Question

Perform the indicated operation. Write all results in lowest terms. $$-\frac{7}{18}+\frac{1}{18}$$

Short answer

Answer: The result is $$\frac{-1}{3}$$.

Step-by-step solution

Identify the common denominator

Since both fractions have the same denominator, which is 18, we can proceed to the next step.

Add the numerators

Next, we add the numerators of both fractions, keeping the same denominator, as follows: $$-\frac{7}{18}+\frac{1}{18}= \frac{-7+1}{18}$$

Simplify the resulting fraction

Now we simplify the result: $$\frac{-7+1}{18} = \frac{-6}{18}$$

Reduce the fraction to lowest terms

To reduce the fraction to its lowest terms, find the greatest common divisor of the numerator and denominator, which is 6, and then divide both by 6: $$\frac{-6}{18} = \frac{-6 \div 6}{18 \div 6} = \frac{-1}{3}$$ So the final answer is: $$-\frac{7}{18}+\frac{1}{18}=\frac{-1}{3}$$