UNIT RATE DEFINITION 

About "Unit rate definition"

Unit rate definition (or) Definition of unit rate : 

Unit rate compares the given amount to one unit of another measure

(or)

The ratio between the given value and 1 

(or)

Comparing the given amount or value to 1

Examples :

1. If 8 dolls are made in 4 days, 

then number of dolls made in 1 day  =  2

2. If David earns $180 in 9 hours, 

then number of dollars earned by him in 1 hour  =  $ 20

3. If there are 16 cups in 4 quarts,

then the number of cups in 1 quart = 4 

Liquid Measurements - Unit rates

From the above picture, we can get the following unit rates related liquid measurements.

1 gallon  =  16 cups

1 gallon  =  8 pints

1 gallon  = 4 quarts 

1 quart  =  2 pints

1 quart  =  4 cups 

1 pint  =  2 cups 

Unit rate definition - Practice problems

To have better understanding on unit rate definition, let us look some practice problems.

Problem 1 :

In a business, if A can earn $ 7500 in 2.5 years, find the unit rate of his earning per month. 

Solution : 

Given : Earning in 2.5 years  =  $ 7500

1 year  =  12 months 

2.5 years  =  2.5 x 12  =  30 months   

Then, earning in 30 months  =  $ 7500

Therefore, earning in 1 month  =  7500 / 30  =  $ 250

Hence, the unit rate of his earning per month is $ 250

Let us look at the next problem on "Unit rate definition"

Problem 2 :

If David can prepare 2 gallons of juice in 4 days, how many  cups of juice can he prepare per day ? 

Solution : 

No of gallons of juice prepared in 4 days  =  2 gallons

1 gallon  =  16 cups

So, no. of cups of juice prepared in 4 days  =  2 x 16  =  32 cups

Therefore, David can prepare 32 cups of juice in 4 days. 

Then, no. of cups of juice prepared in 1 day  =  32 / 4  =  8

Hence, David can prepare 8 cups of juice in 1 day. 

Let us look at the next problem on "Unit rate definition"

Problem 3 :

If John can cover 360 miles in 3 hours, find the number of miles covered by John in 1 minute.  

Solution : 

No of miles covered in 3 hours  =  360 

Then, no. of miles covered in 1 hour  =  360 / 3  =  180 

1 hour  =  60 minutes

So, no. of miles covered in 60 minutes  =  180

Then, no. of miles covered 1 minute  =  180 / 60  =  3

Hence, John can cover 3 miles in 1 minute. 

Let us look at the next problem on "Unit rate definition"

Problem 4 : 

75 basketballs cost $1,143.75. Find the unit rate in price per basketball. 

Solution :

Given : 75 basketballs cost $1,143.75

Then, price pf one basket ball  =  1143.75 / 75  =  15.25

Hence, the unit rate in price per basket ball is $ 15.25

Let us look at the next problem on "Unit rate definition"

Problem 5 :

In 36.5 weeks, Miguel raised $2,372.50 for cancer research. How was his unit rate in price per week? 

Solution :

Given : Miguel raised $2, 372.50 in 36.5 weeks 

Then, amount raised in one week  =  2372.5 / 36.5  =  65

Hence, the unit rate in price per week was $ 65

Let us look at the next problem on "Unit rate definition"

Problem 6 : 

Shanel walks 2/ 5 of a mile every 1/7 hour. Express her speed as a unit rate in miles per hour. 

Solution : 

Given : Shanel walks 2/ 5 of a mile every 1/7 hour

We know the formula for speed.

That is,  Speed  =  Distance / time

Speed  =  (2/5)  /  (1/7)

Speed  =  (2/5)  x  (7/1)

Speed  =  14 / 5

Speed  =  2.8 miles per hour. 

Hence, the speed of Shanel is 2.8 miles per hour

Let us look at the next problem on "Unit rate definition"

Problem 7 : 

Declan use 2 /35 of a gallon of gas for every 4 /5 of a mile that he drives. At this rate, how many miles can he drive on one gallon of gas? 

Solution : 

Given : In 2 /35 of a gallon of gas, 4 /5 of a mile is traveled

Then, in  1 gallon of gas  =  (4/5) x (35/2) miles traveled. 

in  1 gallon of gas  =  14 miles traveled. 

Hence, Declan can drive 14 miles in 1 gallon of gas

Let us look at the next problem on "Unit rate definition"

Problem 8 : 

A person can cover a distance of 84 miles in 4 gallons of fuel. If he has 2.5 gallons, how many miles can he cover ?

Solution : 

Given : 84 miles can be traveled in 4 gallons. 

Then, no. of miles traveled in 1 gallon  =  84 / 4  =  21

Therefore, no. of miles traveled in 2.5 gallons  =  21 x 2.5  =  52.5   

Hence, 52.5 miles traveled in 2.5 gallons of fuel  

Let us look at the next problem on "Unit rate"

Problem 9 : 

If a person drinks 8 cups of apple juice per month, how many gallons will he drink in one year?

Solution : 

Given : 8 cups in one month 

1 year  =  12 months 

So, no. of cups in 1 year  =  8 x 12  =  96 cups

1 gallon  =  16 cups

Therefore, no. of gallons in 1 year  =  96 / 16  =  6 

Hence, he will drink 6 gallons of apple juice in 1 year

Let us look at the next problem on "Unit rate"

Problem 10 :

My David earns $416 in 8 hours. How much does earn in 2.8 hours ?

Solution : 

Given : Earning in 8 hours  =  $ 416

Earning in 1 hour  =  $ 52

Earning in 2.8 hours  =  52 x 2.8  =  145.6

Hence, Mr. David will earn $145.6 in 2.8 hours

We hope that the students would have understood the stuff given on "Definition of unit rate". 

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