WORKSHEET ON ADDITION AND SUBTRACTION OF ALGEBRAIC EXPRESSIONS

Find the sum of the following expressions

1)  7p + 6q, 5p – q, q + 16p

2)  a + 5b + 7c, 2a + 10b + 9c

3)  mn + t, 2mn – 2t, -3t + 3mn

4)  u + v, u – v, 2u + 5v, 2u – 5v

5)  5xyz – 3xy, 3zxy – 5yx

Solution

6)  (7j3 – 2) + (5j3 – j – 3)

7)  (8a5 – 4 ) + (3a5 + a – 2)

8)  (6m5 + 1) + (2m5 + 9m – 1)

9)  (3m5 + 1) + (9m5 + 3m – 2)

10)  (-5x2 – x + 4) + (-3x2 – 5x + 2)

11)  Add 4 (m2 + 2) to 3m2 + 7m

Solution

12)  (2y2 - y) + (y2 + 3y - 1)

13)  (20.2x2 + 6x + 5) + (1.7x2 - 3x - 8)

Solution

Answers :

1)  28p + 6q

2)  3a + 15b + 16c

3)   6mn – 4t

4)  6u

5)  8xyz – 8xy

6)  12j3 – j – 5

7)  11a5 + a - 6

8)  8m5 + 9m

9)  12m5 + 3m - 1

10)  -8x2 - 6x + 6

11)   7m2 + 7m + 8

12)  3y2 + 2y - 1

13)  21.9x2 + 3x - 3

Find the difference of the following expressions

1)  13x + 12y – 5 from 27x + 5y – 43

2)  3p + 5 from p – 2q + 7

3)  m + n from 3m – 7n

4)  2y + z from 6z – 5y

Solution

5)  (-x2 + x – 4) – (3x2 – 8x – 2)

6)  (8x2 – 3x) – (5x – 5 – 8x2)

7)  (-x2 – 5x – 3) – (-7x2 – 8x – 8)

8)  (-2x3 + x) – (7x – 3 – 7x3)

9)  (3x3 + 3x2 + 9) – (5x3 – 7x2 + 6x – 9)

10)  t4 – 3t2 + 7 from 5t3 – 9.

11)  y5 – y4 from y2 + 3y4.

Solution

12)  (2x2 + 6x) - (4x2)

13)  (k4 - 2k) - (3k4 - 3k + 1)

Solution

Answers :

1)  14x – 7y - 38

2)  -2p - 2q + 2

3)   2m – 8n

4)  5z – 7y

5)  -4x+ 9x - 2

6)  16x2 - 8x + 5

7)  6x2 + 3x + 5

8)  5x3 – 6x + 3

9)  -2x3 + 10x2 – 6x + 18

10)  -t4 + 5t3 + 3t2 - 16

11)  - y5 + 4y4 + y2

12)  -2x2 + 6x

13)  -3k4 + k - 1

Simplify the following expressions 

1)  (x + y – z) + (3x – 5y + 7z) – (14x + 7y – 6z)

2)  p + p + 2 + p + 3 – p – 4 – p – 5 + p + 10

3)  n + (m + 1) + (n + 2) + (m + 3) + (n + 4) + (m + 5)

Solution

4)  (3x + 1/2) + (7x - 4 1/2)

5)  (-0.25x - 3) - (1.5x + 1.4)

6)  (5x - 3y + 4z) + (1.5x + 0.4y + 8)

7)  (2a - 3b + c) - (4b - 3a + c)

Solution

8)  3(x– 2x + 3) – 4(4x + 1) – (3x2 – 2x)

9)  (0.5x2 + 4.25x - .9) - .5(x2 + 7x – 3)

Solution

Answers :

1)  -10x – 11y + 12z

2)   2p + 6

3)  3m + 3n + 15

4)  10x - 4

5)  -1.75x - 4.4

6)  6.5x - 2.6y + 4z + 8

7)  5a - 7b

8)   -20x + 5

9)  0.75x + 0.6 

Write the algebraic expressions for the following

1)  Sum of x and twice y

2)  Subtraction of z from y

3)  Twice the sum of m and n

4)  b is  decreased by twice a

5)  Sum of x squared and y squared

6)  Two times the product of a and b divided by 5

7)  Product of p and q added to 7

8)  x more than two-thirds of y

9)  Half a number x decreased by 3

10)  Sum of numbers m and n decreased by their product

11)  4 times x less than sum of y and 6

12)  Double the sum of one third of a and m.

Solution

Answers :

1)  x + 2y

2)  y - z

3)  2(m + n)

4)  b - 2a

5)  x2 + y2

6)  2ab/5

7)  pq + 7

8)  x + (2/3)y

9)  (x/2) - 3

10)  (m + n) - mn

11)  4x - (y + 6)

12)  2[(1/3)a + m]

Word problems on evaluating algebraic expressions

Problem 1 :

The cost C of hiring a squash court for h hours is given by

C  =  12h + 5

dollars. Find the cost of hiring a court for :

a) 1 hour   b) 30 mins c) 1 hour 15 mins.

Problem 2 :

The volume of water in a tank t minutes after a tap is switched on, is given by

V  =  5000 - 20t liters.

a) Find V when t = 0. What does this mean?

b) Find the volume of water left in the tank after:

(i) 5 minutes  (ii)  1 hour  (iii)  3  1/2 hours.

Problem 3 :

To add the whole numbers from 1 to n we can use the formula

Sn  =  n(n+1)/2

Use the formula to add all the whole numbers from 1 up to:

(i) 50   (ii) 200   (iii) 1000

Problem 4 :

Michelle has $2000 in a bank account. Each week she deposits a further $120.

a) Explain why the amount of money in her account after n weeks is given by

M = 2000 + 120n pounds.

b) How much money does she have in her bank account after :

(i) 3 weeks   (ii) 6 months   (iii) 1  1/2 years?

Problem 5 :

The cost C of hiring a room for a function is given by

C = 150 + 30g

euros where g is the number of guests. Find the cost of hiring the room for :

a) 20 guests   b) 50 guests   c) 90 guests

Solution

Answers :

1)  a)  $17,   b)  $11   c)  $20

2)  a)  5000   b)  (i)  4900 liter  (ii)  4980 liter  (iii)  4930 liter

3)  (i)  1275   (ii)  20100   (iii)  500500

4)  a)  Every week he is depositing 120. 

if n  =  0, M  =  2000 (Already he has)

if n  =  1, M  =  2120 (he has 2120)

if n  =  1, M  =  2240 (he has 2240)

b)  (i)  2360 pounds   (ii)  4880 pounds   (iii)  11120 pounds

5)  a)  $750   b)  $1650   c)  $2850

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