Solve the Fraction Equation: 2/3 × ? = 1/4

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

Dividing by a fraction is the same thing as multiplying by its reciprocal! When you see $ ? = \frac{1}{4} \div \frac{2}{3} $, it's easier to flip $ \frac{2}{3} $ to get $ \frac{3}{2} $ and multiply.

Q: How do I find the reciprocal of a fraction?

Simply flip the numerator and denominator! The reciprocal of $ \frac{2}{3} $ is $ \frac{3}{2} $. For whole numbers like 5, write it as $ \frac{5}{1} $ first, then flip to get $ \frac{1}{5} $.

Q: Can I solve this by guessing and checking the answers?

While you could test each option, understanding the reciprocal method is much faster and helps you solve any similar problem! Plus, you'll understand why $ \frac{3}{8} $ is correct.

Q: What if I get a mixed number as my answer?

In this problem, $ \frac{3}{8} $ is already in simplest form as an improper fraction. If you got a mixed number, convert it back to an improper fraction to match the answer choices.

Q: How do I check if my answer is right?

Substitute your answer back into the original equation! $ \frac{2}{3} \times \frac{3}{8} = \frac{6}{24} = \frac{1}{4} $. Since this equals the right side, your answer is correct!

Fraction Division with Reciprocal Method

$\frac{2}{3}\times?=\frac{1}{4}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the unknown together.

00:08 First, we'll isolate the unknown, so it's all by itself on one side.

00:14 Now, change division to multiplication by using the reciprocal, then calculate the results.

00:20 And there you have it! That's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{2}{3}\times?=\frac{1}{4}$

Step-by-step solution

To solve this problem, we’ll follow the division of fractions method:

Step 1: Start with the given equation $\frac{2}{3} \times ? = \frac{1}{4}$ .
Step 2: To isolate the unknown, divide both sides of the equation by $\frac{2}{3}$ . This can be done by multiplying $\frac{1}{4}$ by the reciprocal of $\frac{2}{3}$ , which is $\frac{3}{2}$ .
Step 3: The calculation becomes: $\frac{1}{4} \times \frac{3}{2} = \frac{1 \times 3}{4 \times 2} = \frac{3}{8}$ .

Therefore, the solution to the problem is $? = \frac{3}{8}$ . Hence, the correct choice is option 2.

Final Answer

$\frac{3}{8}$

Key Points to Remember

Essential concepts to master this topic

Rule: To divide by a fraction, multiply by its reciprocal
Technique: $\frac{1}{4} \div \frac{2}{3} = \frac{1}{4} \times \frac{3}{2} = \frac{3}{8}$
Check: Substitute back: $\frac{2}{3} \times \frac{3}{8} = \frac{6}{24} = \frac{1}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Cross-multiplying incorrectly when solving for the unknown
Don't try to cross-multiply when you have $\frac{2}{3} \times ? = \frac{1}{4}$ = confusion with wrong setup! Cross-multiplication only works with two fractions equal to each other. Always isolate the unknown by dividing both sides by $\frac{2}{3}$ , which means multiplying by its reciprocal.

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{3}\times\frac{5}{7}=$

FAQ

Everything you need to know about this question

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

Dividing by a fraction is the same thing as multiplying by its reciprocal! When you see $? = \frac{1}{4} \div \frac{2}{3}$ , it's easier to flip $\frac{2}{3}$ to get $\frac{3}{2}$ and multiply.

How do I find the reciprocal of a fraction?

Simply flip the numerator and denominator! The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$ . For whole numbers like 5, write it as $\frac{5}{1}$ first, then flip to get $\frac{1}{5}$ .

Can I solve this by guessing and checking the answers?

While you could test each option, understanding the reciprocal method is much faster and helps you solve any similar problem! Plus, you'll understand why $\frac{3}{8}$ is correct.

What if I get a mixed number as my answer?

In this problem, $\frac{3}{8}$ is already in simplest form as an improper fraction. If you got a mixed number, convert it back to an improper fraction to match the answer choices.

How do I check if my answer is right?

Substitute your answer back into the original equation! $\frac{2}{3} \times \frac{3}{8} = \frac{6}{24} = \frac{1}{4}$ . Since this equals the right side, your answer is correct!

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