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Mathematics

Grade 8

The number system

(natural and whole numbers)

Module 5

Multiplication in algebra

CLASS ASSIGNMENT 1

  • Discover more and more about multiplication in ALGEBRA!

1. Indicate what the following will be equal to...

1.1: 2 x 2 x 2 = ....................... (and what the exponent form will be .....................)

1.2: 2² x 2² x 2 3 x 3² x 3 3 = .........................

(and what the exponent form will be ......................... )

  • :a x a x a = .........................

1.4: a ² x a ² x a 3 = .........................

Now write out a general rule for the multiplication of exponents:

1.5: 2( a - b ) = .........................

distributive law: (2 x a ) - (2 x b )

1.6: 3 0 = .........................

1.7: a ( a + b ) 0 = .........................

Therefore: (anything) to the power of 0 = .........................

1.8: 3 1 = .........................

1.9: 1 200 = .........................

2. What does each of the following mean? Also provide the simplified answer for each one

2.1: a ² =

2.2: 2 a b =

2.3: -3( a + b ) =

2.4: 4( a )² =

2.5: ( a 3 )² =

2.6: (3 a ²) 3 =

2.7: 2 p x 3 p =

2.8: a b² x a ² b 3 x a b 6 =

2.9: ( 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} a 3 ) 4 =

2.10: 2( a 3 )² =

2.11: 6(2 a - 3 b ) =

2.12: -7 a ( a ² - 2 b ² ) =

3. Can you recall the order of operations for the following? Write it down.

3.1 Now make use of everything you have learnt up till now to calculate the following:

3.1.1: a x a x aaa + a 4

3.1.2: 2( a + b ) - 3( a - b )

3.1.3: 3 a x 2 a ² b + 5 a ² x (-3 a b )

3.1.4: -5 a ( a - b 3 ) + 7 a b 3 - 2 a 5

3.1.5: -3( a ² b 4 )² - 5 a 3 (-2 a 4 b ²) 3

4. What is the meaning of the word substitution?

Provide an example as explanation:

5. Supposing that a = 5 ; b = -1 and c = 3 , calculate the value of each of the following:

5.1: 5 a ² - 3 b

5.2: 2 ab 2 3a size 12{ { {2 bold "ab" rSup { size 8{2} } } over {3a} } } {}

5.3: a + a b size 12{ { {a" "+" "b²} over {a` - `b} } } {}

5.4: (2 a b ² c

5.5: -3 a b 3 - 2 a b 3 c

HOMEWORK ASSIGNMENT 1

1. Simplify each of the following:

1. ( a 5 ) 6

1.2: 5(3 a - 7 a

1.3: -5(3 a - 2 b )

1.4: (3 a )² . [ (2 a )² ] 3

1.5: p x 2 x m x q

1.6: w ² x 3 b x 1 / 3 b x w

1.7: -5 a ( 3 a - 5 a b)

1.8: (3 a )² (2 a ) + (4 a ²) (-2 a )

1.9: (5 a b ²) 4 - (- 6 b 6 a 4 )

1.10: -6 a ² b ( 2 a ² - 3 a b 3 + 5)

2. Supposing that x size 12{x} {} = -2 and y = -1 , determine the value of ...

2.1: (2 y )(2 x size 12{x} {}

2.2: -3 x size 12{x} {} 3 - 2 y 5

2.3: (2 y + 2 x size 12{x} {}

3. Supposing m = 2 ; n = -3 en q = 5, determine the value of each of the following expressions:

3.1: m + n + q

3.2: 4 m - 2 n - 3 q

3.3: 2( m ² + q ²) - n ²

3.4: m / 3 + n / 4 - q

3.5: 3m( n + q ) - 2( m + n ²)

4. A challenge: See if the knowledge that you have acquired is able to help you solve the problems that follow.

4.1 The average speed of an Intercape Mainliner is 5 a 4 kilometres per hour.What is the distance that the bus can complete in (5 a 3 + 5 a - 6) hours?

4.2 Miss South Africa buys ( a - b + 2 c ) litres of milk at 4 ab rands per litre and 5 ab litres of fruit juice at (2 a + 5 b - 3 c ) rands per litre.

What will these purchases cost in total?

Assessment

Assessment of myself: by myself: Assessment by Teacher:
I can… 1 2 3 4 Critical Outcomes 1 2 3 4
write expressions in exponent form; (Lo 2.2; 1.6.3) Critical and creative thinking
successfully add exponents together; (Lo 2.2; 1.6.3) Collaborating
successfully subtract exponents from each other; (Lo 2.2; 1.6.3) Organising en managing
successfully multiply exponents with each other; (Lo 2.2; 2.8.3&.4) Processing of information
solve expressions with brackets; (Lo 2.2; 2.8.5) Communication
apply the correct order of calculations; (Lo 2.2; 2.8.5) Problem solving
determine values of expressions with substitution. (Lo 2.2; 2.8.5; 1.6.2; 1.6.3)
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:
Signature: Date : Signature: Date :

Memorandum

Claswork assignment 1

  • :2 3
  • :2 12
  • :a 3
  • :a 7

Multiply and bases are the same: you add the exponents.

  • :2 a – 2 b
  • :1

1.7 :a

  • :3
  • :1
  • :a x a
  • :2 x a x b
  • :–3 a – 3 b
  • :4 x a x a = 4 a 2
  • :a 3 x a 3 a 6
  • :27 a 6
  • :6 p 2
  • :a 4 b 11
  • : 1 16 size 12{ { {1} over {"16"} } } {} a 12
  • :2 a 6
  • :12 a – 18 b
  • :–7 a 3 + 14 ab 2

3.1 :1: ( )

:2: of

3: x or ÷ from left to right

4: + or – from left to right

  • :a 5 + a 4
  • :2 a + 2 b – 3 a + 3 b = - a + 5 b
  • :–18 a 6 b 2
  • : –5 a 2 + 5 ab 3 + 7 ab 3 – 2 a 5

:=-5 a 2 + 12 ab 3 + 7 ab 3 – 2 a 5

  • :–3 a 4 b 8 + 10 a 15 b 6

4. put another value in unknown place

  • :5(5) 2 –3(–1)

= 125 + 3 = 128

  • : 2 ( 5 ) ( 1 ) 2 3 ( 5 ) size 12{ { {2 \( 5 \) \( - 1 \) rSup { size 8{2} } } over {3 \( 5 \) } } } {}

= 10 15 size 12{ { {"10"} over {"15"} } } {} = 2 3 size 12{ { {2} over {3} } } {}

  • : ( 5 ) + ( 1 ) 2 5 ( 1 ) size 12{ { { \( 5 \) + \( - 1 \) rSup { size 8{2} } } over {5 - \( - 1 \) } } } {}

= 6 6 size 12{ { {6} over {6} } } {} = 1

  • :[2(5)(–1) 2 (3)] 2

= [30] 2 = 900

  • :–3(5)(–1) 3 –2(5)(–1) 3 (3)

= 15 + 30 = 45

Classwork assignment1

  • :9 30
  • :5(–4 a ) 2 = 80 a 2
  • :–15 a + 10 b
  • :9 a 2 . 64 a 6 = 576 a 8
  • :2 mpq
  • :b 2 w 3
  • :–15 a 2 + 25 a 2 b
  • :6 a 3 – 8 a 3 = –2 a 3
  • :625 a 4 b 8 + 6 a 4 b 6
  • :–12 a 4 b + 18 a 3 b 4 – 30 a 2 b
  • :[2(–1)][2(2)] 2

=(–2)(16) = –32

  • :–3(–2) 3 –2(–1) 5

= 24 + 2 = 26

  • :[2(–1) + 2(–2)] 2

= [–2–4]

= (–6) 2

= 36

  • :2 + (–3) + = 4
  • :4(2) – 2(–3) – 3(5)

= 8 + 6 – 15 = –1

  • :2[(2) 2 + (5) 2 ] – (–3) 2

= 2[4 + 25] – (–3) 2

= 58 – 9 = 49

3.4 : 2 3 size 12{ { {2} over {3} } } {} + 3 4 size 12{ { { - 3} over {4} } } {} – 5

= 1 4 size 12{ { { - 1} over {4} } } {} – 5 = 5 1 4 size 12{ { {1} over {4} } } {}

3.5 :3(2)[–3 + 5] – 2 [2 + (–3) 2 ]

= 6[2] – 2[11]

= 12 – 2

= –10

  • :5 a 4 (5 a 3 + 5 a – 6)

= 25 a 7 + 25 a 5 – 30 a 4

  • :4 ab ( a b + 2 c ) + 5 ab (2 a + 5 b – 3 c )

= 4 a 2 b – 4 ab 2 + 8 ab c + 10 a 2 b + 25 ab 2 – 15 ab c

= 14 a 2 b + 21 ab 2 – 7 ab c

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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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