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The problem asks to determine how many pieces Zhen cuts her board into.

### Given:
- The board length is \( \frac{3}{2} \) feet.
- Each piece is \( \frac{1}{4} \) foot long.

To find the number of pieces, we need to divide the total length of the board by the length of each piece:

\[
\text{Number of pieces} = \frac{\text{Total length of board}}{\text{Length of each piece}} = \frac{\frac{3}{2}}{\frac{1}{4}}
\]

To divide fractions, we multiply the first fraction by the reciprocal of the second:

\[
\frac{3}{2} \div \frac{1}{4} = \frac{3}{2} \times \frac{4}{1} = \frac{12}{2} = 6
\]

### Answer:
Zhen can cut her board into **6 pieces**.

Would you like more details on the steps, or have any questions? Here are 5 related questions you might explore:

1. How do you multiply and divide fractions?
2. What happens when the divisor is larger than the dividend in fraction division?
3. How can you visually represent fraction division on a number line?
4. If each piece were \( \frac{1}{3} \) foot long, how many pieces would there be?
5. What if Zhen’s board was \( 2 \frac{1}{2} \) feet long and she still cuts pieces \( \frac{1}{4} \) foot long?

### Tip:
When dividing by a fraction, remember to multiply by the reciprocal of that fraction for an easier solution!

Zhen starts with a board that is 3/2 feet long. She cuts her board into pieces that are each 1/4 foot long for her stacking game. How many pieces does Zhen cut her board into?

Learn how to divide fractions using a real-world example: Zhen cuts a 3/2 foot long board into 1/4 foot pieces. This problem demonstrates key concepts of fraction division and multiplication by reciprocals, perfect for students in Grades 5-6.

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