Question
Which expressions can be used to find 23×4 ? Check the THREE that apply.(3 points)Responses23+23+23+232 thirds plus 2 thirds plus 2 thirds plus 2 thirds43+43+434 thirds plus 4 thirds plus 4 thirds(4×3)2the fraction with numerator open paren 4 times 3 close paren and denominator 24×234 times 2 thirds(4×2)3
Answers
GPT-4o mini
To find \( 23 \times 4 \), we are looking for expressions that represent the same multiplication. Let's break down the options:
1. **\(23 + 23 + 23 + 23\)**: This expression adds \( 23 \) four times, which is equivalent to \( 23 \times 4 \). **(Valid)**
2. **\(2\, \text{thirds} + 2\, \text{thirds} + 2\, \text{thirds} + 2\, \text{thirds}\)**: Assuming '2 thirds' represents a quantity rather than effectively multiplying 23, this does not relate back to \( 23 \times 4 \). **(Not valid)**
3. **\(43 + 43 + 43\)**: This adds \( 43 \) three times, which does not equal to \( 23 \times 4 \). **(Not valid)**
4. **\(4\, \text{thirds} + 4\, \text{thirds}\)**: Similar to option 2, this doesn't hold as a valid expression for \( 23 \times 4 \). **(Not valid)**
5. **\((4 \times 3)2\)**: This is unclear, but \( (4 \times 3) \times 2 \) would equal \( 24 \), which isn't \( 23 \times 4\). This seems to misrepresent the multiplication. **(Not valid)**
6. **\((2 \times 4 \, \text{thirds})\)**: Assuming this means \( 2 \times 4 = 8 \), the units do not match the \( 23 \). **(Not valid)**
7. **\((4 \times 2)3\)**: This is unclear. If it's meant as \( (4 \times 2) \times 3 = 24 \), it doesn't match \( 23 \times 4 \). **(Not valid)**
To directly conclude:
- **Valid expressions to represent \( 23 \times 4 \)**:
1. \(23 + 23 + 23 + 23\)
None of the others correctly represent \( 23 \times 4 \).
- **Final Answer**:
Only **one** valid expression exists: **\( 23 + 23 + 23 + 23 \)**.
If you intended to look for three different valid conversions from possible expressions that point to computing \( 23 \times 4 \), there may need some alternate interpretations, as the currently assessed expressions do not yield sufficient valid options.
1. **\(23 + 23 + 23 + 23\)**: This expression adds \( 23 \) four times, which is equivalent to \( 23 \times 4 \). **(Valid)**
2. **\(2\, \text{thirds} + 2\, \text{thirds} + 2\, \text{thirds} + 2\, \text{thirds}\)**: Assuming '2 thirds' represents a quantity rather than effectively multiplying 23, this does not relate back to \( 23 \times 4 \). **(Not valid)**
3. **\(43 + 43 + 43\)**: This adds \( 43 \) three times, which does not equal to \( 23 \times 4 \). **(Not valid)**
4. **\(4\, \text{thirds} + 4\, \text{thirds}\)**: Similar to option 2, this doesn't hold as a valid expression for \( 23 \times 4 \). **(Not valid)**
5. **\((4 \times 3)2\)**: This is unclear, but \( (4 \times 3) \times 2 \) would equal \( 24 \), which isn't \( 23 \times 4\). This seems to misrepresent the multiplication. **(Not valid)**
6. **\((2 \times 4 \, \text{thirds})\)**: Assuming this means \( 2 \times 4 = 8 \), the units do not match the \( 23 \). **(Not valid)**
7. **\((4 \times 2)3\)**: This is unclear. If it's meant as \( (4 \times 2) \times 3 = 24 \), it doesn't match \( 23 \times 4 \). **(Not valid)**
To directly conclude:
- **Valid expressions to represent \( 23 \times 4 \)**:
1. \(23 + 23 + 23 + 23\)
None of the others correctly represent \( 23 \times 4 \).
- **Final Answer**:
Only **one** valid expression exists: **\( 23 + 23 + 23 + 23 \)**.
If you intended to look for three different valid conversions from possible expressions that point to computing \( 23 \times 4 \), there may need some alternate interpretations, as the currently assessed expressions do not yield sufficient valid options.