# 2.1 Use the language of algebra  (Page 3/8)

 Page 3 / 8

Use [link] to fill in the appropriate $\text{symbol},\text{=},\text{<},\text{or}\phantom{\rule{0.2em}{0ex}}\text{>}.$

1. MPG of Prius_____MPG of Versa
2. MPG of Mini Cooper_____ MPG of Corolla

1. >
2. >

Use [link] to fill in the appropriate $\text{symbol},\text{=},\text{<},\text{or}\phantom{\rule{0.2em}{0ex}}\text{>}.$

1. MPG of Fit_____ MPG of Prius
2. MPG of Corolla _____ MPG of Fit

1. <
2. <

Grouping symbols in algebra are much like the commas, colons, and other punctuation marks in written language. They indicate which expressions are to be kept together and separate from other expressions. [link] lists three of the most commonly used grouping symbols in algebra.

Common Grouping Symbols
parentheses $\left(\phantom{\rule{0.5em}{0ex}}\right)$
brackets $\left[\phantom{\rule{0.5em}{0ex}}\right]$
braces $\left\{\phantom{\rule{0.5em}{0ex}}\right\}$

Here are some examples of expressions that include grouping symbols. We will simplify expressions like these later in this section.

$8\left(14-8\right)\phantom{\rule{4em}{0ex}}21-3\left[2+4\left(9-8\right)\right]\phantom{\rule{4em}{0ex}}24÷\left\{13-2\left[1\left(6-5\right)+4\right]\right\}$

## Identify expressions and equations

What is the difference in English between a phrase and a sentence? A phrase expresses a single thought that is incomplete by itself, but a sentence makes a complete statement. “Running very fast” is a phrase, but “The football player was running very fast” is a sentence. A sentence has a subject and a verb.

In algebra, we have expressions and equations . An expression is like a phrase. Here are some examples of expressions and how they relate to word phrases:

Expression Words Phrase
$3+5$ $3\phantom{\rule{0.2em}{0ex}}\text{plus}\phantom{\rule{0.2em}{0ex}}5$ the sum of three and five
$n-1$ $n$ minus one the difference of $n$ and one
$6·7$ $6\phantom{\rule{0.2em}{0ex}}\text{times}\phantom{\rule{0.2em}{0ex}}7$ the product of six and seven
$\frac{x}{y}$ $x$ divided by $y$ the quotient of $x$ and $y$

Notice that the phrases do not form a complete sentence because the phrase does not have a verb. An equation    is two expressions linked with an equal sign. When you read the words the symbols represent in an equation, you have a complete sentence in English. The equal sign gives the verb. Here are some examples of equations:

Equation Sentence
$3+5=8$ The sum of three and five is equal to eight.
$n-1=14$ $n$ minus one equals fourteen.
$6·7=42$ The product of six and seven is equal to forty-two.
$x=53$ $x$ is equal to fifty-three.
$y+9=2y-3$ $y$ plus nine is equal to two $y$ minus three.

## Expressions and equations

An expression is a number, a variable, or a combination of numbers and variables and operation symbols.

An equation    is made up of two expressions connected by an equal sign.

Determine if each is an expression or an equation:

1. $\phantom{\rule{0.2em}{0ex}}16-6=10$
2. $\phantom{\rule{0.2em}{0ex}}4·2+1$
3. $\phantom{\rule{0.2em}{0ex}}x÷25$
4. $\phantom{\rule{0.2em}{0ex}}y+8=40$

## Solution

1. This is an equation—two expressions are connected with an equal sign.
2. This is an expression—no equal sign.
3. This is an expression—no equal sign.
4. This is an equation—two expressions are connected with an equal sign.

Determine if each is an expression or an equation:

1. $\phantom{\rule{0.2em}{0ex}}23+6=29\phantom{\rule{0.4em}{0ex}}$
2. $\phantom{\rule{0.2em}{0ex}}7·3-7$

1. equation
2. expression

Determine if each is an expression or an equation:

1. $\phantom{\rule{0.2em}{0ex}}y÷14\phantom{\rule{0.4em}{0ex}}$
2. $\phantom{\rule{0.2em}{0ex}}x-6=21$

1. expression
2. equation

## Simplify expressions with exponents

To simplify a numerical expression means to do all the math possible. For example, to simplify $4·2+1$ we’d first multiply $4·2$ to get $8$ and then add the $1$ to get $9.$ A good habit to develop is to work down the page, writing each step of the process below the previous step. The example just described would look like this:

$4·2+1$
$8+1$
$9$

Suppose we have the expression $2·2·2·2·2·2·2·2·2.$ We could write this more compactly using exponential notation. Exponential notation is used in algebra to represent a quantity multiplied by itself several times. We write $2·2·2$ as ${2}^{3}$ and $2·2·2·2·2·2·2·2·2$ as ${2}^{9}.$ In expressions such as ${2}^{3},$ the $2$ is called the base and the $3$ is called the exponent. The exponent tells us how many factors of the base we have to multiply.

#### Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
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..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
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
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
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.
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
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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 ?
Bob Reply
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?
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Good
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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