# Review of past work  (Page 5/8)

 Page 5 / 8
$\begin{array}{ccc}\hfill e-F& =& -\left(F-e\right)\hfill \\ \hfill 2-11& =& -\left(11-2\right)=-9\hfill \end{array}$

You can even combine these tips: for example, you can use Tip 1 on $-10+3$ to get $3-10$ and then use Tip 3 to get $-\left(10-3\right)=-7$ .

## Negative numbers

1. Calculate:
 (a) $\left(-5\right)-\left(-3\right)$ (b) $\left(-4\right)+2$ (c) $\left(-10\right)÷\left(-2\right)$ (d) $11-\left(-9\right)$ (e) $-16-\left(6\right)$ (f) $-9÷3×2$ (g) $\left(-1\right)×24÷8×\left(-3\right)$ (h) $\left(-2\right)+\left(-7\right)$ (i) $1-12$ (j) $3-64+1$ (k) $-5-5-5$ (l) $-6+25$ (m) $-9+8-7+6-5+4-3+2-1$
2. Say whether the sign of the answer is $+$ or $-$
 (a) $-5+6$ (b) $-5+1$ (c) $-5÷-5$ (d) $-5÷5$ (e) $5÷-5$ (f) $5÷5$ (g) $-5×-5$ (h) $-5×5$ (i) $5×-5$ (j) $5×5$

## Rearranging equations

Now that we have described the basic rules of negative and positive numbers and what to do when you add, subtract, multiply and divide them, we are ready totackle some real mathematics problems!

Earlier in this chapter, we wrote a general equation for calculating how much change ( $x$ ) we can expect if we know how much an item costs ( $y$ ) and how much we have given the cashier ( $z$ ). The equation is:

$x+y=z$

So, if the price is R10 and you gave the cashier R15, then write R15 instead of $z$ and R10 instead of $y$ .

$x+10=15$

Now that we have written this equation down, how exactly do we go about finding what the change is? In mathematical terms, this is known as solving an equationfor an unknown ( $x$ in this case). We want to re-arrange the terms in the equation, so that only $x$ is on the left hand side of the $=$ sign and everything else is on the right.

The most important thing to remember is that an equation is like a set of weighing scales. In order to keep the scales balanced, whatever is done to oneside must be done to the other.

## Method: rearranging equations

You can add, subtract, multiply or divide both sides of an equation by any number you want, as long as you always do it to both sides.

So for our example we could subtract $y$ from both sides

$\begin{array}{ccc}\hfill x+y& =& z\hfill \\ \hfill x+y-y& =& z-y\hfill \\ \hfill x& =& z-y\hfill \\ \hfill x& =& 15-10\hfill \\ \hfill & =& 5\hfill \end{array}$

Now we can see that the change is the price subtracted from the amount paid to the cashier. In the example, the change should be R5. In real life wecan do this in our heads; the human brain is very smart and can do arithmetic without even knowing it.

When you subtract a number from both sides of an equation, it looks like you just moved a positive number from one side and it became a negative on the other,which is exactly what happened. Likewise, if you move a multiplied number from one side to the other, it looks like it changed to a divide. This is because youreally just divided both sides by that number and a number divided by itself is just 1

$\begin{array}{ccc}\hfill a\left(5+c\right)& =& 3a\hfill \\ \hfill a\left(5+c\right)÷a& =& 3a÷a\hfill \\ \hfill \frac{a}{a}×\left(5+c\right)& =& 3×\frac{a}{a}\hfill \\ \hfill 1×\left(5+c\right)& =& 3×1\hfill \\ \hfill 5+c& =& 3\hfill \\ \hfill c& =& 3-5=-2\hfill \end{array}$

However, you must be careful when doing this, as it is easy to make mistakes.

The following is the WRONG thing to do

$\begin{array}{ccc}\hfill 5a+c& =& 3a\hfill \\ \hfill 5+c& =& 3\hfill \end{array}$

Can you see why it is wrong? It is wrong because we did not divide the $c$ term by $a$ as well. The correct thing to do is

$\begin{array}{ccc}\hfill 5a+c& =& 3a\hfill \\ \hfill 5+c÷a& =& 3\hfill \\ \hfill c÷a& =& 3-5=-2\hfill \end{array}$

## Rearranging equations

1. If $3\left(2r-5\right)=27$ , then $2r-5=.....$
2. Find the value for $x$ if $0,5\left(x-8\right)=0,2x+11$
3. Solve $9-2n=3\left(n+2\right)$
4. Change the formula $P=A+Akt$ to $A=$
5. Solve for $x$ : $\frac{1}{ax}+\frac{1}{bx}=1$

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
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
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
Difference between extinct and extici spicies
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