# Lesson Rate, unit rate and unit prices

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 This Lesson (Rate, unit rate and unit prices) was created by by PrateekJain(0)  : View Source, ShowAbout PrateekJain: 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. This lesson has been accessed 100983 times.