Bot GPT 4-o mini To solve the division of \( 5 \frac{9}{14} \div \frac{6}{7} \), we first convert the mixed number \( 5 \frac{9}{14} \) into an improper fraction.
- Convert \( 5 \frac{9}{14} \) to an improper fraction:
\[ 5 \frac{9}{14} = \frac{5 \times 14 + 9}{14} = \frac{70 + 9}{14} = \frac{79}{14} \]
- Now we have the problem:
\[ \frac{79}{14} \div \frac{6}{7} \]
- To divide by a fraction, we multiply by its reciprocal:
\[ \frac{79}{14} \times \frac{7}{6} \]
- Multiply the fractions:
\[ \frac{79 \times 7}{14 \times 6} \]
- Calculate the multiplication:
\[ \frac{553}{84} \]
- Now simplify the fraction \( \frac{553}{84} \). First, we check if there's a common factor:
- The numerator (553) is a prime number, and the denominator (84) is not divisible by 553.
Since there are no common factors, \( \frac{553}{84} \) is already in its simplest form.
- Optionally, we can convert it back to a mixed number:
\[ 553 ÷ 84 = 6 \text{ R } 49 \]
So,
\[ 6 \frac{49}{84} \]
- Finally, simplify \( \frac{49}{84} \):
- The greatest common divisor of 49 and 84 is 7, so:
\[ \frac{49 \div 7}{84 \div 7} = \frac{7}{12} \]
Thus, the final result as a mixed number is:
\[ 6 \frac{7}{12} \]
Therefore, the final answer is:
\[ \frac{553}{84} \text{ or } 6 \frac{7}{12}. \]
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