Unit Rates and Unit Prices

A rate is a form of ratio in which the two terms are in different units. For example price of wheat is $2 for 3 Kgs, then the rate would be $2 for 3 Kgs and the unit of rate would be $/Kg. Similarly if a car goes 100 miles in 1.5 hour, then the rate is 100 miles per 1.5 hour and unit is miles/hr. Note that ratios are usually unit less. 
Unit rate is a rate in which the rate is expressed as a quantity of 1. Simply put is rate which has denominator of 1. For example, if a car goes 60 miles in 1 hour, then the unit rate is 60 miles per hour. Other examples are $5 per Kg, 5 mt per second and $80 per barrel. 
Unit price is the rate when it is expressed in unit currency like dollar or cent. An example is price of corn is $2 per ounce and price of petrol is $5 per gallon. Remember that the price is always the numerator and the unit is the denominator. 
Converting rate to unit rate/price 
Rate can be converted to unit rate simply by dividing the first term by second term. Consider an example: 
Q1. If a car travels 45 miles in 30 min, what is the rate at which the car is travelling?
Solution: If we express the rate in miles/hr, the rate would simply be 45/0.5 miles per hr which is 90 miles per hr. If we want to express in minutes, then the rate would be 45/30 = 1.5 miles per minute. 
Q2. If John bought 2.5 Kgs of rice for $7.5, then what is the unit price of rice?
Solution: Here the denominator should be 2.5 Kg and numerator is the price $7.5. The unit price of rice would thus be 7.5/2.5 = 3 $/Kg.
Rates and unit rates are used to solve many real world problems. For example consider the problem: It takes 30 minutes for a tap to fill one bucket. How much time would it take to fill 6 buckets? The problem can be done using the concept of unit rate. The unit rate to fill the buckets would be 1/0.5 bucket per hour which is 2 buckets per hr. Thus to fill 6 buckets, it would take 6/2 = 3 hours. Such problems can also be solved easily using proportions. However, unit rates are still more convenient for comparison since they are already in simplified form and the denominator is 1.
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