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

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

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

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

Solution

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

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

S_n  =  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

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