Solve Fraction Division: 3/4 ÷ 3/8 Step-by-Step

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

In division, you always flip the divisor (the second fraction). Think of it like this: $ \frac{3}{4} \div \frac{3}{8} $ means "how many $ \frac{3}{8} $'s fit into $ \frac{3}{4} $?" So you multiply by the reciprocal of what you're dividing by.

Q: What's the reciprocal of a fraction?

The reciprocal means flipping the numerator and denominator. So the reciprocal of $ \frac{3}{8} $ is $ \frac{8}{3} $. Remember: multiply any number by its reciprocal and you get 1!

Q: How do I simplify fractions like 24/12?

Find the greatest common factor (GCF) of the numerator and denominator. For $ \frac{24}{12} $, the GCF is 12, so $ \frac{24}{12} = \frac{24÷12}{12÷12} = \frac{2}{1} = 2 $.

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

Yes! First convert any mixed numbers to improper fractions, then use the reciprocal method. For example: $ 1\frac{1}{2} \div \frac{3}{4} $ becomes $ \frac{3}{2} \div \frac{3}{4} = \frac{3}{2} \times \frac{4}{3} $.

Fraction Division with Reciprocal Method

Solve the following:

$\frac{3}{4}:\frac{3}{8}=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following:

$\frac{3}{4}:\frac{3}{8}=$

Step-by-step solution

To solve this problem, we'll perform the division of two fractions $\frac{3}{4}$ and $\frac{3}{8}$ using the reciprocal method.

Step 1: Identify the reciprocal of the divisor.
Step 2: Multiply the dividend by the reciprocal of the divisor.
Step 3: Simplify the result to get the final answer.

Let's work through each step:

Step 1: The problem asks us to divide $\frac{3}{4}$ by $\frac{3}{8}$ . The reciprocal of $\frac{3}{8}$ is $\frac{8}{3}$ .

Step 2: Multiply $\frac{3}{4}$ by $\frac{8}{3}$ .

$\frac{3}{4} \times \frac{8}{3} = \frac{3 \times 8}{4 \times 3} = \frac{24}{12}$

Step 3: Simplify the fraction $\frac{24}{12}$ .

$\frac{24}{12} = 2$

Therefore, the solution to the problem is $2$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Rule: To divide fractions, multiply by the reciprocal of divisor
Technique: $\frac{3}{4} \div \frac{3}{8} = \frac{3}{4} \times \frac{8}{3} = \frac{24}{12}$
Check: Multiply answer by divisor: $2 \times \frac{3}{8} = \frac{6}{8} = \frac{3}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing numerators and denominators separately
Don't divide $\frac{3}{4} \div \frac{3}{8}$ by doing 3÷3=1 and 4÷8= $\frac{1}{2}$ to get $\frac{1}{1/2}$ ! This creates confusion and wrong answers. Always flip the second fraction and multiply instead.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

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

FAQ

Everything you need to know about this question

Why do I flip the second fraction instead of the first?

In division, you always flip the divisor (the second fraction). Think of it like this: $\frac{3}{4} \div \frac{3}{8}$ means "how many $\frac{3}{8}$ 's fit into $\frac{3}{4}$ ?" So you multiply by the reciprocal of what you're dividing by.

What's the reciprocal of a fraction?

The reciprocal means flipping the numerator and denominator. So the reciprocal of $\frac{3}{8}$ is $\frac{8}{3}$ . Remember: multiply any number by its reciprocal and you get 1!

Do I always get a whole number when dividing fractions?

Not always! In this problem we got 2, but many fraction divisions give fractional answers. For example, $\frac{1}{2} \div \frac{2}{3} = \frac{3}{4}$ . The key is to simplify your final answer.

How do I simplify fractions like 24/12?

Find the greatest common factor (GCF) of the numerator and denominator. For $\frac{24}{12}$ , the GCF is 12, so $\frac{24}{12} = \frac{24÷12}{12÷12} = \frac{2}{1} = 2$ .

Can I use this method for mixed numbers too?

Yes! First convert any mixed numbers to improper fractions, then use the reciprocal method. For example: $1\frac{1}{2} \div \frac{3}{4}$ becomes $\frac{3}{2} \div \frac{3}{4} = \frac{3}{2} \times \frac{4}{3}$ .

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