Bot GPT 4-o mini To divide the mixed numbers \( 2 \frac{3}{4} \) by \( 1 \frac{7}{8} \), we first convert each mixed number into an improper fraction.
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Convert \( 2 \frac{3}{4} \): \[ 2 \frac{3}{4} = 2 \times 4 + 3 = 8 + 3 = 11 \] So, \( 2 \frac{3}{4} = \frac{11}{4} \).
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Convert \( 1 \frac{7}{8} \): \[ 1 \frac{7}{8} = 1 \times 8 + 7 = 8 + 7 = 15 \] So, \( 1 \frac{7}{8} = \frac{15}{8} \).
Now, we need to divide \( \frac{11}{4} \) by \( \frac{15}{8} \): \[ \frac{11}{4} \div \frac{15}{8} = \frac{11}{4} \times \frac{8}{15} \]
Multiply the fractions: \[ \frac{11 \times 8}{4 \times 15} = \frac{88}{60} \]
Next, we simplify \( \frac{88}{60} \): Both the numerator and denominator can be divided by their greatest common divisor, which is 4: \[ \frac{88 \div 4}{60 \div 4} = \frac{22}{15} \]
Thus, \( \frac{22}{15} \) is an improper fraction. We can convert it to a mixed number: \[ 22 \div 15 = 1 \quad \text{(with a remainder of } 7 \text{)} \] So, \( \frac{22}{15} = 1 \frac{7}{15} \).
In conclusion, the answer is: \[ \boxed{\frac{22}{15}} \text{ or } 1 \frac{7}{15} \]
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