How is a unit rate lie a ratio? How is it different?
A unit rate is indeed a type of ratio, but it has a specific characteristic that distinguishes it from other ratios. To understand this, let's first consider what a ratio is.
In mathematics, a ratio is a comparison of two quantities or numbers. It expresses the relationship between the two quantities, often in the form of a fraction or a colon (:). For example, if you have 2 apples and 3 oranges, the ratio of apples to oranges can be written as 2/3 or 2:3.
Now, a unit rate is a special kind of ratio where the denominator equals 1 unit. It represents the amount of one quantity relative to 1 unit of another quantity. For instance, if you drive 100 miles in 2 hours, the unit rate of your speed is 100 miles per 2 hours, which can be simplified to 50 miles per hour.
What sets unit rates apart from other ratios is that they explicitly state the relationship between the quantities in terms of a straightforward comparison per one unit. This makes them useful for comparison and calculation purposes.
To find a unit rate, you need to divide one quantity by another, making sure the denominator is 1. This enables us to determine the amount of one quantity in relation to exactly one unit of the other quantity.