A proportion is a mathematical relationship between two equal ratios. In other words, it's a statement that two ratios are equivalent.
To determine if a proportion is true, you compare the terms across the ratios. The numerators and denominators of the fractions must be proportional to each other. This means that if you multiply the numerator of one fraction by a certain number, you should also multiply the denominator of that fraction by the same number to get the other fraction.
Here's an example of a proportion: Let's say you have a pizza with 8 slices, and out of those, 5 slices are plain cheese. We can express this as a ratio: 5/8. Now, suppose you have a larger pizza with 20 slices, and you want to know how many slices would be plain cheese if it had the same proportion. To find out, you use the proportion: 5/8 = x/20, where x represents the unknown number of plain cheese slices in the larger pizza.
To solve this proportion, you cross-multiply: 5 * 20 = 8 * x. Simplifying this equation gives you 100 = 8x. Divide both sides by 8, and you find that x = 12.5. Therefore, in the larger pizza, there would be approximately 12.5 slices of plain cheese if the same proportion remains constant.
This example demonstrates how proportions allow us to compare ratios and solve for unknown values based on known relationships between quantities.