Rate Definition

Have you heard the term “heart rate” of human beings?

It’s all about the number of times our heart beats in one minute.

This is how we compare quantities which have different units, and this ratio is termed as rate.
Rate is an important ratio used in our day-to-day lives, be it grocery shopping, traveling, medicine, and many others. 

So, let’s get started to know more rate!

Explore the unit rate calculator given below. Enter the values with different units to get the unit rate.

In this mini lesson, we'll learn about rate, what is rate, the unit rate calculator, the ratio definition and unit rate examples.

Lesson Plan

What Is Rate?

A rate is a ratio that compares two different kinds of numbers, such as miles per hour or dollars per ounce.

The little word "per" gives a clue that we are dealing with a rate. The word "per" can be further replaced by the symbol "/" in problems.

Example:

A car travels 150 miles in 3 hours,

150 miles divided by 3 hours= 150 miles/3 hours = 50 miles/hour.

'Per' means for every or for each one.

50 miles/ hour means the car travels at an average speed of 50 miles each hour.

Now, 50 miles/ hour is an example of unit rate.

What is unit rate?

A unit rate is about comparing a quantity to its unit of measure.

Let's explore some more examples around us!

  • In grocery shopping, we use rate as the cost of any item per pound or per gallon.

Application of rate at grocery store

  • We say that we read 20 pages/day or that we should have 12 glasses of water/day for our body to function well.

Can you think of a few more examples?


What Is a Ratio?

Ratio Definition

A ratio is used to compare two or more like quantities or numbers with the same units.

It is often written with a colon, and when used in words, we say the ratio of one quantity "to" the second quantity.

For example, the ratio of girls and boys in a class.

Some problems may give you just two numbers, such as comparing two quantities, while some may have more than two quantities.

For example, the ratio of different ingredients used in a recipe.

Let's take another example:

If a person has two oranges and six strawberries, that makes it a total of eight fruits.

6 strawberries and 2 oranges

The ratio of 2 oranges to the total 8 pieces of fruits will be written as 2:8. Simplifying it further gives 1:4

Similarly, the ratio of 2 oranges to 6 strawberries will be written as 2:6. Simplifying it further gives 1:3


What Is the Difference between Rate and Ratio?

Both rates and ratios are utilized in comparison of numbers. 

A rate compares two numbers with different units, whereas a ratio compares two or more numbers with the same unit.


What Are three examples of Rate?

Three examples of rate:

  • Time rate: Distance per unit time, average speed (miles/ hour) and interest (simple or compound) rates
  • Cost Price: cost/pound, quantity per cost (20 oz of juice/ 4 dollars) or for comparing prices.
  • Other examples can be the literacy rate, the population and other rates which provide specific data.

How Is Rate Calculated?

Ben rode his bike for 2 hours and traveled 24 miles.

Ben travelled 24 miles in 2 hrs

What is the rate of speed?

We use the formula

\(\text { Speed = distance/time }\)

or 

\(\mathrm{s}=\mathrm{d} / \mathrm{t}\)

or

\(\mathrm{r}=\mathrm{d} / \mathrm{t}\)

That gives, 24 miles divided by 2 hours, so:

r = 24 miles ÷ 2 hours = 12 miles per hour.

Now, this is an example of unit rate.

What is unit rate?

A unit rate which has the denominator as 1, compares a quantity to the other, which is its unit of measure.

If a person runs three miles in 30 minutes, he runs at a rate of one mile every 10 minutes.

The rate "miles per minute" gives the distance traveled per unit of time.

How to calculate unit rate?

In order to calculate unit rate, we divide the denominator with the numerator in such a way that the denominator becomes 1.

For example, if 260 miles are covered in 2 hours, the unit rate will be 260 miles/2 hours which is equal to 130 miles/hour.

In other words, the denominator is always 1 in a unit rate.

Other examples of Unit rate are: Revolutions/minute, salary/month, frequency/minute, etc.

 
important notes to remember
Important Notes
  1. A unit price is a rate comparing the price of an item to its unit of measure.

  2. 'Per' means to divide, for per hour, you need to place hours in the denominator.

  3. Exchange Rates, Literacy Rates, and Electric Field are examples of ratios with non-time denominator.

Solved Examples

Example 1

 

 

A farmer harvests 150 acres per day and gets 150 bushels of wheat per acre.

How many bushels of wheat does he harvest in a day?

Wheat harvest on acres of land

Solution

Land harvested in a day = 150 acres

Wheat harvested per acre = 150 bushels

Wheat harvested in a day = 150 acres/1 day X 150 bushels/acre = 150 X 150 bushels/day = 22,500 bushels/day.

\(\therefore\)22,500 bushels/day
Example 2

 

 

Fred is fond of baking and he bakes wonderful cakes.

He bakes 32 cakes in 8 hours.

Can you find his rate of baking cakes per hour?

Solution

32 cakes in 8 hrs

Therefore, 1 cake will take = 8/32 hrs =  1/4 hrs

\(\therefore\) \(\frac{1}{4}\) hrs
Example 3

 

 

Wiiliam and his family planned for a vacation to the Disney World.

They travelled 1000 miles and used 50 gallons of gas.

Can you help him calculate the average number of miles/gallon.

William thinking for the gallons of gas used up during the trip

Solution

Total distance traveled = 1000 miles

Total gas used = 50 gallons

Average number of miles/gallon = 1000 miles/50 gallons = 20 miles/gallon

\(\therefore\) 20 miles/gallon

Interactive Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 

 
 
 
 
 
Challenge your math skills
Challenging Question
  1. Brook started playing a video game at 12:05 p.m. and the game got over by 12:25 p.m. He earned 300 credit points at the end of the game. Calculate the number of credit points earned by him per minute. 

Brook playing video game and earning credit points

Let's Summarize

The mini-lesson targeted the fascinating concept of Rate Definition. The math journey around Rate Definition starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


Frequently Asked Questions(FAQs)

1. What is the difference between a Rate and a Percentage?

A rate is a comparison of two numbers with different quantities or units. A percentage is a ratio out of hundred.

2. What is a Rate example?

A few examples of rate can be listed as - miles/ hour, cost/pound, 20 oz of juice/4 dollars, etc.

3. What is another name for rate? 

Another name for rate is ratio because it compares two different kinds of numbers, like miles per hour.

  
More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus