Question
Find the product and write it in simplest form: twoandthreeeighthstimesoneandtwothirds_large
(1 point)
Responses
twoandsixtwentyfourths_large
Image with alt text: twoandsixtwentyfourths_large
threeandtwentythreetwentyfourths_large
Image with alt text: threeandtwentythreetwentyfourths_large
threeandthreefourths_large
Image with alt text: threeandthreefourths_large
ninetyfiveeighths_large
(1 point)
Responses
twoandsixtwentyfourths_large
Image with alt text: twoandsixtwentyfourths_large
threeandtwentythreetwentyfourths_large
Image with alt text: threeandtwentythreetwentyfourths_large
threeandthreefourths_large
Image with alt text: threeandthreefourths_large
ninetyfiveeighths_large
Answers
GPT-4o mini
To find the product of two and three-eighths (2 3/8) and one and two-thirds (1 2/3), we first convert both mixed numbers into improper fractions.
1. **Convert 2 3/8 to an improper fraction**:
\[
2 \times 8 + 3 = 16 + 3 = 19 \quad \Rightarrow \quad \frac{19}{8}
\]
2. **Convert 1 2/3 to an improper fraction**:
\[
1 \times 3 + 2 = 3 + 2 = 5 \quad \Rightarrow \quad \frac{5}{3}
\]
3. **Multiply the improper fractions**:
\[
\frac{19}{8} \times \frac{5}{3} = \frac{19 \times 5}{8 \times 3} = \frac{95}{24}
\]
4. **Convert the result back to a mixed number**:
- Divide 95 by 24:
\[
95 \div 24 = 3 \quad (\text{remainder } 3)
\]
- This gives us:
\[
3 \frac{3}{24} \quad \Rightarrow \quad 3 \frac{1}{8} \quad (\text{since } \frac{3}{24} \text{ simplifies to } \frac{1}{8})
\]
So the product of two and three-eighths and one and two-thirds is **three and one-eighth** or **3 1/8**.
However, looking through the options given, the equivalent improper fraction \( \frac{95}{24} \) is what we're ultimately interested in. This does not match any of the given answer choices, which seem to have some inaccuracies.
The correct answer should be presented as **ninety-five twenty-fourths**. If the choice was represented in mixed number form, it should show as \( 3 \frac{1}{8} \) or \( \frac{95}{24} \).
Given the choices presented, assuming they're intended to approximate \( \frac{95}{24} \), it would likely correspond to **three and three-fourths** which is also simplified, but it's not accurate to \( \frac{95}{24} \) exactly.
If all forms are taken into consideration, **the best match from the options would likely be interpreted as:**
**three and three fourths (though technically incorrect mathematically)**.
1. **Convert 2 3/8 to an improper fraction**:
\[
2 \times 8 + 3 = 16 + 3 = 19 \quad \Rightarrow \quad \frac{19}{8}
\]
2. **Convert 1 2/3 to an improper fraction**:
\[
1 \times 3 + 2 = 3 + 2 = 5 \quad \Rightarrow \quad \frac{5}{3}
\]
3. **Multiply the improper fractions**:
\[
\frac{19}{8} \times \frac{5}{3} = \frac{19 \times 5}{8 \times 3} = \frac{95}{24}
\]
4. **Convert the result back to a mixed number**:
- Divide 95 by 24:
\[
95 \div 24 = 3 \quad (\text{remainder } 3)
\]
- This gives us:
\[
3 \frac{3}{24} \quad \Rightarrow \quad 3 \frac{1}{8} \quad (\text{since } \frac{3}{24} \text{ simplifies to } \frac{1}{8})
\]
So the product of two and three-eighths and one and two-thirds is **three and one-eighth** or **3 1/8**.
However, looking through the options given, the equivalent improper fraction \( \frac{95}{24} \) is what we're ultimately interested in. This does not match any of the given answer choices, which seem to have some inaccuracies.
The correct answer should be presented as **ninety-five twenty-fourths**. If the choice was represented in mixed number form, it should show as \( 3 \frac{1}{8} \) or \( \frac{95}{24} \).
Given the choices presented, assuming they're intended to approximate \( \frac{95}{24} \), it would likely correspond to **three and three-fourths** which is also simplified, but it's not accurate to \( \frac{95}{24} \) exactly.
If all forms are taken into consideration, **the best match from the options would likely be interpreted as:**
**three and three fourths (though technically incorrect mathematically)**.