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Simplify. Express your answer as a single fraction in simplest form. \newline12+vw3\frac{1}{2} + \frac{vw}{3}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline12+vw3\frac{1}{2} + \frac{vw}{3}
  1. Identify LCD: Identify the least common denominator (LCD) for the fractions 12\frac{1}{2} and vw3\frac{vw}{3}. The LCD for 22 and 33 is 66. We will use this to combine the fractions.
  2. Rewrite fractions: Rewrite each fraction with the common denominator of 66.\newline12\frac{1}{2} becomes 1×32×3=36\frac{1\times 3}{2\times 3} = \frac{3}{6}\newlinevw3\frac{vw}{3} becomes vw×23×2=2vw6\frac{vw\times 2}{3\times 2} = \frac{2vw}{6}
  3. Add fractions: Add the fractions with the common denominator.\newline(36)+(2vw6)=3+2vw6(\frac{3}{6}) + (\frac{2vw}{6}) = \frac{3 + 2vw}{6}
  4. Check for simplification: Check if the fraction (3+2vw)/6(3 + 2vw)/6 can be simplified further.\newlineSince 3+2vw3 + 2vw does not have a common factor with 66 other than 11, the fraction is already in its simplest form.

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