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Evaluate the expression shown below and write your answer as a fraction in simplest form. (5)/(8)+(2)/(7) Answer:

Evaluate the expression shown below and write your answer as a fraction in simplest form.\newline58+27 \frac{5}{8}+\frac{2}{7} \newlineAnswer:

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Full solution

Q. Evaluate the expression shown below and write your answer as a fraction in simplest form.\newline58+27 \frac{5}{8}+\frac{2}{7} \newlineAnswer:
  1. Identify LCD: Identify the Least Common Denominator (LCD) for the fractions 58\frac{5}{8} and 27\frac{2}{7}. The denominators are 88 and 77, which are both prime numbers. Therefore, the LCD is their product, which is 8×7=568 \times 7 = 56.
  2. Convert to Equivalent Fraction: Convert each fraction to an equivalent fraction with the LCD as the denominator.\newlineFor 58\frac{5}{8}, we multiply the numerator and denominator by 77 to get (5×7)/(8×7)=3556\left(5 \times 7\right) / \left(8 \times 7\right) = \frac{35}{56}.\newlineFor 27\frac{2}{7}, we multiply the numerator and denominator by 88 to get (2×8)/(7×8)=1656\left(2 \times 8\right) / \left(7 \times 8\right) = \frac{16}{56}.
  3. Add Fractions: Add the equivalent fractions.\newlineNow that both fractions have the same denominator, we can add them directly:\newline3556+1656=(35+16)56=5156\frac{35}{56} + \frac{16}{56} = \frac{(35 + 16)}{56} = \frac{51}{56}.

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