CONVERT UNIT RATES WORD PROBLEMS 

About "Convert Unit Rates Word Problems"

Convert Unit Rates Word Problems :

In this section, we are going to learn , how to convert the given rates into unit rates.  

First let us understand what is unit rate. 

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 

Convert Unit Rates Word Problems - Practice Questions

Question 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 ⋅ 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.

Question 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 ⋅ 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. 

Question 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  =  120 

1 hour  =  60 minutes

So, no. of miles covered in 60 minutes  =  120

Then, no. of miles covered 1 minute  =  120 / 60  =  2

Hence, John can cover 2 miles in 1 minute. 

Question 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 of one basket ball  =  1143.75 / 75  =  15.25

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

Question 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.

Question 6 :

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  is

=  21 ⋅ 2.5  

=  52.5   

Hence, 52.5 miles traveled in 2.5 gallons of fuel. 

Question 7 :

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 ⋅ 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.

Question 8 :

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 ⋅ 2.8  =  145.6

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

After having gone through the stuff given on "Convert unit rates word problems", we hope that the students would have understood how to solve problems using unit rates.

Apart from the stuff given on "Convert unit rates word problems", if you need any other stuff in math, please use our google custom search here.