https://file.aiquickdraw.com/mathbot/file/17272807080394ffjxpcr.jpg

Let's focus on the problem shown in the image.

We have this equation: 
\[
\frac{1}{4} \div 2 = \frac{1}{4} \times \underline{\hspace{0.5cm}} = \underline{\hspace{0.5cm}}
\]

To solve the first part:
\[
\frac{1}{4} \div 2
\]
Dividing by 2 is equivalent to multiplying by the reciprocal of 2 (which is \(\frac{1}{2}\)):
\[
\frac{1}{4} \times \frac{1}{2} = \frac{1 \times 1}{4 \times 2} = \frac{1}{8}
\]

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

Now for the multiplication part:
\[
\frac{1}{4} \times \underline{\hspace{0.5cm}} = \frac{1}{8}
\]

This means we need to find a number that when multiplied by \(\frac{1}{4}\) gives \(\frac{1}{8}\). Let’s solve for \(x\):
\[
\frac{1}{4} \times x = \frac{1}{8}
\]
Multiply both sides by 4:
\[
x = \frac{1}{8} \times 4 = \frac{4}{8} = \frac{1}{2}
\]

Thus, the missing number is \(\frac{1}{2}\), and the complete equation is:
\[
\frac{1}{4} \div 2 = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}
\]

Would you like further explanation or more details on this? Here are some related questions for practice:

1. What is \(\frac{1}{3} \div 2\)?
2. Solve \(\frac{1}{5} \div 4\).
3. If \(\frac{1}{6} \times x = \frac{1}{12}\), what is \(x\)?
4. What is the reciprocal of \(\frac{1}{8}\)?
5. How do you multiply fractions?

**Tip:** When dividing fractions, multiply by the reciprocal of the divisor.

Learn how to solve fraction problems like 1/4 ÷ 2 = 1/4 × ___ through multiplication and division of fractions. This example uses reciprocal multiplication to divide and solve the equation. Suitable for students in Grades 6-8.

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