Practice Activities
Name
Chapter 2, Lessons 1 – 3
Write each as a numerical expression.
1. one fourth the difference of the opposite of 8 and 6 2. 2 greater than the product of 6 cubed and 9
__
​ 1 ​(28 2 6) or ______
​ 28 2 6 ​ 4
4
63(9) 1 2
3. 3 less than the opposite of the quotient of 10 and 25 2[10 4 (25)] 2 3
Write each as an algebraic expression. Use n as the variable.
4. a number increased by 5
n15
5. Twice the quotient of 15 and a number
2(15 4 n)
6. The sum of 7 and 8 divided by a number
8
____
​ 7 1
​ n Write a word phrase for each expression. Possible answers shown. the sum of 29 squared and 4
Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra.
7. (29)2 1 4
8. 2[24 2 (28)] twice the difference of 24 and 28
9. [4(5) 2 3]2
the difference of the product of 4 and 5 and 3, squared
10. 4(a 2 3)
p24
11. _____
​ ​ 3
4 times the difference of a number, a, and 3
12. y(7 2 11)
a number, y, multiplied by the difference of 7 and 11
The difference of a number, p, and 4, divided by 3
Evaluate each expression using the values of the variables given
in the chart.
a
b
c
e
n
r
6
�7
10
�4
3
�9
1 8207-W_G7_CH02_PA2-2
3. n2 1 r
14. c 2 (2b)
15. e(r 2 n)
0
3
48
16. ______
​ ec ​ b2n
4
17. ___
​ 21
n (​ 2an)
a2(r 1 | b |)
18. __________
​ ​
a 6
212
19. |r 2 2 c 2| • 2c
20. (b 2 c)[n 2 (2e)] 1 r
21. __
​ ec ​• (e 2 r)
2190
8
22
Course I, Chapter 2
(continued)
Practice Activities
Name
Chapter 2, Lessons 1 – 3
Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra.
Simplify each expression by combining like terms.
22. 5a 2 (29) 2 7a 2 12
23. 6 2 7m2 1 4n2 2 8 2 9m2 2 n2
22a 2 3
2
2
216m 1 3n 2 2
24. 7 2 9j3k2 2 (24j2k3) 1 3j3k2 2 (28)
25. 2 1 14rt 2 5(r 1 rt) 1 6r 2 3
2 3
3 2
4j k 2 6j k 1 15
9rt 1 r 2 1
26. 7(a 2 2ab 1 2) 2 8a 1 (215) 1 11ab
27. 13xy 2 4x(6 2 5y) 1 12x
23ab 2 a 2 1
33xy 2 12x
28. 28(23f 1 ef 2 3) 1 2(24e 2 ef 2 6)
29. 2c(23d 1 6) 2 (4cd 2 13cd)
24f 2 8e 1 10ef 1 12
223cd 1 12c
Write an equation for each sentence. Label each equation numerical or algebraic.
30. 7 less than 4 is equal to 23.
4 2 7 5 23; numerical
31. The product of a number, e, and 3 is 12.
3e 5 12; algebraic
32. 2 is the quotient when 5 minus 7 is divided by 21.
2 5 ____
​ 5 2 7 ​ ; numerical
21
33. 6 times the difference of 7 and 3 is equal to twice 12. 6(7 2 3) 5 2(12); numerical
34. Twice a number, g, times the difference of a
number, g, and 3 is equal to 24.
2g(g 2 3) 5 24; algebraic
35. The sum of three times a number, h, and 2,
divided by 4 is equal to 2.
(3h 1 2) 4 4 5 2; algebraic
Identify whether the equation is open or closed. If it is closed, identify if
it is true or false. Then explain why.
36. 2(28 2 45) 5 17
37. 3x2 2 8x 5 25
closed; true
open
38. 64 4 42 5 16
39. 4x(6 2 3) 5 24
closed; false since 4 ≠ 16
open
Course I, Chapter 2
(continued)
Practice Activities
Name
Chapter 2, Lessons 1 – 3
Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra.
Determine whether either of the given values is a solution of the equation.
40. 11 1 u 5 20, when u 5 29, u 5 31
41. x 1 6 5 5, when x 5 21, x 5 7
neither is a solution
solution: x 5 21
42. 8 2 w 5 10, when w 5 2, w 5 22
43. 9 2 10 2 k 5 24, when k 5 23, k 5 3
solution: w 5 22
solution: k 5 3
44. 4 1 (220) 4 g 5 2, when g 5 10, g 5 5
45. 26y 2 14 5 28, when y 5 1, y 5 22
solution: g 5 10
neither is a solution
46. 3t 2 8 5 16, when t 5 4, t 5 8
47. 16 4 r 2 6 5 22, when r 5 14, r 5 4
solution: t 5 8
solution: r 5 4
Solve. Show your work.
48. Kim has m more miles remaining to walk
this week. She has already walked 4 miles.
Write an expression to represent the
number of miles she will walk in all this
week.
4 1 m miles
49. Last month, Karla babysat 3 hours more
than 4 times the number of hours, h,
that Mike babysat. Write an expression
to represent the number of hours Karla
babysat. If Mike babysat 6 hours last
month, how many hours did Karla?
4h 1 3; h 5 6; 4(6) 1 3 5 24 1 3 5 27
Last month, Karla babysat for 27 hours.
50. Wendell drove m miles per hour and
250 miles in 5 hours. Write an equation
that represents this information. Decide
whether the equation is open or closed.
If it is closed, tell why it is true or false.
5m 5 250; open
Course I, Chapter 2