Ratios are used to compare two or more quantities. They are expressed as a fraction or a division of one quantity by another. For example, if you have 5 red marbles and 3 blue marbles, the ratio of red marbles to blue marbles is 5:3. Ratios can also be expressed as decimals or percentages.

Proportions are used to show how two ratios are related to each other. When two ratios are proportional, it means that they have the same relationship between the quantities being compared. For example, if 5 red marbles are to 3 blue marbles as 15 red marbles are to x blue marbles, we can solve for x by setting up a proportion:

5/3 = 15/x

To solve for x, we can cross-multiply and simplify:

5x = 45

x = 9

So if we have 15 red marbles, we would need 9 blue marbles to maintain the same ratio as 5:3.

Understanding ratios and proportions can be useful in many real-world situations, such as cooking and baking, scaling drawings or models, and calculating distances or speeds.