# UNIT RATE DEFINITION

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 to 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

## 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.

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  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.

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.

Problem 4 :

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

Solution :

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

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

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.

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)    (7/1)

Speed  =  14 / 5

Speed  =  2.8 miles per hour

Hence, the speed of Shanel is 2.8 miles per hour.

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

2/35 of a gallon of gas -----> 4/5 of a mile

1 gallon of gas -----> (4/5)  (35/2) miles

1 gallon of gas -----> 14 miles

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

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 is

=  21 ⋅ 2.5

=  52.5

Hence, 52.5 miles traveled in 2.5 gallons of fuel.

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  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.

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  2.8  =  145.6

Hence, Mr. David will earn \$145.6 in 2.8 hours. Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 