## proportion

### In mathematics, a proportion is a statement that shows the equality between two ratios

In mathematics, a proportion is a statement that shows the equality between two ratios. It relates two ratios in the form of “a:b = c:d”, where a, b, c, and d are numbers or quantities. Proportions express the concept of a consistent relationship between different quantities.

For example, let’s say we have two ratios: 3:4 and 6:8. We can compare these ratios by setting up a proportion:

3:4 = 6:8

In this proportion, the first ratio (3:4) is equivalent to the second ratio (6:8) because the cross products are equal: 3 * 8 = 4 * 6. This means that the relationship between 3 and 4 is the same as the relationship between 6 and 8.

Proportions are often used in real-life scenarios, such as cooking or scaling measurements. For instance, if a recipe asks for 2 cups of flour and 3 eggs, and you want to adjust the recipe to make more muffins, you can set up a proportion to determine the new quantities. If you want to make 6 cups of flour, you can calculate the new number of eggs using the proportion:

2:3 = 6:x

By cross-multiplying, we find that 2x = 18, and dividing by 2 gives x = 9. So, in this case, you need 9 eggs to make 6 cups of flour.

In summary, proportions are used to compare two ratios and show how they are related. They play an important role in various mathematical concepts, practical applications, and problem-solving scenarios.

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