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Simplify. Express your answer as a single fraction in simplest form. \newline53+w\frac{5}{3} + w

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline53+w\frac{5}{3} + w
  1. Convert whole number to fraction: To combine the fraction 53\frac{5}{3} with the whole number ww, we need to express ww as a fraction with a denominator of 33. We can do this by multiplying ww by 33\frac{3}{3}, which is equivalent to 11.\newlineCalculation: w×(33)=w×33w \times \left(\frac{3}{3}\right) = \frac{w \times 3}{3}
  2. Rewrite expression with fraction: Now we rewrite the original expression with ww as a fraction.\newlineCalculation: 53+w=53+w×33\frac{5}{3} + w = \frac{5}{3} + \frac{w \times 3}{3}
  3. Combine fractions with common denominator: Since both terms now have the same denominator, we can combine them into a single fraction by adding the numerators.\newlineCalculation: (5+w×3)/3(5 + w \times 3)/3
  4. Simplify final fraction: The expression is now a single fraction in simplest form, as there are no common factors between the numerator and the denominator that can be simplified further.\newlineFinal Answer: (5+3w)/3(5 + 3w)/3

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