Algebraic expressions 1

Page 69

Exercise 6.1, page 69

1. One CD costs R150.

a) How much will 2 CDs cost?

b) How much will 4 CDs cost?

c) How much will 7 CDs cost?

d) How much will CDs cost?

e) How many CDs can you buy for R300?

f) How many CDs can you buy for R900?

g) How many CDs can you buy for R?

2 x R150 = R3004 x R150 = R6007 x R150 = R1 050 x R150

= 2

𝑅𝑥𝑅150

= 6

2. What change (in cents) is given if an item that costs 75 cents is paid for with:

a) 90 cents

b) R5

c) cents

d) R

e) R and cents

90c – 75c = 15c500c – 75c = 425c – 75c

100 – 75c(100 + ) – 75c

3. The sides of the shape below all have a length of units. What is the perimeter of the shape in terms of ?

There are 16 sides. Each side is units long.

erimeter = 16 x or 16

6. The sum of Olwethu and Nolita’s ages is 20 years.

a) If Olwethu is 11 years old, how old is Nolita?

b) If Olwethu is 7 years old, how old is Nolita?

c) If Olwethu is years old, how old is Nolita?

20 – 11 = 9

20 – 7 = 13

20 –

7. Loyiso is years old.

a) How old was he last year?

b) How old will he be in 5 years time?

c) How old was he years ago?

d) How old will he be in years time?

e) How old is someone that is double his age?

-1 years

+ 5 years

- years

+ years

2 x years or 2 years

DO: Exercise 6.1 # 9 - 12Page 70

Exercise 6.1: ANSWERS

9a) R9,75 + R3,25 = R13

b) 3(R9,75) + 4(R3,25) = R42,25

c) (R9,75) + (R3,25) = 9,75 + 3,25

d) = 7

e)

f) 1 pen; 17 pencils 4 pens; 8 pencils

2 pens; 14 pencils 5 pens; 5 pencils

3 pens; 11 pencils 6 pens; 2 pencils

10 a) 1 x 100 = 100km

b) 5 x 100 = 500km

c) x 100 = 100

11) R100 – R – R

12 a) 10 + 3 = 13

b) + 2 + 3 = + 5

c) 2 + 3

d) 1 – + 3 = 4 -

Variables and operations – Page 71

The sum of 5 and 4

The difference between 5 and 4

The product of 5 and 4

The quotient when 5 is divided by 4

The sum of 5 and a number

The difference between 5 and a number

The product of 5 and a number

The quotient when 5 is divided by a number

5 + 45 - 4

5 x 454

5 + 5 -

5 x or 55𝑥

Exercise 6.3: Page 73

1. + 5

2. 12 –

3. 6 x or 6

4. 3

5. 3

6. 2

7.

8. 3

9. + 1

10. – 3

11. 5

12.

13. 2

14.

15. 8 -

16. + 4

17. + 3

18. - 7

Exercise 6.6 Page 75

3. What is the next natural number after the natural number ?

4. What is the sum of 3 consecutive natural numbers, being the smallest?

5. Write down an expression in terms of for: a) any even number

b) any odd number

+ 1

( + 2)( + 1) +

+

2 𝑥 + 1

Do: Exercise 6.4 Page 74 All

Exercise 6.4: Answersa) 2( – 8)

b) (5 x ) – 10 or 5 - 10

c) 3 x or 3

d) ( x 5) + 2 or 5 +2

e) ( + 2) x 6 or 6( + 2)

f) ( + 5)2

g) ( x ) – 20 or - 20

h) 2(7 – )

i) + (9 x 2) or + 92

Algebra Multiplication – Page 74

NB! Same rules as multiplying exponents

3 steps:

1. Sign

2. Coefficients

3. Letters

Remember! Anything multiplied by zero = zero

SIMPLIFY:

1. x (-1)= -

2. -4 x (-)

= 4

3. 3 x x

= 3

4. x 2 x x (-4)

= -8

5. –a x (-db)

= abd

6. 3 x 2x 4

= 24

7. 3 x 0 x x

= 0

8. (-4 x 2) x 2

= -8 x 2

= -16 DO: Exercise 6.5 Page 75 #1 Middle; #2ALL

Exercise 6.6 Page 75 # 1; 6 - 9

Exercise 6.5: Answers

1 b) 5

e) –

h)

k) 6

n) 0

q) 5

2 a) 7

b) 4

c)

d) 10

e)

f)

g) 6

h) 12

i)

j)

k) 24

l) –5

Exercise 6.6: Answers

1 a) 2

b) + 10

c) 2 – 3

d) + + 2 +

6 a) x =

b) + + +

7 a) 4( + ) or 4 + 4

b) - 4( + )

c) 4 + 3

Exercise 6.6: Answers8) Total:

Male:

Female: 2 + 15

Learners: – – (2 +15)

9) R5:

R2: 2

50c:

20c:

Total in cents: 500() + 200(2) + 50() + 20()

500 + 400 + 50 + 20

Expressions and terms – Page 77An expression consists of a number of terms

Terms can only be separated by + or – signsMultiplication and division does not

separate terms

How many terms in the following expressions?

1. 22 + 4 + 1

2. 4 + 3(2)

3. (2 + ) – (3 – )

4. - 3

3 terms2 terms2 terms2 terms

Brackets are considered as 1 term

Division is considered as 1 term

Naming expressionsBinomial: An expression with 2 terms

Trinomial: An expression with 3 terms

Polynomial: An expression with more than 3 terms

Constants and coefficients – Page 79

Variable: A letter a.k.a unknown

Coefficient: The number in front of a variable

Constant: A number not attached to a letter

Index: The small number above a letter (Exponent)

Consider the following expression:

53 2 + 4Variable of the 1st and 2nd term:

Variable of the 3rd term:

Coefficient of the 2nd term:

Coefficient of the 3rd term:

Index of the 1st term:

Index of the 2nd term:

Constant term:

𝑥𝑦−123

3

24

DO: Ex 6.8 Pg 80 # 1 - 5

Exercise 6.8: Answers1 a) 3

b) 1

c) 2

d) 1

e) 3

f) 1

g) 2

h) 3

i) 1

j) 2

k) 2

l) 1

2 a) 3 b) 2c) 3d) 2e) 1f) 3g) 7h) -2i) 10j) -1

3 a) 1 b) 2c) 1d) -1e) f)

4 a) 5b) 2c)

5 a) Variable

b) Constant

c) 9d) 2

e) 2

Addition and subtraction of like terms

Are these like or unlike?

and

and

and

and

and

Are these like or unlike?

and

and

and 2

and

and

5 and

4 and 4

Addition and subtraction of like terms – Page 81

UnlikeLike

Unlike

UnlikeLikeLike

Unlike

NB: Look at the letters and exponents!Ignore the

coefficients

1. + 3 =

2. 5 9 =

3. 7 3 2 =

4. 6 + 3 =

5. + + =

6. 8 + 3 + 4 =

7. 7 +7 =

Addition and subtraction of like terms – Page 81

NB! Only LIKE terms can be added and subtracted from one another.

4

−4 𝑥2

6 + 3

+ +

4 + 37 + 7

8. 2 + 2 + 2 + 2 …. 8 terms

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 =

9. 32 – 2 + 52 + 6 =

10. 43 – 22 + + 22 + 3 + (-23) =

16

82 + 4

23 + 4

DO: Exercise 6.9 Page 82 # (1 – 3) RHS

Exercise 6.10 Page 84 # (1- 2) RHS

Exercise 6.9: Answers

1 c) 3

f) 52

2 c) + 2

f) -7 – 7

i) +

l) 2

o) 17

r) 8

3 b) 10

d) 7

f) 24

h) 23

j) 17

l) 9

n) -7 + 3

p) -5

r) 2

t) 11

Exercise 6.10: Page 84

1 b) + 5

d) 3 + 8

f) 2 + 5

h) 7 + 12

j) 6 + 12

2 b) 11 + 5

d) 3 + 4

f) 10 + 12

h) 3

Using algebraic expressions to find values - Page 84

Example 1: A recipe for roasting a piece of beef is 35minutes for each kilogram plus an extra 15minutes for browning

a) Write down an expression for the time needed to roast a piece of beef. Time (in minutes) is represented

by and mass(in kilograms) by .

= 35 + 15

b) Use the expression to determine how long a 5kg piece of beef should stay in the oven.

= 35 + 15

= 35(5) + 15

= 190 minutes

Example 2: Determine the perimeter (P) of the hexagon in terms of

P = 6 x

P = 6

These lines mean the sides are equal in length

Exercise 6.11, Page 85

1. = 3, = 1 and = 2

a)

i) P = 4

ii) P = 4(3)

P = 12 units

b)

i) P = 2 + 2

ii) P = 2(3) + 2(1)

P = 6 + 2

P = 8 units

DO: Ex 6.11 Pg.85 #1 c – g; #2

Ex 6.12 Pg.86 ALL

Exercise 6.11: Answers

1 c) i) P = 3

ii) P = 3(3)

= 9 units

d) i) P = 2 +

ii) P = 2(3) + 1

= 6 + 1

= 7 units

e) i) P = 4

ii) P = 4(2)

= 8 units

f) i) P = 5

ii) P = 5(3)

= 15 units

g) i) P = + 2 + 2

ii) P = 3 + 2(1) + 2(2)

= 3 + 2 + 4

= 9 units

2a)

b) A = R80 000 – (R2000 x 15)

= R50 000

Number of months (t)

Amount still owing (A)

1 80 000 – (2 000 x 1)

2 80 000 – (2 000 x 2)

3 80 000 – (2 000 x 3)

4 80 000 – (2 000 x 4)

5 80 000 – (2 000 x 5)

10 80 000 – (2 000 x 10)

t 80 000 – (2 000 x t)

Exercise 6.12: Answers

1 a) ii) 5; 1; -1

b) iii) 4

c) ii) -27

2 a) T4 = 3(4) – 1

= 12 – 1

= 11

b) T17 = 3(17) – 1

= 51 – 1

= 50

3 a) 2 5

b) 2 + 2

c) 4 6

d) + 3

e) – 2

f) 2 5

4 a) 4( – 10) + 7

b)

c) 2[2 – (x – 2) ]

d)a) 4( – 10) + 7

= 4((16) – 10) + 7

= 4(6) + 7

= 31

b)

=

=

=

= 62

c) 2[2 – ( – 2)] = 2[2(16) – ((16) – 2)] = 2[32 – 14] = 2(18) = 36