# Review of past work  (Page 4/8)

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Subtraction is actually the same as adding a negative number .

In this example, $a$ and $b$ are positive numbers, but $-b$ is a negative number

$\begin{array}{c}\hfill a-b=a+\left(-b\right)\\ \hfill 5-3=5+\left(-3\right)\end{array}$

So, this means that subtraction is simply a short-cut for adding a negative number and instead of writing $a+\left(-b\right)$ , we write $a-b$ . This also means that $-b+a$ is the same as $a-b$ . Now, which do you find easier to work out?

Most people find that the first way is a bit more difficult to work out than the second way. For example, most people find $12-3$ a lot easier to work out than $-3+12$ , even though they are the same thing. So $a-b$ , which looks neater and requires less writing is the accepted way of writing subtractions.

[link] shows how to calculate the sign of the answer when you multiply two numbers together. The first column shows the sign of the firstnumber, the second column gives the sign of the second number and the third column shows what sign the answer will be.

 $a$ $b$ $a×b$ or $a÷b$ $+$ $+$ $+$ $+$ $-$ $-$ $-$ $+$ $-$ $-$ $-$ $+$

So multiplying or dividing a negative number by a positive number always gives you a negative number, whereas multiplying or dividing numbers which have thesame sign always gives a positive number. For example, $2×3=6$ and $-2×-3=6$ , but $-2×3=-6$ and $2×-3=-6$ .

Adding numbers works slightly differently (see [link] ). The first column shows the sign of the first number, the second column gives the sign of the second number and the third column showswhat sign the answer will be.

 $a$ $b$ $a+b$ $+$ $+$ $+$ $+$ $-$ ? $-$ $+$ ? $-$ $-$ $-$

If you add two positive numbers you will always get a positive number, but if you add two negative numbers you will always get a negative number. If thenumbers have a different sign, then the sign of the answer depends on which one isbigger.

## Living without the number line

The number line in [link] is a good way to visualise what negative numbers are, but it can get very inefficient to use it every timeyou want to add or subtract negative numbers. To keep things simple, we will write down three tips that you can use to make working with negative numbers alittle bit easier. These tips will let you work out what the answer is when you add or subtract numbers which may be negative, and will also help you keep yourwork tidy and easier to understand.

## Negative numbers tip 1

If you are given an expression like $-a+b$ , then it is easier to move the numbers around so that the expression looks easier. In this case, we have seen thatadding a negative number to a positive number is the same as subtracting the number from the positive number. So,

$\begin{array}{ccc}\hfill -a+b& =& b-a\hfill \\ \hfill -5+10& =& 10+\left(-5\right)\hfill \\ \hfill & =& 10-5\hfill \\ \hfill & =& 5\hfill \end{array}$

This makes the expression easier to understand. For example, a question like “What is $-7+11$ ?” looks a lot more complicated than “What is $11-7$ ?”, even though they are exactly the same question.

## Negative numbers tip 2

When you have two negative numbers like $-3-7$ , you can calculate the answer by simply adding together the numbers as if they were positive and then putting anegative sign in front.

$\begin{array}{ccc}\hfill -c-d& =& -\left(c+d\right)\hfill \\ \hfill -7-2& =& -\left(7+2\right)=-9\hfill \end{array}$

## Negative numbers tip 3

In [link] we saw that the sign of two numbers added together depends on which one is bigger. This tip tells us that all we need todo is take the smaller number away from the larger one and remember to give the answer the sign of the larger number. In this equation, $F$ is bigger than $e$ .

can someone help me with some logarithmic and exponential equations.
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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