# Review of past work  (Page 3/8)

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$\begin{array}{c}\hfill a×b÷b=a\\ \hfill 5×4÷4=5\end{array}$

Sometimes you will see a multiplication of letters as a dot or without any symbol. Don't worry, its exactly the same thing. Mathematicians areefficient and like to write things in the shortest, neatest way possible.

$\begin{array}{ccc}\hfill abc& =& a×b×c\hfill \\ \hfill a·b·c& =& a×b×c\hfill \end{array}$

It is usually neater to write known numbers to the left, and letters to the right. So although $4x$ and $x4$ are the same thing, it looks better to write $4x$ . In this case, the “4” is a constant that is referred to as the coefficient of $x$ .

## Commutativity for multiplication

The fact that $ab=ba$ is known as the commutative property of multiplication. Therefore, both addition and multiplication are described as commutative operations.

## Brackets

Brackets Sometimes people say “parentheses” instead of “brackets”. in mathematics are used to show the order in which you must do things. This is important as you can get different answers depending on the order in which youdo things. For example:

$\left(5×5\right)+20=45$

whereas

$5×\left(5+20\right)=125$

If there are no brackets, you should always do multiplications and divisions first and then additions and subtractions Multiplying and dividing can be performed in any order as it doesn't matter. Likewise itdoesn't matter which order you do addition and subtraction. Just as long as you do any $×÷$ before any $+-$ . . You can always put your own brackets into equations using this rule to make things easier for yourself, for example:

$\begin{array}{ccc}\hfill a×b+c÷d& =& \left(a×b\right)+\left(c÷d\right)\hfill \\ \hfill 5×5+20÷4& =& \left(5×5\right)+\left(20÷4\right)\hfill \end{array}$

If you see a multiplication outside a bracket like this

$\begin{array}{c}\hfill a\left(b+c\right)\\ \hfill 3\left(4-3\right)\end{array}$

then it means you have to multiply each part inside the bracket by the number outside

$\begin{array}{ccc}\hfill a\left(b+c\right)& =& ab+ac\hfill \\ \hfill 3\left(4-3\right)& =& 3×4-3×3=12-9=3\hfill \end{array}$

unless you can simplify everything inside the bracket into a single term. In fact, in the above example, it would have been smarter to have done this

$3\left(4-3\right)=3×\left(1\right)=3$

It can happen with letters too

$3\left(4a-3a\right)=3×\left(a\right)=3a$

## Distributivity

The fact that $a\left(b+c\right)=ab+ac$ is known as the distributive property.

If there are two brackets multiplied by each other, then you can do it one stepat a time:

$\begin{array}{ccc}\hfill \left(a+b\right)\left(c+d\right)& =& a\left(c+d\right)+b\left(c+d\right)\hfill \\ \hfill & =& ac+ad+bc+bd\hfill \\ \hfill \left(a+3\right)\left(4+d\right)& =& a\left(4+d\right)+3\left(4+d\right)\hfill \\ \hfill & =& 4a+ad+12+3d\hfill \end{array}$

## What is a negative number?

Negative numbers can be very confusing to begin with, but there is nothing to be afraid of. The numbers that are used most often are greater than zero. Thesenumbers are known as positive numbers .

A negative number is a number that is less than zero. So, if we were to take a positive number $a$ and subtract it from zero, the answer would be the negative of $a$ .

$0-a=-a$

On a number line, a negative number appears to the left of zero and a positive number appears to the right of zero.

## Working with negative numbers

When you are adding a negative number, it is the same as subtracting that number if it were positive. Likewise, if you subtract a negative number, it is the sameas adding the number if it were positive. Numbers are either positive or negative and we call this their s ign. A positive number has a positive sign ( $+$ ) and a negative number has a negative sign ( $-$ ).

#### Questions & Answers

can someone help me with some logarithmic and exponential equations.
sure. what is your question?
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
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
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
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
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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