what is the difference between a ratio and a rate? what is a non-unit rate?
A ratio is an expression which compares quantities relative to each other. The most common examples involve two quantities, but in theory any number of quantities can be compared. Mathematically they are represented by separating each quantity with a colon, for example the ratio 2:3, which is read as the ratio "two to three". AND
A rate is a special kind of ratio, indicating a relationship between two measurements. A rate may be defined using two numbers of the same units resulting in a dimensionless quantity (for example, "1 in 10 people"), or may be defined by two different measurements with different units (for example, "meters per second" used in speed).
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A ratio is a comparison of two quantities, typically expressed as a fraction, while a rate is a special type of ratio that involves two different units of measurement.
To understand the difference, let's look at an example. Suppose we have a recipe that calls for 2 cups of flour and 1 cup of sugar. The ratio of flour to sugar is 2:1, which means there are two parts of flour for every one part of sugar.
Now, let's say we want to make more batches of the recipe. We can calculate the rate at which we use flour and sugar. If we make 3 batches, we would need 3 times the amount of flour and 3 times the amount of sugar. The rate of using flour is 2 cups per batch (2 cups/batch), and the rate of using sugar is 1 cup per batch (1 cup/batch).
A non-unit rate is a rate that is not equal to 1. In the example above, the rates of using flour and sugar were both non-unit rates because they were greater than 1. Non-unit rates are useful for comparing quantities that involve more or less than one unit of measurement, such as distance traveled per hour or dollars earned per day.
To summarize, a ratio is a comparison of two quantities, while a rate is a special type of ratio that involves different units of measurement. A non-unit rate is a rate that is not equal to 1 and is useful for comparing quantities involving more or less than one unit of measurement.