Question

Perform the indicated operation. Write all results in lowest terms. $$-\frac{1}{6}+\frac{1}{10}$$

Short answer

Question: Perform the operation and present the result in its lowest terms: \(-\frac{1}{6}+\frac{1}{10}\) Answer: \(-\frac{1}{15}\)

Step-by-step solution

Find a common denominator

To add fractions with unlike denominators, we must first find a common denominator, which is the lowest common multiple (LCM) of both denominators. In this case, the denominators are 6 and 10. The LCM of 6 and 10 is 30. So, the common denominator will be 30.

Rewrite the fractions with the common denominator

Next, rewrite the fractions using the common denominator found in Step 1. Multiplying the first fraction by \(\frac{5}{5}\) and the second fraction by \(\frac{3}{3}\) will result in them having the common denominator 30. $$- \frac{1}{6} \cdot \frac{5}{5} = - \frac{5}{30}$$ $$\frac{1}{10} \cdot \frac{3}{3} = \frac{3}{30}$$ So, the revised operation becomes: $$- \frac{5}{30} + \frac{3}{30}$$

Add the fractions

Now, simply add the numerators of the fractions, keeping the common denominator 30. $$- \frac{5}{30} + \frac{3}{30} = \frac{-5 + 3}{30} = \frac{-2}{30}$$

Simplify the sum

Finally, simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 2 and 30 is 2. $$\frac{-2}{30} \div \frac{2}{2} = \frac{-1}{15}$$ The final answer, in lowest terms, is: $$-\frac{1}{6}+\frac{1}{10} = -\frac{1}{15}$$