<< Chapter < Page Chapter >> Page >

Mathematics

Grade 8

The number system

(natural and whole numbers)

Module 4

Addition and subtraction in algebra

CLASS ASSIGNMENT 1

  • Discover more and more about addition and subtraction in ALGEBRA ….
  • When we do addition and subtraction in Algebra, we can only add together or subtract like terms (terms of the same type) from one another.
  • e.g. 3 a + 5 a = 8 a ( a is the same for both terms)
  • e.g. 3 a + 5 a ² (cannot be added together, because one term is a and the other a ² - not of the same type)
  • remember: -8(+5) means: -8 x (+5) = -40(two signs must not be placed next to one another; multiply the two signs by one another)

1. Can you still do the following with integers?

1.1: -8 - 12 + 8

1.2: 7 - (+8) - (-6)

1.3: 15 - (-9) + (+7)

1.4: 2(-6) - 5(-6)

1.5: 50 - 70 + 15

2. WOW! Look at this! Quite easy….

2.1 2 a + 2 a = (yes, they are alike; I can add)

2.2 3 a - 6 y + 7 a + 15 y = (look for like terms)

3 a + 7 a =

-6 y + 15 y =

(now write the answer alongside the question)

2.3 Add the following expressions together:

2.3.1: 6 a - 7 b - 9 c ; -7 a + 15 b - 29 c

2.3.2: -9 a ² - 16 a + 17 b ; -17 a ² -40 ; -29 b + 30

3. How about subtracting? Look at the following example:Subtract 6 from 15 . How would you write this? 15 - (+6) = 15 - 6 = 9

Explanation: (-) x (+) = (-) THEREFORE: 15 - 6

Look at the following: Subtract -6 a + 5 b from 16 a - 3 b

It will look like this: 16 a - 3 b - (-6 a + 5 b )

= 16 a - 3 b + 6 a - 5 b (multiply (-) within the brackets)

= 16 a + 6 a - 3 b - 5 b

= 22 a - 8 b

  • Important: Begin by deciding which expression should be written first!

3.1 Calculate each of the following:

3.1.1 Subtract the second from the first: -7 a + 3 ; 6 a - 9

3.1.2 Subtract -7 a ² - 5 a + 8 from 18 a ² - 15

3.1.3 Reduce -15 x size 12{x} {} ² - 7 x size 12{x} {} + 20 by -6 x size 12{x} {} ² + 76

HOMEWORK ASSIGNMENT 1

1. Add the following expressions together: -3 p ² - 2 p - 5 ; 6 p ² + 8 ; -15 p - 28

2. Subtract -5 p ² - 3 p from 8 - 7 a ²

3. Subtract 6 a - 8 y from 1

4. 3 a 3 + 6 a - 7 a - 5 - 2(8 a 3 - 4 a ² + 17 a + 8) - 15 a

5. Increase 6 p + 15 y - 3 a b y -13 y - 18 p + 34 a

6. By how much is -8 a ² + 6 a bigger than 15 a ² + 3 a - 5 ?

7. By how much is 4 a ² - 5 a + 1 smaller than 16 a ² + 3 a - 7 ?

8. What must be added to 5 a ² + 3 a to get -3 a + 6 ?

Assessment

Assessment of myself: by myself: Assessment by Teacher:
I can… 1 2 3 4 Critical Outcomes 1 2 3 4
Identify like terms in an expression; (Lu 2.8.1; 2.8.2) Critical and creative thinking
Add like terms together; (Lu 2.8.2; 2.8.4) Collaborating
Subtract like terms from each other; (Lu 2.8.2; 2.8.4) Organising en managing
Add and subtract constant values; (Lu 2.8.4) Processing of information
Add a range of expressions together; (Lu 2.8.2; 2.8.4; 2.8.6) Communication
Subtract a range of expressions from each other. (Lu 2.8.2; 2.8.4; 2.8.6) Problem solving
Independence

good average not so good

Comments by the learner: My plan of action: My marks:
I am very satisfied with the standard of my work. < Date :
I am satisfied with the steady progress I have made. Out of:
I have worked hard, but my achievement is not satisfactory. Learner :
I did not give my best. >
Comments by parents: Comments by teacher:
Parent signature: Date Signature: Date :

Memorandum

Class assignment 1

  • -12
  • 5
  • 31
  • 18
  • –5
  • 4a
  • 10 a + 9 a
  • - a + 8 b – 38 c
  • –26 a 2 – 16 a – 12 b – 10
  • -7 a + 3 – (6 a – 9)

= -7 a +3 – 6 a + 9

= -13 a + 12

  • 18 a 2 – 15 – (-7 a 2 – 5 a + 8)

= 18 a 2 – 15 + -7 a 2 + 5 a – 8

= 25 a 2 + 5 a – 23

  • -15 x 2 – 7 x + 20 – (-6 x 2 + 76)

= -15 x 2 – 7 x + 20 + -6 x 2 – 76

= -9 x 2 – 7 x – 56

Homework assignment 1

1. 3 p 2 – 17 p – 25

2. 8 – 7 a 2 – (-5 p 2 – 3 p )

= 8 – 7 a 2 + 5 p 2 + 3 p )

-2 a 2 + 3 p + 8

3. 1 – (6 a – 8 y ) = 1 – 6 a + 8 y

4. 3 a 3 + 6 a – 7 a – 5 – 16 a 3 + 8 a 2 – 34 a – 16 – 15 a

= -13 a 3 + 8 a 2 – 50 a – 21

5. 24 p + 28 y – 37 a

6. -23 a 2 + 3 a + 5

7. 12 a 2 + 8 a – 8

8. -6 a + 6 – 5 a 2

Questions & Answers

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
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
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
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
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Mathematics grade 8' conversation and receive update notifications?

Ask