5. \( \frac{1}{5}+\frac{2}{3}= \)

To solve \( \frac{1}{5}+\frac{2}{3} \), we first need a common denominator. The least common multiple of 5 and 3 is 15. Now, we convert each fraction: - \( \frac{1}{5} = \frac{3}{15} \) - \( \frac{2}{3} = \frac{10}{15} \) Now, we can add them together: \( \frac{3}{15} + \frac{10}{15} = \frac{13}{15} \). So, the answer is \( \frac{13}{15} \). For those who enjoy history, did you know that fractions have been around since ancient Egypt? They used a system of unit fractions, like \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4} \), and others, recorded in hieroglyphics! It’s fascinating how we've carried on this tradition of dividing and conquering numbers through the ages. In real-world applications, understanding fractions is crucial for cooking, carpentry, and even budgeting! If a recipe calls for \( \frac{1}{5} \) of a cup of sugar and you want to double the recipe, knowing how to handle fractions and convert them to common denominators is essential to getting that perfect batch of cookies. Happy cooking!