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Addition and subtraction in Algebra

Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

Grade 8

THE NUMBER SYSTEM

(Natural and whole numbers)

Module 4

ADDITION AND SUBTRACTION IN ALGEBRA

CLASS ASSIGNMENT1

  • 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. 3a + 5a = 8a (a is the same for both terms)
  • e.g. 3a + 5a² (cannot be added together, because one term is a and the othera² - 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 2a + 2a = (yes, they are alike; I can add)

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

3a + 7a =

-6y + 15y =

(now write the answer alongside the question)

2.3 Add the following expressions together:

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

2.3.2: -9a² - 16a + 17b ; -17a² -40 ; -29b + 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 -6a + 5b from 16a - 3b

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

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

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

= 22a - 8b

  • 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: -7a + 3 ; 6a - 9

3.1.2 Subtract -7a² - 5a + 8 from 18a² - 15

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

HOMEWORK ASSIGNMENT1

1. Add the following expressions together: -3p² - 2p - 5 ; 6p² + 8 ; -15p - 28

2. Subtract -5p² - 3p from 8 - 7a²

3. Subtract 6a - 8y from 1

4. 3a3 + 6a - 7a - 5 - 2(8a3 - 4a² + 17a + 8) - 15a

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

6. By how much is -8a² + 6a bigger than 15a² + 3a - 5 ?

7. By how much is 4a² - 5a + 1 smaller than 16a² + 3a - 7 ?

8. What must be added to 5a² + 3a to get -3a + 6 ?

Assessment

Table 1
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

Table 2
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.     >          
Table 3
Comments by parents:   Comments by teacher:
     
     
     
Parent signature: Date   Signature: Date:

Memorandum

CLASS ASSIGNMENT 1

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

= -7a +3 – 6a + 9

= -13a + 12

  • 18a 2 – 15 – (-7a 2 – 5a + 8)

= 18a 2 – 15 + -7a 2 + 5a – 8

= 25a 2 + 5a – 23

  • -15x2 – 7x + 20 – (-6x2 + 76)

= -15x2 – 7x + 20 + -6x2 – 76

= -9x2 – 7x – 56

HOMEWORK ASSIGNMENT 1

1. 3p2 – 17p – 25

2. 8 – 7a2 – (-5p2 – 3p)

= 8 – 7a2 + 5p2 + 3p)

-2a2 + 3p + 8

3. 1 – (6a – 8y) = 1 – 6a + 8y

4. 3a3 + 6a – 7a – 5 – 16a3 + 8a2 – 34a – 16 – 15a

= -13a3 + 8a2 – 50a – 21

5. 24p + 28y – 37a

6. -23a2 + 3a + 5

7. 12a2 + 8a – 8

8. -6a + 6 – 5a2

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