To add the fractions $\frac{1}{2} + \frac{2}{3}$, we need to find a common denominator.

Step 1: Find the Least Common Denominator (LCD)

The denominators are 2 and 3. The least common denominator is the smallest number that both 2 and 3 can divide into, which is 6.

Step 2: Convert Each Fraction to Have the LCD as the Denominator

• For $\frac{1}{2}$, multiply the numerator and denominator by 3: $\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$
• For $\frac{2}{3}$, multiply the numerator and denominator by 2: $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$

Step 3: Add the Fractions

Now that both fractions have the same denominator, we can add them directly: $\frac{3}{6} + \frac{4}{6} = \frac{3 + 4}{6} = \frac{7}{6}$

Conclusion

The sum of $\frac{1}{2} + \frac{2}{3}$ is:

$\frac{7}{6}$

Would you like more details on this or have any questions?

Here are 5 related questions to explore further:

1. How do you add fractions with different denominators?
2. What is the process to subtract fractions with different denominators?
3. How do you convert improper fractions to mixed numbers?
4. How do you multiply and divide fractions?
5. What is the concept of the least common multiple (LCM)?

Tip: Always ensure fractions have a common denominator before adding or subtracting them.