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Simplify:\newline216−712+142 \frac{1}{6}-\frac{7}{12}+\frac{1}{4}

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Full solution

Q. Simplify:\newline216−712+142 \frac{1}{6}-\frac{7}{12}+\frac{1}{4}
  1. Convert to Improper Fraction: Convert mixed number to improper fraction: 216=(2×6+1)/6=1362 \frac{1}{6} = (2 \times 6 + 1)/6 = \frac{13}{6}.
  2. Find Common Denominator: Find a common denominator for 136\frac{13}{6}, −712-\frac{7}{12}, and 14\frac{1}{4}. The common denominator is 1212.
  3. Convert to Common Denominator: Convert all fractions to have the common denominator: \newline136=(13×2)(6×2)=2612\frac{13}{6} = \frac{(13 \times 2)}{(6 \times 2)} = \frac{26}{12}, \newline−712-\frac{7}{12} stays the same, \newline14=(1×3)(4×3)=312\frac{1}{4} = \frac{(1 \times 3)}{(4 \times 3)} = \frac{3}{12}.
  4. Add Fractions: Add the fractions with the common denominator: 2612−712+312=(26−7+3)12=2212.\frac{26}{12} - \frac{7}{12} + \frac{3}{12} = \frac{(26 - 7 + 3)}{12} = \frac{22}{12}.

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