In a math class, students learned about ratios, which compare two quantities by division, such as the ratio of boys to girls in a classroom. They also discussed rates, which compare two quantities with different units, like miles per hour or dollars per item. The concept of unit rate was introduced, which is a rate with a denominator of 1, like $3 per apple. The teacher explained that when two ratios are equal, they form a proportion. Students practiced cross-multiplication to solve proportions, ensuring that the products of the means and extremes are equal. For example, if 4/5 = 8/x, solving for x involves cross-multiplying to find x = 10. They also worked on simplifying ratios and converting percentages to ratios, such as turning 50% into 1:2. In word problems, they learned how to use ratios to find missing values, such as calculating the number of red apples when given the total and the ratio of red to green apples. The teacher emphasized the importance of understanding these concepts for real-world applications, such as calculating discounts and comparing prices.