Question

Perform the indicated operation. Write all results in lowest terms. $$-\frac{5}{6}+\frac{2}{5}$$

Short answer

Answer: \(\frac{-13}{30}\)

Step-by-step solution

Find the Least Common Multiple of the denominators

Observe the denominators of both fractions, 6 and 5. Since they do not have any common factors, the least common multiple (LCM) of the denominators is equal to their product: \(6 \times 5 = 30\).

Rewrite the fractions with least common denominator

We must find an equivalent fraction for each of the given fractions that has the denominator of the LCM. We can multiply the numerator and denominator of each fraction by the necessary factor: $$ -\frac{5}{6} \cdot \frac{5}{5} = -\frac{25}{30} $$ $$ \frac{2}{5} \cdot \frac{6}{6} = \frac{12}{30} $$ So we can rewrite the given expression as \(-\frac{25}{30}+\frac{12}{30}\).

Perform the indicated operation

Now that both fractions have the same denominator, we can directly add them: $$ -\frac{25}{30}+\frac{12}{30} = \frac{-25 + 12}{30} = \frac{-13}{30} $$ The result is already in lowest terms, since the numerator and denominator do not share any common factors. So we have: $$ -\frac{5}{6}+\frac{2}{5} = \frac{-13}{30} $$