Solve Fraction Division: Calculate 1/9 ÷ 1/3 Step-by-Step

Q: Why do I flip the second fraction instead of the first one?

You always flip the divisor (the fraction you're dividing by). Think of it like this: dividing by $ \frac{1}{3} $ is the same as asking 'how many thirds fit into something?' which equals multiplying by 3.

Q: What's the reciprocal of a fraction?

The reciprocal means flipping the fraction upside down! The reciprocal of $ \frac{1}{3} $ is $ \frac{3}{1} $ or just 3. For $ \frac{2}{5} $, it's $ \frac{5}{2} $.

Q: Do I always need to simplify my answer?

Yes! Always check if your final fraction can be simplified. Look for the greatest common divisor (GCD) of the numerator and denominator, like we did with $ \frac{3}{9} = \frac{1}{3} $.

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

Absolutely! Just convert mixed numbers to improper fractions first, then use the same flip-and-multiply method. For example: $ 1\frac{1}{2} $ becomes $ \frac{3}{2} $.

Q: Why does multiplying by the reciprocal work?

Division and multiplication are opposite operations. When you multiply by a reciprocal, you're undoing the division effect. Think: dividing by 2 is the same as multiplying by $ \frac{1}{2} $!

Fraction Division with Reciprocal Method

Complete the following exercise:

$\frac{1}{9}:\frac{1}{3}=\text{?}$

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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 Divide the top numbers by the top numbers, and the bottom numbers by the bottom numbers.

00:14 Now, let's find those quotients.

00:18 Great job! That's the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following exercise:

$\frac{1}{9}:\frac{1}{3}=\text{?}$

Step-by-step solution

To solve the division of the fractions $\frac{1}{9}$ and $\frac{1}{3}$ , we'll employ the method of "invert and multiply":

Step 1: Identify the reciprocal of the divisor. The divisor is $\frac{1}{3}$ , and its reciprocal is $\frac{3}{1}$ .
Step 2: Convert the division into a multiplication. Therefore, $\frac{1}{9} \div \frac{1}{3}$ becomes $\frac{1}{9} \times \frac{3}{1}$ .
Step 3: Carry out the multiplication of the two fractions.
$\frac{1}{9} \times \frac{3}{1} = \frac{1 \times 3}{9 \times 1} = \frac{3}{9}$ .
Step 4: Simplify the resulting fraction.
$\frac{3}{9}$ simplifies to $\frac{1}{3}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

Therefore, the solution to the problem $\frac{1}{9} \div \frac{1}{3}$ is $\frac{1}{3}$ .

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: To divide fractions, multiply by the reciprocal of the divisor
Technique: $\frac{1}{9} \div \frac{1}{3} = \frac{1}{9} \times \frac{3}{1} = \frac{3}{9}$
Check: Simplify final answer by dividing by GCD: $\frac{3}{9} = \frac{1}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Trying to divide numerators and denominators directly
Don't divide $\frac{1}{9} \div \frac{1}{3}$ as $\frac{1÷1}{9÷3} = \frac{1}{3}$ by accident! This might give the right answer here but fails with other fractions like $\frac{2}{5} \div \frac{1}{3}$ . 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 instead of the first one?

You always flip the divisor (the fraction you're dividing by). Think of it like this: dividing by $\frac{1}{3}$ is the same as asking 'how many thirds fit into something?' which equals multiplying by 3.

What's the reciprocal of a fraction?

The reciprocal means flipping the fraction upside down! The reciprocal of $\frac{1}{3}$ is $\frac{3}{1}$ or just 3. For $\frac{2}{5}$ , it's $\frac{5}{2}$ .

Do I always need to simplify my answer?

Yes! Always check if your final fraction can be simplified. Look for the greatest common divisor (GCD) of the numerator and denominator, like we did with $\frac{3}{9} = \frac{1}{3}$ .

Can I use this method with mixed numbers too?

Absolutely! Just convert mixed numbers to improper fractions first, then use the same flip-and-multiply method. For example: $1\frac{1}{2}$ becomes $\frac{3}{2}$ .

Why does multiplying by the reciprocal work?

Division and multiplication are opposite operations. When you multiply by a reciprocal, you're undoing the division effect. Think: dividing by 2 is the same as multiplying by $\frac{1}{2}$ !

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