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Some phrases and sentences do not translate directly. We must be careful to read them properly. The word from often appears in such phrases and sentences. The word from means "a point of departure for motion." The following translation will illustrate this use.

The translation of a verbal expressions 'Fifteen is subtracted from some quantity' into mathematical expressions is x minus fifteen.

The word from indicates the motion (subtraction) is to begin at the point of "some quantity."

Eight less than some quantity. Notice that less than could be replaced with from .
x 8

Practice set b

Translate the following phrases and sentences into mathematical expressions or equations.

A number divided by sixteen, plus one, is five.

x 16 + 1 = 5

Seven times two more than a number is twenty-one.

7 ( 2 + x ) = 21

A number divided by two more than itself is zero.

x 2 + x = 0

A number minus five is divided by twice the number plus three and the result is seventeen.

x 5 2 x + 3 = 17

Fifty-two is subtracted from some quantity.

x 52

An unknown quantity is subtracted from eleven and the result is five less than the unknown quantity.

11 x = x 5


For the following problems, translate the following phrases or sentences into mathematical expressions or equations.

A quantity less four.

a 4

Eight more than a number.

A number plus seven.

b + 7

A number minus three.

Negative five plus an unknown quantity.

5 + c

Negative sixteen minus some quantity.

Fourteen added to twice a number.

2 d + 14

Ten added to three times some number.

One third minus an unknown quantity.

1 3 e

Twice a number is eleven.

Four ninths of a number is twenty-one.

4 9 f = 21

One third of a number is two fifths.

Three times a number is nine more than twice the number.

3 g = 2 g + 9

Five times a number is that number minus two.

Twice a number added to six results in thirty.

2 h + 6 = 30

Ten times a number less four results in sixty-six.

A number less twenty-five is equal to 3.019 .

k 25 = 3.019

Seven more than some number is five more than twice the number.

When a number is divided by four, the result is sixty-eight.

m 4 = 68

Eleven fifteenths of two more than a number is eight.

One tenth of a number is that number less one.

n 10 = n 1

Two more than twice a number is one half the number less three.

A number is equal to itself plus four times itself.

x = x + 4 x

Three fifths of a quantity added to the quantity itself is thirty-nine.

A number plus seven is divided by two and the result is twenty-two.

Q + 7 2 = 22

Ten times a number minus one is divided by fourteen and the result is one.

A number is added to itself then divided by three. This result is then divided by three. The entire result is fifteen.

r + r 3 3 = 15

Ten divided by two more than a number is twenty-one.

Five divided by a number plus six is fourteen.

5 s + 6 = 14

Twelve divided by twice a number is fifty-five.

Twenty divided by eight times a number added to one is nine.

20 8 x + 1 = 9

A number divided by itself, plus one, results in seven.

A number divided by ten, plus four, results in twenty-four.

v 10 + 4 = 24

A number plus six, divided by two, is seventy-one.

A number plus six, divided by two, plus five, is forty-three.

w + 6 2 + 5 = 43

A number multiplied by itself added to five is thirty-one.

A quantity multiplied by seven plus twice itself is ninety.

7 y + 2 y = 90

A number is increased by one and then multiplied by five times itself. The result is eighty-four.

A number is added to six and that result is multiplied by thirteen. This result is then divided by six times the number. The entire result is equal to fifty-nine.

( z + 16 ) 13 6 z = 59

A number is subtracted from ten and that result is multiplied by four. This result is then divided by three more than the number. The entire result is equal to six.

An unknown quantity is decreased by eleven. This result is then divided by fifteen. Now, one is subtracted from this result and five is obtained.

x 11 15 1 = 5

Ten less than some number.

Five less than some unknown number.

n 5

Twelve less than a number.

One less than an unknown quantity.

m 1

Sixteen less than some number is forty-two.

Eight less than some unknown number is three.

p 8 = 3

Seven is added to ten less than some number. The result is one.

Twenty-three is divided by two less than twice some number and the result is thirty-four.

23 2 n 2 = 34

One less than some number is multiplied by three less than five times the number and the entire result is divided by six less than the number. The result is twenty-seven less than eleven times the number.

Exercises for review

( [link] ) Supply the missing word. The point on a line that is associated with a particular number is called the of that number.


( [link] ) Supply the missing word. An exponent records the number of identical in a multiplication.

( [link] ) Write the algebraic definition of the absolute value of the number a .

| a | = { a , i f a 0 a , i f a < 0

( [link] ) Solve the equation 4 y + 5 = 3 .

( [link] ) Solve the equation 2 ( 3 x + 1 ) 5 x = 4 ( x 6 ) + 17 .

x = 3

Questions & Answers

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
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
characteristics of micro business
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Basic mathematics review. OpenStax CNX. Jun 06, 2012 Download for free at http://cnx.org/content/col11427/1.2
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