Unit Rate: Definition, Formula, Importance & Examples

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Unit rate is actually a ratio in which we compare two quantities related to different units. The word 'unit rate' is commonly known as per unit of something. There are different types of unit rates. Some of the commonly used unit rates are per unit of mass, per unit of length, per unit of time etc.

Also Read: How to Calculate Percentage

Table of Content

Definition of Unit Rate
Formula for Unit Rate
Importance of Unit Rate
Things to Remember
Sample Questions

Key Takeaways: Unit Rate, Ratio, Length, Distance, Quantities

Unit Rate Definition

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Unit rate is defined as the ratio of two quantities used to find the amount associated with per unit of quantity. In our everyday life, we come across various rates of ample quantities. From buying groceries to driving a car, from measuring length to recording the time everything is associated with some kind of rate. Literally finding the unit rate of something means to calculate how much quantity or rate is associated with its 1 unit or per unit.

Unit Rate

Unit Rate

This could be understood with the examples:

Example: If buying 5 pencils from a book store costs him a total of Rs 50. Calculate what is the price of per unit of pencil. Here the question is finding the per unit price of a pencil. However it can easily be found using the concept of unitary method.

Price of per unit of pencil = \(Total\quad price\quad of\quad pencil\over Total\quad quantity \)

Price of per unit of pencil = 50 / 5 = 10 Rs

Example: A man drives a car from city A to city B in three hours. He traverses a distance of 300 kms from city A to City B. Calculate the speed of the car in per unit of time.

In the aforementioned question, we have used the concept of the unitary method. In the same way the speed per unit of time can be found.Speed per unit time = \(Total\quad distance \quad travelled \over Total\quad time \quad taken\)

Speed per unit time = 300 km / 3 hours

Speed per unit time = 100 km per hour

In the above examples, it can be said that the pencil can be bought at a rate of 10 Rs per pencil and the car travels at a rate of 100 km per hour.

Read Also:

Measurement of Length	Quadratic Equations	Real Numbers

Formula for Unit Rate

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The formula to calculate the unit rate of a quantity is the ratio of two quantities with two different units.

Unit Rate = Ratio of two different quantities with different units.

Unit Rate = A / B

Unit Rate = A : B

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Profit and Loss Formula	Ratio to Percentage	Least Count Error

Importance of Unit Rate

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As the definition of unit rate is discussed, it is obvious that unit rate is very much important in everyday life. The concept of unit rate helps one to understand how much quantity is related to the one unit of something. It compares the rates of two different quantities.

Unit Rate Example

Unit Rate Example

For example, a man is going to a grocery store to buy some noodles. In the grocery store there are two deals. The first one says that 3 packets of noodles can be bought for a price of 81 rupees while the second one says that 5 packets of noodles can be bought for 115 rupees. After finding the unit rate of the noodles for both the deals it is observed that the unit rate of the first deal is 27 Rs per noodle pack and the unit rate of the second deal is 23 Rs per noodle pack. Now after finding the unit rate of both the deals it is more obvious that the second deal is better. Thus, the above example suggests that unit rate is important in our day to day life in various situations.

Read Also:

Proportion Formula	Equivalent Fractions	Algebra Symbols

Things to Remember

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The rate is the ratio of comparison of two different quantities having different units whereas unit rate corresponds with how many quantities are compared with the single quantity.
There are few examples of unit rate written in the form like kilometer/hour, meter/sec, miles/hour, salary/month.
It shows how many units of quantity are there in relation to the single unit of another quantity.
Unit rate has many real-life applications.

Also Read:

Sets	Conic sections	Plane

Sample Questions

Ques. What is the unit rate? Is unit rate the same as unitary method? (2 Marks)

Ans. A unit rate is a ratio of two different quantities having different units. It is used to find the per unit quantity of something. The unit rate and unitary method is the same thing. Both the things are associated with finding out the quantity associated with 1 unit .

Ques. Find out the unit rate of a man who travels 400 kilometers in 10 hours. (3 Marks)

Ans. In the question, it is given that a man travels 400 kilometers in 10 hours. Here, we have to find the unit rate. It can be written mathematically as;

= 400 kilometers/10 hours

= 400 km/10 hr

= 40 km/1hr

Therefore, the unit rate of 400 kilometers per 10 hour is 40 kilometer/hour.

Ques. A student types 3200 words in 8 minutes. Find the unit rate. (3 Marks)

Ans. Total no. of words typed = 3200

Total time taken = 8 minutes

Words typed per minute = 3200 words / 8 minute

= 400 words per minute

Ques. Find out the unit rate of a person who travels 20 kilometers from Bhopal to Vidisha in 2 hours? (3 Marks)

Ans. Here, it is given that a man travels 20 kilometers in 2 hours from one place to another.

We need to find the unit rate.

Mathematically,it can be written as 20 kilometers/hour.

On simplifying the equation, we get;

= 20/2

= 10/1

Hence, the unit rate for the above is 10 km/hr.

Ques. An elephant eats 35 kgs of leaves per week. Find the unit rate? (2 Marks)

Ans. Total weight of leaves = 35 kgs

No. of days = 7 days

No. of leaves eaten per day = 35 kgs / 7 days

= 5 kgs per day

Ques. A man travels around 500 kilometers in 10 hours then find the unit rate? (3 Marks)

Ans. In the question, it is given that a man travels 500 kilometers in 10 hours,

Here, we have to find the unit rate. It can be written mathematically as;

= 500 kilometers/10 hours

= 500 km/10 hr

= 50 km/1hr

Therefore, the unit rate of 500 kilometers per 10 hour is 50 kilometer/hour or 50 km per hour.

Ques. A farmer harvests a land of 16 acres every day and gets around 160 bushels of wheat each acre. Find out the number of bushels of wheat required harvest in a day using the unit rate formula? (5 Marks)

Ans. Land harvested by the farmer = 16 acres

Let x be the quantity harvested and y be the number of days.

Now we have to find the quantity per day,

Then, bushels of wheat harvested each acre = 16 × 160

= 2,560 Bushels

By using the unit rate formula: unit rate = x/y,

Then, bushels of wheat harvested per day = 2560 / 1 = 2560

Therefore, the wheat harvested by the farmer per day = 2560 Bushels

Ques. The cost of a dozen blueberries in a fruit shop is Rs. 48. Then find the unit rate? (5 Marks)

Ans. Now according to the question we know,

Price of 12 blueberries = 48

Let a be the cost and b be the dozen of blueberries

To find the cost per dozen;

By using the unit rate formula: unit rate= a/b,

Cost per unit of blueberries = Price of blueberries / Number of blueberries

= 48/12 = Rs 4

Therefore, the per-unit cost of blueberries = Rs. 4.

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Real Numbers	Real Number Formula	Error Arithmetic Operations of Significant Figures

Unit Rate: Definition, Formula, Importance & Examples

Unit Rate Definition

Formula for Unit Rate

Importance of Unit Rate

Things to Remember

Sample Questions

CBSE X Related Questions

1.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

2.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

3.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

4.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

5.
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

6.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

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Unit Rate: Definition, Formula, Importance & Examples

Unit Rate Definition

Formula for Unit Rate

Importance of Unit Rate

Things to Remember

Sample Questions

CBSE X Related Questions

1.In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

2.Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

3.Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent. Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

4.Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

5.The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

6.If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

2.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

3.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

4.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

5.
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

6.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals