Describe what makes a proportion. Give an example of a proportion.
A proportion is a statement that two ratios or fractions are equal to each other. For a proportion to be true, the numerator (top number) of one ratio must be proportional to the numerator of the other ratio, and the denominator (bottom number) of one ratio must be proportional to the denominator of the other ratio.
For example, the following is a proportion:
2/5 = 4/10
In this proportion, the numerator 2 of the left side is proportional to the numerator 4 of the right side, and the denominator 5 of the left side is proportional to the denominator 10 of the right side. Thus, the proportion holds true.
A proportion is a mathematical equation that states that two ratios or fractions are equal to each other. In other words, it shows the relationship between two equal ratios. The symbol used to represent proportion is (=:).
For example, let's consider the following proportion:
2/3 = 4/6
In this proportion, the left side represents the ratio of 2 parts to 3 parts, while the right side represents the ratio of 4 parts to 6 parts. The proportion tells us that these two ratios are equivalent or equal.
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.