ 1/3 Step-by-Step

Q: What does 'reciprocal' mean exactly?

The reciprocal means flipping a fraction upside down. For $ \frac{1}{3} $, the reciprocal is $ \frac{3}{1} $ or just 3. Think of it as switching the numerator and denominator!

Q: Why do I multiply by the reciprocal instead of just dividing?

Division by a fraction is the same as multiplication by its reciprocal. This rule makes calculations much easier! Instead of complex division, you get simple multiplication.

Q: How do I know when to simplify my answer?

Always check if your final fraction can be reduced. Look for common factors in the numerator and denominator. $ \frac{3}{6} $ simplifies to $ \frac{1}{2} $ because both 3 and 6 divide by 3.

Q: What if I forget to flip the second fraction?

You'll get the multiplication result instead of division! Remember: division means 'how many times does the second number go into the first?' Flipping helps you find this answer correctly.

Q: Can I use this method for mixed numbers too?

Yes! But first convert mixed numbers to improper fractions, then apply the same reciprocal rule. The process stays exactly the same.

Fraction Division with Reciprocal Method

Complete the following exercise:

$\frac{1}{6}:\frac{1}{3}=\text{?}$

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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 First, divide the top number by the top number. Then, divide the bottom number by the bottom number.

00:16 Now, calculate each result. You've got this!

00:20 And that's how you find the solution. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following exercise:

$\frac{1}{6}:\frac{1}{3}=\text{?}$

Step-by-step solution

To solve the division of fractions problem $\frac{1}{6} \div \frac{1}{3}$ , we'll apply the concept of multiplying by the reciprocal.

Step 1: Identify the reciprocal of the second fraction. The reciprocal of $\frac{1}{3}$ is $\frac{3}{1}$ .
Step 2: Multiply the first fraction by this reciprocal. Therefore, calculate $\frac{1}{6} \times \frac{3}{1}$ .
Step 3: Perform the multiplication. Multiply the numerators: $1 \times 3 = 3$ . Multiply the denominators: $6 \times 1 = 6$ .
Step 4: Simplify the resulting fraction. The fraction $\frac{3}{6}$ simplifies to $\frac{1}{2}$ because both the numerator and denominator can be divided by 3.

Therefore, the solution to the problem is $\frac{1}{2}$ .

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: To divide fractions, multiply by the reciprocal
Technique: $\frac{1}{6} \div \frac{1}{3} = \frac{1}{6} \times \frac{3}{1} = \frac{3}{6}$
Check: Simplify final answer: $\frac{3}{6} = \frac{1}{2}$ by dividing both by 3 ✓

Common Mistakes

Avoid these frequent errors

Multiplying fractions directly instead of using reciprocal
Don't multiply $\frac{1}{6} \times \frac{1}{3} = \frac{1}{18}$ ! This gives the wrong operation result. Always flip the second fraction first, then multiply: $\frac{1}{6} \times \frac{3}{1} = \frac{1}{2}$ .

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

What does 'reciprocal' mean exactly?

The reciprocal means flipping a fraction upside down. For $\frac{1}{3}$ , the reciprocal is $\frac{3}{1}$ or just 3. Think of it as switching the numerator and denominator!

Why do I multiply by the reciprocal instead of just dividing?

Division by a fraction is the same as multiplication by its reciprocal. This rule makes calculations much easier! Instead of complex division, you get simple multiplication.

How do I know when to simplify my answer?

Always check if your final fraction can be reduced. Look for common factors in the numerator and denominator. $\frac{3}{6}$ simplifies to $\frac{1}{2}$ because both 3 and 6 divide by 3.

What if I forget to flip the second fraction?

You'll get the multiplication result instead of division! Remember: division means 'how many times does the second number go into the first?' Flipping helps you find this answer correctly.

Can I use this method for mixed numbers too?

Yes! But first convert mixed numbers to improper fractions, then apply the same reciprocal rule. The process stays exactly the same.

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