 # Unit Rate

Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc. Arithmetic is probably the most basic and ancient branch of mathematics and is quite commonly used in our day-to-day life. This subject is all about the problems based on numerals and operations upon numerals. We do solve problems of arithmetic intentionally or unintentionally during our daily routine. For example – While purchasing vegetables or fruits, in other dealings or in estimating speed of something etc. Also, learn conversion of units here.

Often we are required to find the price or speed or other factors in the arithmetic problems. A concept that we very commonly come across in arithmetic as well as in practical life, is the unit rate. Rate and unit rate are two different concepts. Though they have the same basic idea, their definitions and usage is a little different. In a metric system there are many units defined. In this article, we shall learn about the unit rate. Let us go ahead and know the definition of unit rate and examples based on it.

## Unit Rate Definition

A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. In fact, unit rate is said to be the amount of something in each unit or per unit. Let us understand this using some examples:

• 40 miles/2 hours = 20 miles/hour, Unit rate is 20 miles per hour
• 160 words/4 minutes = 40 words/minutes, Unit rate is 40 minute per minute

The common examples used are:

• Distance per second
• Kilometer per hour
• Meter per second
• Earning per month

Basically gas mileage, speed, acceleration and density etc are the terms that are determined by the calculation of unit rate. Some more examples: Miles per hour, grams per cubic centimetre, words per minute, cost per gram (pound, litre) and miles per gallon.

### Unit Rate Examples

Q.1: A man travels 20 kilometers in 2 hours, find the unit rate.

Solution: Given a man travels 20 kilometers in 2 hours we need to find the unit rate.

It can be written in the form of 20 kilometers/hour

Now by simplifying it, we get;

20/2 = 10/1

So the unit rate form of 20 kilometers per 2 hours is 10 kilometers per hour.

Q.2: Rohan earns INR 30000 working 30 hours. Find the unit rate.

Solution: Given, Rohan earns INR 30000 working 30 hours.

We need to find the unit rate.

Rohan earns INR 30000 working 30 hours can be written in the form of;

= 30000/30

= 3000/3

= 1000/1

Hence, the unit rate of Rohan earning INR 30000/30 hours is INR1000/hour.

Q.3: A man travels 400 kilometers in 10 hours, find the unit rate.

Solution: Given a man travels 400 kilometers in 10 hours we need to find the unit rate.

It can be written in the form of;

=400 kilometers/10 hours

=400 km/10 hr

=40 km/1hr

Hence, the unit rate form of 400 kilometers per 10 hour is 40 kilometer per hour.

### Unit Rate Problems

Solve the problems for better practice.

1. A man can type 24 papers in 8 minutes. Find the unit rate.
2. What will be the unit rate if a man can type 40 papers in 10 minutes?