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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

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
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
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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
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