# 11.5 Applications i: translating words to mathematical symbols

 Page 1 / 2
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.

 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 $x$ (or any symbol)

## Sample set a

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

$\underset{9}{\underbrace{\text{Nine}}}\underset{+}{\underbrace{\text{more than}}}\underset{x}{\underbrace{\text{some number.}}}$

Translation: $9+x$ .

$\underset{18}{\underbrace{\text{Eighteen}}}\underset{-}{\underbrace{\text{minus}}}\underset{x}{\underbrace{\text{a number.}}}$

Translation: $\text{18}-x$ .

$\underset{y}{\underbrace{\text{A quantity}}}\underset{-}{\underbrace{\text{less}}}\underset{5}{\underbrace{\text{five.}}}$

Translation: $y-5$ .

$\underset{4}{\underbrace{\text{Four}}}\underset{\cdot }{\underbrace{\text{times}}}\underset{x}{\underbrace{\text{a number}}}\underset{=}{\underbrace{\text{is}}}\underset{\mathrm{16}}{\underbrace{\text{sixteen.}}}$

Translation: $4x=\text{16}$ .

Translation: $\frac{1}{5}n=\text{30}$ , or $\frac{n}{5}=\text{30}$ .

Translation: $5x=2+2x$ .

## Practice set a

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

Twelve more than a number.

$\text{12}+x$

Eight minus a number.

$8-x$

An unknown quantity less fourteen.

$x-\text{14}$

Six times a number is fifty-four.

$6x=\text{54}$

Two ninths of a number is eleven.

$\frac{2}{9}x=\text{11}$

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

$3+7x=9+5x$

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

$2x-8=3x+1$ or $2x-8=1+3x$

## 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.

$\underset{\left(x}{\underbrace{\text{A number}}}\underset{÷}{\underbrace{\text{divided by}}}\underset{4\right)}{\underbrace{\text{four,}}}\underset{-}{\underbrace{\text{minus}}}\underset{6}{\underbrace{\text{six,}}}\underset{=}{\underbrace{\text{is}}}\underset{\mathrm{12}}{\underbrace{\text{twelve}}}$

Translation: $\frac{x}{4}-6=\text{12}$ .

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.

Translation: $x-\text{20}$ .

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

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

Ten from some number.

Translation: $x-\text{10}$ .

## Practice set b

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

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

$\frac{x}{8}+7=\text{50}$

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

$\frac{2}{3}-6x=x+1$

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
7hours 36 min - 4hours 50 min