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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to translate word to mathematical symbols. By the end of the module students should be able to translate phrases and statements to mathematical expressions and equations.

Section overview

  • Translating Words to Symbols

Translating words to symbols

Practical problems seldom, if ever, come in equation form. The job of the problem solver is to translate the problem from phrases and statements into mathematical expressions and equations, and then to solve the equations.

As problem solvers, our job is made simpler if we are able to translate verbal phrases to mathematical expressions and if we follow the five-step method of solving applied problems. To help us translate from words to symbols, we can use the following Mathematics Dictionary.

Word or Phrase Mathematical Operation
Sum, sum of, added to, increased by, more than, and, plus +
Difference, minus, subtracted from, decreased by, less, less than -
Product, the product of, of, multiplied by, times, per
Quotient, divided by, ratio, per ÷
Equals, is equal to, is, the result is, becomes =
A number, an unknown quantity, an unknown, a quantity x size 12{x} {} (or any symbol)

Sample set a

Translate each phrase or sentence into a mathematical expression or equation.

Nine 9 more than + some number. x

Translation: 9 + x size 12{9+x} {} .

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Eighteen 18 minus - a number. x

Translation: 18 x size 12{"18" - x} {} .

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A quantity y less - five. 5

Translation: y 5 size 12{y - 5} {} .

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Four 4 times a number x is = sixteen. 16

Translation: 4 x = 16 size 12{4x="16"} {} .

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One fifth 1 5  of  a number n  is =  thirty. 30

Translation: 1 5 n = 30 size 12{ { {1} over {5} } n="30"} {} , or n 5 = 30 size 12{ { {n} over {5} } ="30"} {} .

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 Five 5  times  a number x  is =  two 2  more than +  twice 2  the number. x

Translation: 5 x = 2 + 2 x size 12{5x=2+2x} {} .

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Practice set a

Translate each phrase or sentence into a mathematical expression or equation.

Twelve more than a number.

12 + x size 12{"12"+x} {}

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Eight minus a number.

8 x size 12{8 - x} {}

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An unknown quantity less fourteen.

x 14 size 12{x - "14"} {}

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Six times a number is fifty-four.

6 x = 54 size 12{6x="54"} {}

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Two ninths of a number is eleven.

2 9 x = 11 size 12{ { {2} over {9} } x="11"} {}

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Three more than seven times a number is nine more than five times the number.

3 + 7 x = 9 + 5 x size 12{3+7x=9+5x} {}

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Twice a number less eight is equal to one more than three times the number.

2 x 8 = 3 x + 1 size 12{2x - 8=3x+1} {} or 2 x 8 = 1 + 3 x size 12{2x - 8=1+3x} {}

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Sample set b

Sometimes the structure of the sentence indicates the use of grouping symbols. We’ll be alert for commas . They set off terms.

A number ( x divided by ÷ four, 4 ) minus - six, 6 is = twelve 12

Translation: x 4 6 = 12 size 12{ { {x} over {4} } - 6="12"} {} .

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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 statement twenty is subtracted from some number can be broken into three parts and converted into a mathematical expression. Some number becomes x, the phrase, is subtracted from, becomes a minus symbol, and twenty becomes the number 20. This translates to the expression x - 20.

Translation: x 20 size 12{x - "20"} {} .

The word from indicated the motion (subtraction) is to begin at the point of “some number.”

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Ten less than some number. Notice that less than can be replaced by from .

Ten from some number.

Translation: x 10 size 12{x - "10"} {} .

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Practice set b

Translate each phrase or sentence into a mathematical expression or equation.

A number divided by eight, plus seven, is fifty.

x 8 + 7 = 50 size 12{ { {x} over {8} } +7="50"} {}

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A number divided by three, minus the same number multiplied by six, is one more than the number.

2 3 6 x = x + 1 size 12{ { {2} over {3} } - 6x=x+1} {}

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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?
Khizar Reply
7hours 36 min - 4hours 50 min
Tanis Reply

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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