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The problem asks which equation shows the same relationship as \( \frac{1}{4} \div 2 = \frac{1}{8} \).

Let's break down the given equation:

\[
\frac{1}{4} \div 2 = \frac{1}{8}
\]

Dividing by 2 is equivalent to multiplying by the reciprocal of 2, which is \( \frac{1}{2} \). Therefore:

\[
\frac{1}{4} \div 2 = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}
\]

Now, let's check each option:

- **Option A**: \( \frac{1}{4} \times 2 = \frac{1}{8} \)
  
  This is incorrect because \( \frac{1}{4} \times 2 = \frac{2}{4} = \frac{1}{2} \), not \( \frac{1}{8} \).

- **Option B**: \( \frac{1}{4} = 2 \times \frac{1}{8} \)

  This is correct because \( 2 \times \frac{1}{8} = \frac{2}{8} = \frac{1}{4} \), which matches the original equation.

- **Option C**: \( 2 \div \frac{1}{4} = \frac{1}{8} \)

  This is incorrect because \( 2 \div \frac{1}{4} = 2 \times 4 = 8 \), not \( \frac{1}{8} \).

Thus, the correct answer is **B**: \( \frac{1}{4} = 2 \times \frac{1}{8} \).

Would you like more details or have any further questions? Here are 5 related questions to extend your understanding:

1. How do you convert division of fractions into multiplication?
2. Can you explain why dividing by 2 is equivalent to multiplying by \( \frac{1}{2} \)?
3. What is the general rule for dividing fractions?
4. How would the equation change if instead of dividing by 2, you divided by another fraction?
5. What are some other equivalent forms of \( \frac{1}{4} \div 2 \)?

**Tip**: Always remember to convert division problems into multiplication by using the reciprocal of the divisor to simplify your calculations.

Which equation shows the same relationship as 1/4 ÷ 2 = 1/8?

This question asks you to identify an equivalent equation for 1/4 ÷ 2 = 1/8. Learn how to convert division of fractions into multiplication using reciprocals, and understand the step-by-step solution. Suitable for students in Grades 5-7.

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