Solve Fraction Division: 1/5 ÷ 1/10 Step-by-Step

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

The divisor (second fraction) gets flipped because division means "how many times does the divisor fit into the dividend?" Flipping $ \frac{1}{10} $ to $ \frac{10}{1} $ changes division into multiplication.

Q: What does reciprocal mean exactly?

A reciprocal is a fraction "flipped upside down" - the numerator and denominator switch places. The reciprocal of $ \frac{1}{10} $ is $ \frac{10}{1} $ or just 10.

Q: How can I remember the "flip and multiply" rule?

Think of it as "Keep, Change, Flip": Keep the first fraction, Change ÷ to ×, and Flip the second fraction. This turns any division into easier multiplication!

Q: Why is the answer 2 and not a fraction?

When $ \frac{10}{5} $ simplifies to a whole number, that's your final answer! Division problems can have whole number answers - it means $ \frac{1}{10} $ fits into $ \frac{1}{5} $ exactly 2 times.

Q: Can I check my answer a different way?

Yes! Multiply your answer by the divisor: $ 2 × \frac{1}{10} = \frac{2}{10} = \frac{1}{5} $. Since this equals the original dividend, your answer is correct!

Fraction Division with Reciprocal Method

Complete the following exercise:

$\frac{1}{5}:\frac{1}{10}=\text{?}$

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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

00:09 We'll swap the numerator and denominator of the fraction

00:14 We'll make sure to multiply numerator by numerator and denominator by denominator

00:20 Let's calculate the multiplications

00:23 Let's calculate the quotient

00:26 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:

$\frac{1}{5}:\frac{1}{10}=\text{?}$

Step-by-step solution

To solve this problem, we need to divide the fraction $\frac{1}{5}$ by the fraction $\frac{1}{10}$ . When dividing fractions, the procedure involves multiplying by the reciprocal of the divisor (the second fraction).

Let's start with the solution:

First, determine the reciprocal of $\frac{1}{10}$ . The reciprocal of a fraction is obtained by swapping its numerator and denominator. Thus, the reciprocal of $\frac{1}{10}$ is $\frac{10}{1}$ .
Now multiply $\frac{1}{5}$ by the reciprocal of $\frac{1}{10}$ , which is $\frac{10}{1}$ :

$\frac{1}{5} \times \frac{10}{1} = \frac{1 \times 10}{5 \times 1} = \frac{10}{5}$

Simplify the fraction $\frac{10}{5}$ :

$\frac{10}{5} = 2$

Therefore, the result of $\frac{1}{5} : \frac{1}{10}$ is $2$ .

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: $\frac{1}{5} ÷ \frac{1}{10} = \frac{1}{5} × \frac{10}{1}$
Check: Verify $2 × \frac{1}{10} = \frac{1}{5}$ gives original dividend ✓

Common Mistakes

Avoid these frequent errors

Multiplying denominators and numerators straight across
Don't multiply $\frac{1}{5} × \frac{1}{10} = \frac{1}{50}$ ! This gives the product, not the quotient. Always flip the second fraction first, then multiply: $\frac{1}{5} × \frac{10}{1} = 2$ .

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 instead of the first one?

The divisor (second fraction) gets flipped because division means "how many times does the divisor fit into the dividend?" Flipping $\frac{1}{10}$ to $\frac{10}{1}$ changes division into multiplication.

What does reciprocal mean exactly?

A reciprocal is a fraction "flipped upside down" - the numerator and denominator switch places. The reciprocal of $\frac{1}{10}$ is $\frac{10}{1}$ or just 10.

How can I remember the "flip and multiply" rule?

Think of it as "Keep, Change, Flip": Keep the first fraction, Change ÷ to ×, and Flip the second fraction. This turns any division into easier multiplication!

Why is the answer 2 and not a fraction?

When $\frac{10}{5}$ simplifies to a whole number, that's your final answer! Division problems can have whole number answers - it means $\frac{1}{10}$ fits into $\frac{1}{5}$ exactly 2 times.

Can I check my answer a different way?

Yes! Multiply your answer by the divisor: $2 × \frac{1}{10} = \frac{2}{10} = \frac{1}{5}$ . Since this equals the original dividend, your answer is correct!

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Solve Fraction Division: 1/5 ÷ 1/10 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 instead of the first one?

What does reciprocal mean exactly?

How can I remember the "flip and multiply" rule?

Why is the answer 2 and not a fraction?

Can I check my answer a different way?

🌟 Unlock Your Math Potential

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