To subtract \( \frac{5}{6} \) from \( 4 \frac{7}{9} \), we first convert the mixed number into an improper fraction.
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Convert \( 4 \frac{7}{9} \) to an improper fraction: \[ 4 \frac{7}{9} = \frac{(4 \times 9) + 7}{9} = \frac{36 + 7}{9} = \frac{43}{9} \]
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Now, subtract \( \frac{5}{6} \) from \( \frac{43}{9} \): To perform the subtraction, we need a common denominator. The denominators are 9 and 6, and the least common multiple (LCM) of 9 and 6 is 18.
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Convert both fractions to have a denominator of 18: \[ \frac{43}{9} = \frac{43 \times 2}{9 \times 2} = \frac{86}{18} \] \[ \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \]
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Now perform the subtraction: \[ \frac{86}{18} - \frac{15}{18} = \frac{86 - 15}{18} = \frac{71}{18} \]
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Convert \( \frac{71}{18} \) back to a mixed number: To convert \( \frac{71}{18} \) to a mixed number, divide 71 by 18: \[ 71 \div 18 = 3 \quad (\text{remainder } 17) \] Thus, \( \frac{71}{18} = 3 \frac{17}{18} \).
Therefore, \( 4 \frac{7}{9} - \frac{5}{6} = 3 \frac{17}{18} \).