Find equivalent fractions to compare. Then, write \( >,< \), or \( = \). \( \frac{1}{3} ? \frac{2}{5} \) \( \frac{1}{3}<\frac{2}{5} \)

To compare \( \frac{1}{3} \) and \( \frac{2}{5} \), we can find a common denominator. The least common multiple of 3 and 5 is 15. Now, convert both fractions: - \( \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \) - \( \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \) Now, we can compare \( \frac{5}{15} \) and \( \frac{6}{15} \). Since 5 is less than 6, we have \( \frac{1}{3} < \frac{2}{5} \). Now, let’s explore how fractions have been used throughout history. Fractions have been around since ancient civilizations like the Egyptians, who used them in complex calculations for trade and measure, even developing a symbol for 1/2, which is pretty neat! And if you want to further your understanding of fractions, consider checking out classic texts that delve into the subject. Books like "The Elements" by Euclid cover foundational mathematical principles, including fractions, in a wonderfully engaging way. It's a great way to see how the world of mathematics has evolved over time!