CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x/5 + x/4

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Identify the terms to be added: \( \frac{2x}{5} + \frac{x}{4} \). Since these are fractions with different denominators, we need to find a common denominator before adding.

Find the least common denominator (LCD) of 5 and 4. The LCD is the smallest number that both denominators divide into evenly. Calculate the LCD as \( \text{LCD} = 20 \).

Rewrite each fraction with the denominator 20 by multiplying numerator and denominator appropriately: \( \frac{2x}{5} = \frac{2x \times 4}{5 \times 4} = \frac{8x}{20} \) and \( \frac{x}{4} = \frac{x \times 5}{4 \times 5} = \frac{5x}{20} \).

Add the two fractions now that they have the same denominator: \( \frac{8x}{20} + \frac{5x}{20} = \frac{8x + 5x}{20} = \frac{13x}{20} \).

Check if the resulting fraction \( \frac{13x}{20} \) can be simplified further by finding the greatest common divisor (GCD) of 13 and 20. Since 13 is a prime number and does not divide 20, the fraction is already in lowest terms.

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