Question

Perform the indicated operation. Write all results in lowest terms. $$\frac{1}{6}+\frac{1}{2}$$

Short answer

Answer: The sum of the fractions is $$\frac{2}{3}$$.

Step-by-step solution

Find the common denominator

To find the common denominator for the fractions $$\frac{1}{6}$$ and $$\frac{1}{2}$$, we need the least common multiple (LCM) of the denominators, which are 6 and 2. The LCM of 6 and 2 is 6. So, the common denominator is 6.

Adjust the fractions using the common denominator

Now we need to rewrite both fractions with the common denominator. The first fraction, $$\frac{1}{6}$$, already has the correct denominator, so we can leave it as it is. For the second fraction, $$\frac{1}{2}$$, we need to multiply both the numerator and denominator by 3 to get the equivalent fraction with the common denominator: $$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$$

Add the numerators of the adjusted fractions

Now that both fractions have the same denominator, we can add their numerators: $$\frac{1}{6}+\frac{3}{6} = \frac{1+3}{6}$$

Calculate the sum and simplify if necessary

Now, add the numerators and check if the resulting fraction can be simplified: $$\frac{1+3}{6} = \frac{4}{6}$$ We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2: $$\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}$$ So, the sum of the two fractions is $$\frac{2}{3}$$, and the result is already in the lowest terms.