Find the missing term in the proportion: \( \frac{6}{3}=\frac{3}{n} \) \( n=\square \)

To solve for \( n \) in the proportion \( \frac{6}{3}=\frac{3}{n} \), we can cross-multiply. This means we multiply the numerator of one fraction by the denominator of the other fraction, leading to the equation: \( 6n = 3 \times 3 \) Simplifying the right side gives: \( 6n = 9 \) Next, divide both sides by 6: \( n = \frac{9}{6} = \frac{3}{2} \) So, the missing term is \( n = \frac{3}{2} \). Finding proportions has a rich history in mathematics! It dates back to ancient civilizations, such as the Egyptians and Greeks, who used these concepts in trade and architecture. The Greeks, particularly, explored ratios extensively, seeing them as the foundation of mathematics, leading to significant advancements in geometry. In real-world applications, proportional reasoning is everywhere! It's used in cooking (adjusting recipes), mixing solutions in chemistry, and even in finance while calculating interest rates. Understanding how to solve proportions can help you make important decisions in everyday situations, like budgeting your monthly expenses or adjusting ingredient quantities for a dinner party.