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 Kg, then the rate would be $2 for 3 Kg 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 unitless.

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

1hour. Other examples are $5 per Kg,

5 miles 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

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 Kg 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.

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.