1/2 plus 1/3 as a fraction

Understand the Problem

The question is asking to add the fractions 1/2 and 1/3 together and express the result as a single fraction. To solve this, we will find a common denominator and then combine the numerators appropriately.

The result is $\frac{5}{6}$.

The sum of $\frac{1}{2}$ and $\frac{1}{3}$ is $\frac{5}{6}$.

Steps to Solve

1. Identify the denominators

The denominators of the fractions are 2 and 3.

1. Find the least common denominator (LCD)

The least common denominator can be found by determining the least common multiple of the denominators: $$\text{LCD} = \text{lcm}(2, 3) = 6$$

1. Convert the fractions to equivalent fractions with the LCD

Convert each fraction to have the common denominator of 6:

• For $\frac{1}{2}$: $$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$$

• For $\frac{1}{3}$: $$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$$

1. Add the two fractions

Now that both fractions have a common denominator, we can add them together: $$\frac{3}{6} + \frac{2}{6} = \frac{3 + 2}{6} = \frac{5}{6}$$

The sum of $\frac{1}{2}$ and $\frac{1}{3}$ is $\frac{5}{6}$.

• Not simplifying the final fraction: Remember to simplify the fraction if possible, although $\frac{5}{6}$ is already in simplest form.