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Simplify. Express your answer as a single fraction in simplest form. \newlinex4+8x5\frac{x}{4} + \frac{8x}{5}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newlinex4+8x5\frac{x}{4} + \frac{8x}{5}
  1. Identify LCD: Identify the least common denominator (LCD) for the fractions x4\frac{x}{4} and 8x5\frac{8x}{5}. The denominators are 44 and 55, so the LCD is their least common multiple, which is 2020.
  2. Rewrite fractions: Rewrite each fraction with the common denominator of 2020. For x4\frac{x}{4}, multiply both the numerator and the denominator by 55 to get x×54×5=5x20\frac{x\times 5}{4\times 5} = \frac{5x}{20}. For 8x5\frac{8x}{5}, multiply both the numerator and the denominator by 44 to get 8x×45×4=32x20\frac{8x\times 4}{5\times 4} = \frac{32x}{20}.
  3. Add fractions: Add the two fractions with the common denominator.\newline(5x20)+(32x20)=(5x+32x20)=37x20(\frac{5x}{20}) + (\frac{32x}{20}) = (\frac{5x + 32x}{20}) = \frac{37x}{20}.
  4. Check for simplification: Check if the resulting fraction can be simplified further. The numerator 37x37x and the denominator 2020 have no common factors other than 11, so the fraction is already in its simplest form.

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