Question #1e9b2
1 Answer
The difference is mostly in the units given to the values in the comparison. Ratio means units are the same; rate means they differ.
Explanation:
In a ratio, the two quantities being compared have the same units. For example, three people chosen out of ten applicants - the 3 out of 10 (3:10) is a ratio, as both numbers refer to people. If we compare two sides of a triangle measuring 5m and 15m, the expression 5:15 is a ratio as both quantities are in metres.
A rate looks just like a ratio, but the quantities in it have different units. For example, if I walk 3 miles in 45 minutes, the comparison 3:45 is a rate, because the first term is miles (distance) and the second is minutes (time). Of course, this rate is known as speed.
A unit rate is one specifically written with different units but in which the two terms represent equal quantities, with the second value equal to 1. In this way, the value of the rate is one. For example, there are 1609 metres in a mile, so writing this as #(1609 m)/(1 mi) really is a rate whose value is one. The purpose in doing this includes making conversions, and the rate is known as a conversion factor.
For instance: How many metres are there in 20 miles? I would multiply:
I end up with the same distance (32180 m), as I started with (20 miles), because the rate I used as a conversion factor actually has equal distances in numerator and denominator, and in that way, has a value equal to one. It is a unit rate.
