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.
Answer
The result is $\frac{5}{6}$.
Answer for screen readers
The sum of $\frac{1}{2}$ and $\frac{1}{3}$ is $\frac{5}{6}$.
Steps to Solve
- Identify the denominators
The denominators of the fractions are 2 and 3.
- Find the least common denominator (LCD)
The least common denominator can be found by determining the least common multiple of the denominators: $$ \text{LCD} = \text{lcm}(2, 3) = 6 $$
- Convert the fractions to equivalent fractions with the LCD
Convert each fraction to have the common denominator of 6:
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For $\frac{1}{2}$: $$ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} $$
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For $\frac{1}{3}$: $$ \frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6} $$
- 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 $\frac{5}{6}$.
More Information
Adding fractions requires a common denominator, and finding the least common multiple (LCM) of the denominators can help simplify the process. In this case, the LCM of 2 and 3 is 6.
Tips
- Forgetting to find a common denominator: Always identify the least common denominator before adding fractions.
- Not simplifying the final fraction: Remember to simplify the fraction if possible, although $\frac{5}{6}$ is already in simplest form.
