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?
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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