<< Chapter < Page Chapter >> Page >

Ratios and rates

Ratio

A comparison, by division, of two pure numbers or two like denominate numbers is a ratio .

The comparison by division of the pure numbers 36 4 size 12{ { {"36"} over {4} } } {} and the like denominate numbers 8 miles 2 miles size 12{ { {"8 miles"} over {"2 miles"} } } {} are examples of ratios.

Rate

A comparison, by division, of two unlike denominate numbers is a rate .

The comparison by division of two unlike denominate numbers, such as

55 miles 1 gallon and 40 dollars 5 tickets size 12{ { {"55 miles"} over {"1 gallon"} } `"and"` { {"40 dollars"} over {"5 tickets"} } } {}

are examples of rates.

Let's agree to represent two numbers (pure or denominate) with the letters a size 12{a} {} and b size 12{b} {} . This means that we're letting a size 12{a} {} represent some number and b size 12{b} {} represent some, perhaps different, number. With this agreement, we can write the ratio of the two numbers a size 12{a} {} and b size 12{b} {} as

a b or b a

The ratio a b size 12{ { {a} over {b} } } {} is read as " a size 12{a} {} to b size 12{b} {} ."

The ratio b a size 12{ { {b} over {a} } } {} is read as " b size 12{b} {} to a size 12{a} {} ."

Since a ratio or a rate can be expressed as a fraction, it may be reducible.

Sample set b

The ratio 30 to 2 can be expressed as 30 2 size 12{ { {"30"} over {2} } } {} . Reducing, we get 15 1 size 12{ { {"15"} over {1} } } {} .

The ratio 30 to 2 is equivalent to the ratio 15 to 1.

The rate "4 televisions to 12 people" can be expressed as 4 televisions 12 people size 12{ { {4" televisions"} over {"12"`"people"} } } {} . The meaning of this rate is that "for every 4 televisions, there are 12 people."

Reducing, we get 1 television 3 people size 12{ { {1" televisions"} over {3`"people"} } } {} . The meaning of this rate is that "for every 1 television, there are 3 people.”

Thus, the rate of "4 televisions to 12 people" is the same as the rate of "1 television to 3 people."

Practice set b

Write the following ratios and rates as fractions.

3 to 2

3 2 size 12{ { {3} over {2} } } {}

1 to 9

1 9 size 12{ { {1} over {9} } } {}

5 books to 4 people

5 books 4 people size 12{ { {"5 books"} over {"4 people"} } } {}

120 miles to 2 hours

60 miles 1 hour size 12{ { {"60 miles"} over {"1 hour"} } } {}

8 liters to 3 liters

8 3 size 12{ { {8} over {3} } } {}

Write the following ratios and rates in the form " a size 12{a} {} to b size 12{b} {} ." Reduce when necessary.

9 5 size 12{ { {9} over {5} } } {}

9 to 5

1 3 size 12{ { {1} over {3} } } {}

1 to 3

25 miles 2 gallons size 12{ { {"25 miles"} over {"2 gallons"} } } {}

25 miles to 2 gallons

2 mechanics 4 wrenches size 12{ { {"2 mechanics"} over {"4 wrenches"} } } {}

1 mechanic to 2 wrenches

15 video tapes 18 video tapes size 12{ { {"15 video tapes"} over {"18 video tapes"} } } {}

5 to 6

Exercises

For the following 9 problems, complete the statements.

Two numbers can be compared by subtraction if and only if .

They are pure numbers or like denominate numbers.

A comparison, by division, of two pure numbers or two like denominate numbers is called a .

A comparison, by division, of two unlike denominate numbers is called a .

rate

6 11 size 12{ { {6} over {"11"} } } {} is an example of a . (ratio/rate)

5 12 size 12{ { {5} over {"12"} } } {} is an example of a . (ratio/rate)

ratio

7 erasers 12 pencils is an example of a . (ratio/rate)

20 silver coins 35 gold coins is an example of a .(ratio/rate)

rate

3 sprinklers 5 sprinklers is an example of a . (ratio/rate)

18 exhaust valves 11 exhaust valves is an example of a .(ratio/rate)

ratio

For the following 7 problems, write each ratio or rate as a verbal phrase.

8 3 size 12{ { {8} over {3} } } {}

2 5 size 12{ { {2} over {5} } } {}

two to five

8 feet 3 seconds

29 miles 2 gallons

29 mile per 2 gallons or 14 1 2 size 12{"14" { {1} over {2} } } {} miles per 1 gallon

30,000 stars 300 stars

5 yards 2 yards

5 to 2

164 trees 28 trees

For the following problems, write the simplified fractional form of each ratio or rate.

12 to 5

12 5 size 12{ { {"12"} over {5} } } {}

81 to 19

42 plants to 5 homes

42 plants 5 homes size 12{ { {"42"" plants"} over {5"homes"} } } {}

8 books to 7 desks

16 pints to 1 quart

16 pints 1 quart size 12{ { {"16 pints"} over {"1 quart"} } } {}

4 quarts to 1 gallon

2.54 cm to 1 in

2 . 54 cm 1 inch size 12{ { {2 "." "54cm"} over {"1 inch"} } } {}

80 tables to 18 tables

25 cars to 10 cars

5 2 size 12{ { {5} over {2} } } {}

37 wins to 16 losses

105 hits to 315 at bats

1 hit 3 at bats size 12{ { {"1 hit"} over {"3 at bats"} } } {}

510 miles to 22 gallons

1,042 characters to 1 page

1, 042   characters 1   page size 12{ { {1,"042"" characters"} over {1" page"} } } {}

1,245 pages to 2 books

Exercises for review

( [link] ) Convert 16 3 size 12{ { {"16"} over {3} } } {} to a mixed number.

5 1 3 size 12{5 { {1} over {3} } } {}

( [link] ) 1 5 9 of 2 4 7 is what number?

( [link] ) Find the difference. 11 28 7 45 size 12{ { {"11"} over {"28"} } - { {7} over {"45"} } } {} .

299 1260 size 12{ { {"299"} over {"1260"} } } {}

( [link] ) Perform the division. If no repeating patterns seems to exist, round the quotient to three decimal places: 22 . 35 ÷ 17 size 12{"22" "." "35"¸"17"} {}

( [link] ) Find the value of 1 . 85 + 3 8 4 . 1 size 12{1 "." "85"+ { {3} over {8} } cdot 4 "." 1} {}

3.3875

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Contemporary math applications' conversation and receive update notifications?

Ask