1. What is \( 6 \cdot \frac{2}{3} \) ? Show with a tape diagram.

To solve \( 6 \cdot \frac{2}{3} \), we can break it down step by step. 1. **Understanding the multiplication**: The expression \( 6 \cdot \frac{2}{3} \) means we want to find \( 2/3 \) of \( 6 \). 2. **Finding \( \frac{2}{3} \) of \( 6 \)**: To do this, we can first find \( \frac{1}{3} \) of \( 6 \) and then multiply that result by \( 2 \). - \( \frac{1}{3} \) of \( 6 \) is calculated as: \[ \frac{1}{3} \cdot 6 = \frac{6}{3} = 2 \] - Now, we multiply this result by \( 2 \): \[ 2 \cdot 2 = 4 \] 3. **Final result**: Therefore, \( 6 \cdot \frac{2}{3} = 4 \). ### Tape Diagram Representation To visualize this with a tape diagram: - Draw a long rectangle (the tape) and divide it into \( 3 \) equal parts since we are working with \( \frac{2}{3} \). - Each part represents \( \frac{1}{3} \) of \( 6 \), which we calculated to be \( 2 \). - Shade \( 2 \) of the \( 3 \) parts to represent \( \frac{2}{3} \). Here’s a simple representation: ``` |---|---|---| (Total = 6) | 2 | 2 | 2 | |---|---|---| ``` Shaded parts (representing \( 4 \)): ``` |###|###|---| (Shaded = 4) | 2 | 2 | 2 | |---|---|---| ``` Thus, the tape diagram visually confirms that \( 6 \cdot \frac{2}{3} = 4 \).