Solve the Fraction Division: 3/4 ÷ 1/2 Step-by-Step

Q: What exactly is a reciprocal and how do I find it?

A reciprocal is when you flip a fraction upside down. For $ \frac{1}{2} $, the reciprocal is $ \frac{2}{1} $. For whole numbers like 3, write it as $ \frac{3}{1} $ first, then flip to get $ \frac{1}{3} $.

Q: Why does dividing by a fraction make the answer bigger?

When you divide by something smaller than 1 (like $ \frac{1}{2} $), you're asking "how many halves fit into $ \frac{3}{4} $?" Since halves are small pieces, more of them fit, making the answer larger!

Q: Do I always need to convert improper fractions to mixed numbers?

Not always! It depends on what form the problem asks for. $ \frac{3}{2} $ and $ 1\frac{1}{2} $ are both correct - just different ways to write the same answer.

Q: What if I get confused about which fraction to flip?

Remember: flip the second fraction (the one you're dividing BY). In $ \frac{3}{4} \div \frac{1}{2} $, flip $ \frac{1}{2} $ to get $ \frac{2}{1} $, then multiply.

Q: How do I simplify fractions like 6/4?

Find the greatest common factor of both numbers. For 6 and 4, the GCF is 2. Divide both: $ \frac{6 \div 2}{4 \div 2} = \frac{3}{2} $.

Fraction Division with Reciprocal Method

Complete the following exercise:

$\frac{3}{4}:\frac{1}{2}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this problem together.

00:09 First, divide the top number by the top number, and the bottom number by the bottom number.

00:15 Now, calculate those quotients carefully.

00:19 Next, split 3 into 2 plus 1 for easier calculation.

00:29 Break down the fraction into a whole number and a remainder.

00:35 Remember, dividing a number by itself always gives you 1.

00:40 Then, convert it into a mixed fraction.

00:43 And that's how we find the solution to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following exercise:

$\frac{3}{4}:\frac{1}{2}=\text{?}$

Step-by-step solution

To solve this problem, we'll break it into these manageable steps:

Step 1: Identify the fractions:
$\frac{3}{4}$ and $\frac{1}{2}$ .
Step 2: Find the reciprocal of the second fraction:

The reciprocal of $\frac{1}{2}$ is $\frac{2}{1}$ .

Step 3: Change the division into multiplication:

$\frac{3}{4} \div \frac{1}{2}$ becomes $\frac{3}{4} \times \frac{2}{1}$ .

Step 4: Multiply the numerators and the denominators:

Numerator: $3 \times 2 = 6$
Denominator: $4 \times 1 = 4$
So, $\frac{3}{4} \times \frac{2}{1} = \frac{6}{4}$ .

Step 5: Simplify the fraction:

$\frac{6}{4} = \frac{3}{2}$ , since dividing numerator and denominator by 2 gives $\frac{3}{2}$ .

Step 6: Convert the fraction to a mixed number:

$\frac{3}{2}$ can be written as the mixed number $1\frac{1}{2}$ .

Therefore, the result of the division is $1\frac{1}{2}$ .

Final Answer

$1\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Division by a fraction equals multiplication by its reciprocal
Technique: $\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{6}{4}$
Check: Convert $\frac{6}{4} = 1\frac{1}{2}$ and verify 6 ÷ 4 = 1.5 ✓

Common Mistakes

Avoid these frequent errors

Multiplying by the original second fraction instead of its reciprocal
Don't multiply $\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$ ! This gives the wrong operation and wrong answer. Always flip the second fraction first: $\frac{1}{2}$ becomes $\frac{2}{1}$ , then 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

What exactly is a reciprocal and how do I find it?

A reciprocal is when you flip a fraction upside down. For $\frac{1}{2}$ , the reciprocal is $\frac{2}{1}$ . For whole numbers like 3, write it as $\frac{3}{1}$ first, then flip to get $\frac{1}{3}$ .

Why does dividing by a fraction make the answer bigger?

When you divide by something smaller than 1 (like $\frac{1}{2}$ ), you're asking "how many halves fit into $\frac{3}{4}$ ?" Since halves are small pieces, more of them fit, making the answer larger!

Do I always need to convert improper fractions to mixed numbers?

Not always! It depends on what form the problem asks for. $\frac{3}{2}$ and $1\frac{1}{2}$ are both correct - just different ways to write the same answer.

What if I get confused about which fraction to flip?

Remember: flip the second fraction (the one you're dividing BY). In $\frac{3}{4} \div \frac{1}{2}$ , flip $\frac{1}{2}$ to get $\frac{2}{1}$ , then multiply.

How do I simplify fractions like 6/4?

Find the greatest common factor of both numbers. For 6 and 4, the GCF is 2. Divide both: $\frac{6 \div 2}{4 \div 2} = \frac{3}{2}$ .

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