ALGEBRAIC AND NUMERIC EXPRESSIONS WORKSHEET

Problems 1-10 : Calculate the value of the numerical expression.

Problem 1 :

7.25 + 2.75 - 3

Problem 2 :

(17 - 2) ÷ 5

Problem 3 :

(2 + 3)²

Problem 4 :

(8 - 3)²

Problem 5 :

7 + (15 + 3) ÷ 3

Problem 6 :

(-4 ⋅  3) ÷ (-3)

Problem 7 :

3 + 12 ÷ 4 + 1

Problem 8 :

-4 - (2 - 5) - (-3)²

Problem 9 :

2 - 8 ÷ (-2) - 3 - (-12) ÷ (-6) ⋅ (-2)

Problem 10 :

(-11 - 6 - (-5) + 1 + 3 ⋅ 2) ÷ (-5)

Problems 11-15 : Simplify the expression.

Problem 11 :

-9 - 6(-x + 5)

Problem 12 :

-10(-8p + 9) - 8p

Problem 13 :

7(1 + 9y) - 8(-5y - 6)

Problem 14 :

-10(v - 7) - 7(v + 2)

Problem 15 :

-2(-6s - 9) - 4(9 - s)

Problems 16-20 : Evaluate the expression using the values given.

Problem 16 :

x - 2y + 3

Use x = 2 and y = -3.

Problem 17 :

x(y ÷ 3 - x)

Use x = -6 and y = -3.

Problem 18 :

p(r + 3) + 1 + 3 - q 

Use p = 6, q = -5 and r = 2.

Problem 19 :

6 + y  + 5 - (y - x) + 15

Use x = 1 and y = 1.

Problem 20 :

-3 ÷ 3(a + c(b + 5) - (-6 + a))

Use a = 1, b = -6  and c = -4.

Problems 21-23 : Write an algebraic expression for the situationgiven.

Problem 21 :

"Three more than 5 times of a number y"

Problem 22 :

"Two less than 4 times of a number x"

Problem 23 :

"Three times the sum of a number z and 4"

Problem 24 :

The cost of hiring an electrician is a fixed charge of $10 plus $8 per hour. If an electrician is hired for a work which takes x hours, write an algebraic expression which represents the total cost.

Problem 25 :

The cost of a taxi service is a fixed charge of $5 plus $3 per mile. If you use the taxi serivice for m miles, how much do you owe?

Answers

1. Answer :

= 7.25 + 2.75 - 3

= 10 - 3

= 7

2. Answer :

= (17 - 2) ÷ 5

Use the PEMDAS Rule.

= 15 ÷ 5

= 3

3. Answer :

= (2 + 3)²

Use the PEMDAS Rule.

= 5²

= 5 ⋅ 5

= 25

4. Answer :

= (8 - 3)²

Use the PEMDAS Rule.

= 5²

= 5 ⋅ 5

= 25

5. Answer :

= 7 + (15 + 3) ÷ 3

Use the PEMDAS Rule.

= 7 + 18 ÷ 3

= 7 + 6

= 13

6. Answer :

= (-4 ⋅  3) ÷ (-3)

Use the PEMDAS Rule.

= -12 ÷ (-3)

= 4

7. Answer :

= 3 + 12 ÷ 4 + 1

Use the PEMDAS Rule.

= 3 + 3 + 1

= 7

8. Answer :

= -4 - (2 - 5) - (-3)²

Use the PEMDAS Rule.

= -4 - (-3) - (-3)²

= -4 - (-3) - 9

= -4 + 3 - 9

= -1 - 9

= -10

9. Answer :

= 2 - 8 ÷ (-2) - 3 - (-12) ÷ (-6) ⋅ (-2)

Use the PEMDAS Rule.

= 2 + 4 - 3 - (-12) ÷ (-6) ⋅ (-2)

= 2 + 4 - 3 - 2 ⋅ (-2)

= 2 + 4 - 3 + 4

= 10 - 3

= 7

10. Answer :

= (-11 - 6 - (-5) + 1 + 3 ⋅ 2) ÷ (-5)

Use the PEMDAS Rule.

= (-11 - 6 + 5 + 1 + 3 ⋅ 2) ÷ (-5)

= (-11 - 6 + 5 + 1 + 6) ÷ (-5)

= (-5) ÷ (-5)

= 1

11. Answer :

= -9 - 6(-x + 5)

= -9 + 6x - 30

= 6x + 39

12. Answer :

= -10(-8p + 9) - 8p

= 80p - 90 - 8p

= 72p - 90

13. Answer :

= 7(1 + 9y) - 8(-5y - 6)

= 7 + 63y + 40y + 48

= 103y + 55

14. Answer :

= -10(v - 7) - 7(v + 2)

= -10v + 70 - 7v - 14

= -17v + 56

15. Answer :

= -2(-6s - 9) - 4(9 - s)

= 12s + 18 - 36 + 4s

= 16s - 18

16. Answer :

= x - 2y + 3

Substitute x = 2 and y = -3.

= 2 - 2(-3) + 3

= 2 + 6 + 3

= 11

17. Answer :

= x(y ÷ 3 - x)

Substitute x = -6 and y = -3.

= -6(-3 ÷ 3 - (-6))

= -6(-3 ÷ 3 + 6)

= -6(-1 + 6)

= -6(5)

= -30

18. Answer :

= p(r + 3) + 1 + 3 - q 

Substitute p = 6, q = -5 and r = 2.

= 6(2 + 3) + 1 + 3 - (-5)

= 6(5) + 1 + 3 + 5

= 30 + 1 + 3 + 5

= 39

19. Answer :

= 6 + y  + 5 - (y - x) + 15

Substitute x = 1 and y = 1.

= 6 + 1  + 5 - (1 - 1) + 15

= 6 + 1  + 5 - 0 + 15

= 27

20. Answer :

= -3 ÷ 3(a + c(b + 5) - (-6 + a))

Substitute a = 1, b = -6  and c = -4.

= -3 ÷ 3(1 + (-4)(-6 + 5) - (-6 + 1))

= -3 ÷ 3(1 + (-4)(-6 + 5) - (-6 + 1))

= -3 ÷ 3(1 - 4(-1) - (-5))

= -3 ÷ 3(1 + 4 + 5)

= -3 ÷ 3(10)

= -1(10)

= -10

21. Answer :

= 5y + 3

22. Answer :

= 4x - 2

23. Answer :

= 3(z + 4)

24. Answer :

= 10 + 8x

25. Answer :

= 5 + 3m

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