Bot GPT 4-o mini To round the sum of \( \frac{3}{6} + \frac{8}{9} \) to a benchmark fraction, we first find a common denominator and calculate the sum.
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Simplifying \( \frac{3}{6} \):
- \( \frac{3}{6} = \frac{1}{2} \)
Thus, the equation simplifies to: \[ \frac{1}{2} + \frac{8}{9} \]
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Finding a common denominator:
- The least common multiple (LCM) of 2 and 9 is 18.
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Converting to a common denominator:
- Convert \( \frac{1}{2} \) to have a denominator of 18: \[ \frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18} \]
- Convert \( \frac{8}{9} \) to have a denominator of 18: \[ \frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18} \]
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Adding the fractions: \[ \frac{9}{18} + \frac{16}{18} = \frac{25}{18} \]
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Rounding to a benchmark fraction:
- The fraction \( \frac{25}{18} \) is approximately \( 1.39 \), which can be rounded to the nearest benchmark fraction. The common benchmark fractions include \( \frac{1}{2}, \frac{1}{3}, \frac{2}{3}, 1, \frac{3}{2}, 2 \), etc.
- \( \frac{25}{18} \) is closest to \( \frac{1 \frac{7}{18}}{1} \) or approximately \( 1.5 \), which is \( \frac{3}{2} \).
Thus, the final rounded benchmark fraction is: \[ \frac{3}{2} \]
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