Name: Period: Date:
Math 6 Unit 3 Study Guide — Expressions
Show your work on a separate sheet of notebook paper and write your answers in the space provided. Circle your final answer.
GSE6.EE.1: Write and evaluate numerical expressions involving whole-number exponents.
Rewrite using exponents:
1.4 • 4 • 4 • 4
2.a • a • a
Evaluate the following expressions
3.53
4.62 + 24
5.Which expression shows the equivalent expression for 23 x 52?
a)33 b)80 c)200 d)230
6. Write 63 as a product of the same factor. Then find the value.
7. Write 9 × 9 × 9 × 9 × 9 × 9 using an exponent.
Find the value of each expression use order of operations
8. 5 + 4 × 5 – 7
9. 8 × (33 + 2) – 11
10. 30 × 4 – 22 × 5
11. 55 ÷ 5 × 23 ÷ 4
12. Tanya purchased 4 hammers for $11.79 each and 7 screwdrivers for $6.65 each. Write an expression for the total cost of the tools. Then find the total cost.
GSE6.EE.2: Write, read, and evaluate expressions in which letters stand for numbers.
Evaluate each expression if a = 3, b = ?/3, and c = 6. Use substitution.
13. 2a + 5
14. 2c + 3a
15. ?2 + 3a × b
16. Koby took $43 to the movie theater. If he paid for 3 tickets that each cost d dollars, he will have 43 – 3d left. How much does he have left if the tickets cost $9.75 each?
Evaluate each expression if d = 11, e = 3, f = 2, g = 18, and h =9.
17.h + d3 – e
18.2d – h + e – 5
19.2f2 + fg
20.What is the product of seven and eight decreased by “x” if x =15?
a)41 b)56 c)15 d)71
21.Evaluate the expression ab – c + d if a = 10, b = 4, c = 6.5, and d =¼.
a)33.25 b)33.75 c)97.25 d)97.75
GSE6.EE.2a: Write expressions that record operations with numbers and with letters standing for numbers. Forexample, express the calculation “Subtract y from 5” as 5-y.
Choose a variable for the unknown quantity and then write each phrase as an algebraic expression.
22. 16 seconds faster than Najib’s time (Example: 16 + n)
23. one piece more than twice the number of pieces
24. one third of Danielle’s height
25. six meters less than four times the width
26. Devante made and sold 8 pitchers of lemonade at his lemonade stand. He used the same number of lemons in each pitcher. He had 3 lemons left over. Write an expression to represent the total number of lemons Devante had in all.
27. Helen divided her colored pencils evenly among herself and three friends. Write an expression to represent the number of pencils each person received.
28.Which expression represents “the product of 7 and a number increased by 2”?
a)7n + 2 b)7 + n + 2 c) 7 ÷ n + 2d)7 + n – 2
29.Which expression represents “the sum of 14 and a number decreased by three?”
a)14n – 3 b)14 + n + 3 c)14n + 3 d)(14 + n) – 3
30.Oscar bought n ride tickets at the carnival. Sadie bought 4 times as many ride tickets as Oscar. Which expression represents the total number of ride tickets that Oscar and Sadie bought?
a)4n + 4nb)n + 4nc)n + 4 d)4n
31.The table below shows the numbers of calories a 100-pound person burns while swimming different numbers of hours.
CALORIES BURNED BY A 100-POUND PERSONNumber of Hours Swimming (x) / Number of Calories Burned (y)
1 / 180
2 / 360
3 / 540
x
Which of the following expressions could be used to find the number of calories a 100-pound person burns after swimming x hours?
a)90x b)180xc)x÷ 90 d)x÷ 180
32.MusicBiz rents mp3 players by the day. The store charges $6.00 per day and a one-time enrollment fee of $2.50. If x represents the number of days, which expression can be used to determine the total charge, in dollars, to rent a mp3 player for x days?
a)6(x + 2.50) b)2.50x + 6 c)6x + 2.50 d)8.50x
Translate the statements below to algebraic expressions:
33.12 more than a number
34.The quotient of a number and 9
35.15 less than a number
Translate the algebraic expressions below to written statements:
36.23f
37.5x + 8
GSE6.EE.2b : Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient,coefficient); view one or more parts of an expression as a single entity.
Identify the parts of each expression.
38.3 + 2xcoefficient ______
39.4a – 7 / variable ______/ operation ______/ term ______
coefficient ______/ variable ______/ operation ______/ term ______
GSE6.EE.2c : Evaluate expressions at specific values of their variables. Include expressions that arise fromformulas used in real-world problems.
Find the value of each expression.
40.2 + 3 • 4
41.84 ÷ (2 • 6) + 52
42.(50 • 2) – 2(6 • 5)
43.Use the formula V=s3 to find the volume of a cube with a side length of 8 inches.
44. The expression 50 + 8n can be used to find the total price for n people to go to a family Smores festival. Determine the cost for 40 people to attend the family Smores festival.
GSE6.EE.3: Apply the properties of operations to generate equivalent expressions.
Use the Distributive Property to rewrite each algebraic expression.
45. 5(x + 9) 46. 11(12 + r)
47. 9(v + 2) 48. 7(b + 3.5)
49. Mrs. Sosa bought a T-shirt and a pair of socks for each of her 14 grandchildren. The table lists the cost of each item. Use the Distributive Property to find the total amount of money she spent on her grandchildren.
Simplify each expression by combining like terms.
50 7x + 3x + 4x 51. 5(2x + 4y) 52. 6(x + y) + 2y + 9x
Factor each expression. (Hint: Find the GCF!)
53. 9x + 36y 54. 12x + 18y
GSE6.EE.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).
For questions 55 – 56, determine if expressions are equivalent and indicate by writing T or F
55. 4 - z = z – 4 56. 4(3x + 2) = 12x + 2
57. Which expression is equivalent to 6(p + 5)?
a) 30 + 6p / b) 30p / c) 30 + p / d) 11p58.
A. B. C. D.
59. Write an expression to represent the model shown?