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

Q: What exactly is a reciprocal?

A reciprocal is when you flip a fraction upside down. The reciprocal of $ \frac{2}{2} $ is $ \frac{2}{2} $ (which equals 1), and the reciprocal of $ \frac{3}{4} $ would be $ \frac{4}{3} $.

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

Dividing by a fraction is the same thing as multiplying by its reciprocal! This rule makes calculations much easier. Think of it as: "division becomes multiplication with a flip."

Q: Do I always need to simplify my final answer?

Yes, always simplify! In this problem, $ \frac{4}{8} $ simplifies to $ \frac{1}{2} $ by dividing both top and bottom by their greatest common factor (4).

Q: What if the second fraction equals 1?

Great observation! When $ \frac{2}{2} = 1 $, dividing by 1 doesn't change the value. So $ \frac{2}{4} \div 1 = \frac{2}{4} = \frac{1}{2} $ after simplifying.

Q: How can I check if my division is correct?

Use multiplication to check division! If $ \frac{2}{4} \div \frac{2}{2} = \frac{1}{2} $, then $ \frac{1}{2} \times \frac{2}{2} $ should equal $ \frac{2}{4} $. Try it!

Fraction Division with Reciprocal Method

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's solve this problem!

00:13 First, divide the top numbers by each other and the bottom numbers by each other.

00:19 Now, let's find the answer to those divisions.

00:23 And that's how we find the solution to the question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

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

Step-by-step solution

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

Step 1: Identify the fractions — the first fraction is $\frac{2}{4}$ , and the second fraction is $\frac{2}{2}$ .
Step 2: Find the reciprocal of the second fraction. The reciprocal of $\frac{2}{2}$ is $\frac{2}{2}$ , as it simplifies to 1.
Step 3: Multiply the first fraction by the reciprocal of the second fraction:

$\frac{2}{4} \times \frac{2}{2} = \frac{2 \times 2}{4 \times 2} = \frac{4}{8}$

Step 4: Simplify the resulting fraction $\frac{4}{8}$ . Since the greatest common divisor of 4 and 8 is 4, divide both numerator and denominator by 4:

$\frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2}$

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: Division by fraction equals multiplication by its reciprocal
Technique: $\frac{2}{4} \div \frac{2}{2} = \frac{2}{4} \times \frac{2}{2}$
Check: Verify $\frac{1}{2} \times \frac{2}{2} = \frac{2}{4}$ to confirm division ✓

Common Mistakes

Avoid these frequent errors

Incorrectly finding the reciprocal
Don't flip both fractions during division = wrong calculation! Only the second fraction (divisor) gets flipped. Always keep the first fraction unchanged and multiply by the reciprocal of only the second fraction.

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 exactly is a reciprocal?

A reciprocal is when you flip a fraction upside down. The reciprocal of $\frac{2}{2}$ is $\frac{2}{2}$ (which equals 1), and the reciprocal of $\frac{3}{4}$ would be $\frac{4}{3}$ .

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

Dividing by a fraction is the same thing as multiplying by its reciprocal! This rule makes calculations much easier. Think of it as: "division becomes multiplication with a flip."

Do I always need to simplify my final answer?

Yes, always simplify! In this problem, $\frac{4}{8}$ simplifies to $\frac{1}{2}$ by dividing both top and bottom by their greatest common factor (4).

What if the second fraction equals 1?

Great observation! When $\frac{2}{2} = 1$ , dividing by 1 doesn't change the value. So $\frac{2}{4} \div 1 = \frac{2}{4} = \frac{1}{2}$ after simplifying.

How can I check if my division is correct?

Use multiplication to check division! If $\frac{2}{4} \div \frac{2}{2} = \frac{1}{2}$ , then $\frac{1}{2} \times \frac{2}{2}$ should equal $\frac{2}{4}$ . Try it!

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