Question

Perform the indicated operation. Write all results in lowest terms. $$-\frac{1}{6}-\frac{1}{8}$$

Short answer

Answer: The result of the subtraction operation is $\frac{-7}{24}$.

Step-by-step solution

Find a common denominator

To find a common denominator, simply multiply the two denominators of the given fractions, which in this case are 6 and 8. The product of 6 and 8 is 48, thus making the common denominator 48.

Adjust the fractions to the common denominator

Now, we need to adjust each fraction so that their denominator is 48. To do this, we must find the number we multiplied with the original denominator to obtain the common denominator, and then multiply the numerator by the same number. For the first fraction: $$ \frac{-1}{6} \times \frac{8}{8} = \frac{-8}{48} $$ For the second fraction: $$ \frac{1}{8} \times \frac{6}{6} = \frac{6}{48} $$

Perform the operation

Now that both fractions have the same denominator, we can go ahead and perform the subtraction by simply subtracting the numerators: $$ \frac{-8}{48} - \frac{6}{48} = \frac{-8 - 6}{48} = \frac{-14}{48} $$

Simplify the result

Finally, we need to simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that number: The GCD of 14 and 48 is 2, so we can simplify the fraction as follows: $$ \frac{-14}{48} \div \frac{2}{2} = \frac{-14 \div 2}{48 \div 2} = \frac{-7}{24} $$

Final Answer

So the given operation simplifies to: $$ -\frac{1}{6}-\frac{1}{8} = \frac{-7}{24} $$