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

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

Simply flip the numerator and denominator! For $ \frac{1}{2} $, the reciprocal is $ \frac{2}{1} $ or just 2. For $ \frac{3}{4} $, it would be $ \frac{4}{3} $.

Q: Can I solve this without using reciprocals?

You could think of it as "what times 1/2 equals 1/4?" but using reciprocals is the standard method that works for all fraction division problems and prepares you for more complex equations.

Q: Why does 1/4 × 2 equal 1/2 instead of 2/4?

Actually, $ \frac{1}{4} \times 2 = \frac{2}{4} $, and then we simplify: $ \frac{2}{4} = \frac{1}{2} $. Always reduce fractions to their simplest form!

Q: How do I check my answer is correct?

Substitute your answer back into the original equation! If $ \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} $, then you know $ \frac{1}{2} $ is correct.

Fraction Division with Reciprocal Method

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 Isolate the unknown

00:06 Write division as multiplication by the reciprocal

00:09 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

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

Step-by-step solution

To solve the equation $\frac{1}{2} \times ? = \frac{1}{4}$ , we need to find the number that makes this equation true.

Let's perform the operations step-by-step:

Step 1: Start with the given equation: $\frac{1}{2} \times x = \frac{1}{4}$ .
Step 2: To isolate $x$ , divide both sides by $\frac{1}{2}$ . This gives us: $x = \frac{1}{4} \div \frac{1}{2}$ .
Step 3: Dividing by a fraction is the same as multiplying by its reciprocal. Thus, we have: $x = \frac{1}{4} \times \frac{2}{1}$ .
Step 4: Multiply the fractions: $x = \frac{1 \times 2}{4 \times 1} = \frac{2}{4}$ .
Step 5: Simplify the fraction: $x = \frac{1}{2}$ .

Therefore, the missing number is $\frac{1}{2}$ . This matches choice 4 from the given options.

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Division by a fraction equals multiplication by its reciprocal
Technique: $\frac{1}{4} \div \frac{1}{2} = \frac{1}{4} \times \frac{2}{1} = \frac{2}{4}$
Check: Substitute back: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying by the denominator instead of dividing by the fraction
Don't just multiply both sides by 2 to get x = 1/2 directly! This skips the division step and creates confusion about reciprocals. Always divide both sides by the coefficient using the reciprocal method.

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 flip the fraction when dividing?

Dividing by a fraction is the same as multiplying by its reciprocal! The reciprocal of $\frac{1}{2}$ is $\frac{2}{1}$ . This rule makes division problems much easier to solve.

How do I find the reciprocal of a fraction?

Simply flip the numerator and denominator! For $\frac{1}{2}$ , the reciprocal is $\frac{2}{1}$ or just 2. For $\frac{3}{4}$ , it would be $\frac{4}{3}$ .

Can I solve this without using reciprocals?

You could think of it as "what times 1/2 equals 1/4?" but using reciprocals is the standard method that works for all fraction division problems and prepares you for more complex equations.

Why does 1/4 × 2 equal 1/2 instead of 2/4?

Actually, $\frac{1}{4} \times 2 = \frac{2}{4}$ , and then we simplify: $\frac{2}{4} = \frac{1}{2}$ . Always reduce fractions to their simplest form!

How do I check my answer is correct?

Substitute your answer back into the original equation! If $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ , then you know $\frac{1}{2}$ is correct.

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