using an area model

Question

use the area model to show 1/2 divide 4
1/2 divide 4 = 1/___
it takes __ pieces to make up the whole.
so the size of each pieces is ___

Answer 1

To visualize the division of \( \frac{1}{2} \div 4 \) using an area model, we can follow these steps:

1. Understanding the Problem: We are trying to divide \( \frac{1}{2} \) (which can be seen as a half) into 4 equal parts.

2. Creating the Whole: If we consider \( \frac{1}{2} \) as a rectangle where the area is \( \frac{1}{2} \), then we need to visualize dividing this rectangle into 4 equal pieces.

3. Dividing the Area: To divide \( \frac{1}{2} \) into 4 equal sections, we take the area and divide it into 4 equal rectangles.

   • If the total area (the half) is represented as \( \frac{1}{2} \), when we divide this area into 4, we want to find the size of each piece.

4. Calculating the Size of Each Piece:

   • Each piece will be equal to \( \frac{1}{2} \div 4 \).
   • This can be calculated as: \[ \frac{1}{2} \div 4 = \frac{1}{2} \cdot \frac{1}{4} = \frac{1 \cdot 1}{2 \cdot 4} = \frac{1}{8} \]

So, we can summarize:

• \( \frac{1}{2} \div 4 = \frac{1}{8} \)
• It takes 4 pieces to make up the whole \( \frac{1}{2} \).
• So the size of each piece is \( \frac{1}{8} \).

Summary:

1. \( \frac{1}{2} \div 4 = \frac{1}{8} \)
2. It takes 4 pieces to make up the whole.
3. So the size of each piece is \( \frac{1}{8} \).