Question
1. What is \( 6 \cdot \frac{2}{3} \) ? Show with a tape diagram.
Ask by Simpson Erickson. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 6 \cdot \frac{2}{3} = 4 \).
Solution
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 \( 6 \cdot \frac{2}{3} = 4 \).
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Simplify this solution Extra Insights
To find \( 6 \cdot \frac{2}{3} \), you can break it down into understandable pieces. Picture a tape diagram where you have a bar divided into 6 equal sections to represent the number 6. Each section represents 1 whole unit. Since we are multiplying by \(\frac{2}{3}\), you take 2 out of every 3 sections. Thus, you would shade in 4 sections (since \(\frac{2}{3} \times 6 = 4\)) of the 6 total sections. So, \( 6 \cdot \frac{2}{3} = 4 \). To visualize it, imagine a chocolate bar divided into 6 squares (representing the 6). You then take two squares from every three sections. That means in total, you've taken 4 squares! So, you now have 4 squares of chocolate—yummy, right?
