Expressions Chapter Questions

  1. How can the order of operations easily be remembered?
  1. Why is it important to have an “order” to the operations?
  1. Can you name 3 words that indicate each operation (addition, subtraction, multiplication and division)?
  1. How do you evaluate an expression?
  1. Explain how distribution can simplify a problem.
  1. What are like terms?
  1. How do you combine like terms?

Expressions Chapter Problems

Mathematical Expressions

Classwork

  1. Circle the constant and underline the coefficient for each expression below

a. 5x – 3

b. 2x + 7

c. 2 – 4x

d. x + 3

  1. Create an algebraic expression with a coefficient of 7 and a constant of 4.
  2. Create an algebraic expression with a coefficient of -1 and a constant of -12.
  3. Create an equation that contains a coefficient of 6.
  4. Create an equation that contains a coefficient of -13.

Homework

  1. Circle the constant and underline the coefficient for each expression below

a. 3x – 5

b. 2x - 1

c. 7 – 8x

d. x + 2

  1. Create an algebraic expression with a coefficient of 17 and a constant of 3.
  2. Create an algebraic expression with a coefficient of -1 and a constant of -1.
  3. Create an equation that contains a coefficient of 4.
  4. Create an equation that contains a constant of -12.

Order of Operations

Classwork

  1. 9 + 3 x 3 + 10 -1 =
  2. 11 + 9 x 3 + 5 – 1 =
  3. 3 – 3 + 1 + 3 x 12 =
  4. 7 + 63 ÷ 3 =
  5. (7 – 4)2 x 3 =
  6. 1 + 8 x 2 x 22 =
  7. 72 – 82 ÷ 23 + 3 x 5 =
  8. (1 + 4) ÷ 5 =
  9. 5 – (3 – 1) =
  10. (8 + 8) x 3 =
  11. (7 – 4) x 2 ÷ (5 – 3) =
  12. [(6 – 3) x 2] ÷ 3 =
  1. Simplify the expression: 5 x 6 – 6 =
  2. Add parentheses to the expression so that it simplifies to a different answer.
  1. Simplify the expression: 9 ÷ 1 + 9 =
  2. Add parentheses to the expression so that it simplifies to a different answer.
  1. Your brother buys 3 shirts for $9 each. He also buys a pair of jeans for $25.00 that gets a $4.00 discount. How much does he spend?
  2. The repairman charged $36 for parts and $12 per hour for labor to repair a bicycle. If he spent 3 hours repairing the bike, what will the total repair bill be?

Homework

  1. 10 – 2 + 9 + 3 x 5 =
  2. 10 + 4 – 1 + 3 x 2 =
  3. 5 x 8 + 2 – 2 + 12 x 5 + 10 =
  4. 6 x 3 + 32 – 6 =
  5. 43 – 6 ÷ 3 x 5 =
  6. 4+ 43 x 2 ÷ 4 -6 =
  7. 5 x 5 + 7 – 2 x 32 =
  8. (9 – 3) x 6 =
  9. (8 + 4) ÷ 3 – 2 =
  10. (2 + 8) x (7 – 3) =
  11. 36 – (52 + 4 ÷ 2) =
  12. [20 – (10 – 4)] ÷ (8 – 1) =
  1. Simplify the expression: 3 + 12 ÷ 3 =
  2. Add parentheses to the expression so that it simplifies to a different answer.
  1. Simplify the expression: 22 – 6 x 2 =
  1. Add parentheses to the expression so that it simplifies to a different answer.
  1. A landscaping company charges $75 for spring yard clean-up and then $25 each time the grass is cut. If you plan on having the yard cleaned up in the spring, plus the lawn cut 11 times, how much will it cost?
  2. At the clothing store you buy 3 pairs of jeans for $22 each and 4 shirts for $8.50 each. You also have a $20 off coupon. How much do you spend?

Distributive Property

Classwork

  1. Use the Distributive Property to rewrite the expressions without parentheses
  2. (x + 4)
  3. 8(x – 2)
  4. 6(x + 4)
  5. 1(x – 4)
  6. (x + 2)8
  1. Marla did 65 sit-ups each day for one week. Write an expression using the Distributive Property to find the total number of sit-ups Marla did during the week. Solve the expression.
  1. Tickets for the school play cost $9 each. Tessa wrote the expression 9 x 26 to find the cost of 26 tickets to the play. Tessa used the Distributive Property to find the product. Write Tessa’s expression after she used addition and the Distributive Property.

Homework

  1. Use the Distributive Property to rewrite the expressions without parentheses
  2. 5(x + 4)
  3. 7(x – 12)
  4. 3(x - 14)
  5. 1(x – 2)
  6. (x - 2)5
  1. Coach Brown bought 6 basketballs for $16 each and 6 footballs for $24 each. The expression 6 x 16 + 6 x 24 gives the total cost in dollars of the basketballs and footballs. Use the Distributive Property to write this expression another way. Then evaluate.
  1. Jessica took her mother to a movie. She paid $9 each for 2 tickets, $4 each for 2 nachos, and $3 each for 2 bottles of water. Use the Distributive Property to show two different ways to solve the problem. How much did she spend?

Like Terms

Classwork

  1. Create a like term for the given term.
  2. 4x
  3. 13y
  4. 15x2
  5. 16xy
  6. x
  7. Simplify the expression if possible by combining like terms.
  8. 7x + 8x
  9. 6x + 8y + 2x
  10. 15x2 + 5x2
  11. 5x +2(x + 8)
  12. 10y + 4y
  13. 9(x + 5) + 7(x – 3)
  14. 8 + (x – 4)2
  15. 7y + 8x + 3y + 2x
  16. x + 2x
  17. x2 + 5x2
  18. 2x + 4x + 3
  19. 6y – 3y
  20. 9y + 4y – 2y + y
  21. x + 5x + x + 12
  22. 8x – 3x + 2x + 15

Homework

  1. Create a like term for the given term.
  2. 6x
  3. y
  4. 10x2
  5. 14xy
  6. 5x
  1. Simplify the expression if possible by combining like terms.
  2. 17x + 18x + 3
  3. 6x + 8y - 2x – y
  4. 15x2 + 5x2 + 2x
  5. 5x +2(x + 8) + 3
  6. 10y + 4y – 5
  7. 9(x + 5) + 7(x + 3)
  8. 18 + (x – 4)2 – 4
  9. 7y + 8x + 3y + 2x + 9
  10. x + 2x + x + 5x
  11. 6x2 + 5x2
  12. 12x + 14x + 3y
  13. 6y – 3y + 6xy + 4xy
  14. 9y + 4y – 2y + y + y2
  15. x + 5x + x + 12 – 7x
  16. 8x – 3x + 2x + 15 – 7y

Translating between Words & Expressions

Classwork

Translate the words into an algebraic expression.

  1. 4 times x
  2. The sum of x and 6
  3. The product of 9 and y
  4. w less than 8
  5. 5 more than x
  6. The difference of 6 and x
  7. 9 times the product of x and 4
  8. The product of 5 and y, divided by 3
  9. The quotient of 300 and the quantity of x times 2
  10. x less than 32
  11. The quotient of 35 and the quantity of x minus 7
  12. The product of 7 and x, minus the quantity of 4 less than y
  13. The quantity of 9 more than x divided by the quantity of 12 less than y
  14. Adult ticket prices are $3 more than child ticket prices. Determine the adult ticket price, given the child ticket price.

Child Ticket Price / Adult Ticket Price
$5
$7
$10
$12
  1. Write an expression that represents the adult price, if the child price is “x”
  1. For NJASK testing, 25 students are placed in each classroom. Determine the number of classrooms needed, given the number of students testing.

Number of Students Testing / Number of Classroom Needed
250
325
400
520
  1. Write an expression that represents the number of classrooms needed, if the number of students testing is “x”
  1. Mary has ½ the amount of money that Jim has. Determine the amount of money that Mary has, given Jim’s amount of money.

Jim’s Amount of Money / Mary’s Amount of Money
$50
$100
$175
$220
  1. Write an expression that represents the amount of money Mary has, given theamount of Jim’s money.
  2. Each person running in the race paid $20. Determine the amount of money collected, given the amount of people running in the race.

Number of People Running / Amount of Money Collected
150
230
410
520
  1. Write an expression that represents the amount of money collected, given the number of people running in the race.

Write an expression for each of the following situations.

  1. Bob weighs 7 more pounds than Jack. Jack weighs x pounds. Bob’s weight:
  1. Tiffany has 6 dollars less than Jessica. Jessica has x dollars. Tiffany’s money:
  1. Samantha has 12 more stickers than Mike. Mike has x stickers. Samantha’s sticker amount:
  1. The recipe calls for twice the amount of sugar than flour. There is f amount of flour in the recipe. Amount of sugar:
  1. Mark’s quiz grade is one more than twice Ted’s quiz grade. Ted’s quiz grade is x. Mark’s quiz grade:
  1. Laura paid x dollars for her prom dress. Beth paid four dollars less than Laura. Beth’s prom gown price:
  1. David ran the 5k in x minutes. Harry ran the same race in five minutes less than double David’s time. Harry’s time:
  1. The beans grew k inches. The tomatoes grew 3 inches more than triple the height of the beans. Tomato height:

Create a scenario for the following expressions:

  1. x + 5
  1. 2(x – 3)

Homework

Translate the words into an algebraic expression.

  1. The product of 14 and x
  2. The quotient of x and 5
  3. The sum of 19 and w
  4. w less than 8
  5. 7 less than x
  6. The difference of 16 and y
  7. 9 times the quotient of x and 20
  8. The product of 6 and x, less 3
  9. The quotient of 100 and the sum of x and 2
  10. x less than 2
  11. The product of 5 and the quantity of x less than 7
  12. The product of 27 and y, divided by the quantity of 4 more than y
  13. The quantity of 6 less than x divided by the quantity of 2 more than y

Homework

  1. Child ticket prices are $3 less than adult ticket prices. Determine the child ticket price, given the adult ticket price.

Adult Ticket Price / Child Ticket Price
$10
$15
$20
$25
  1. Write an expression that represents the child price, if the adult price is “x”
  1. For busing, 40 students are assigned to each bus. Determine the number of buses needed, given the number of students riding.

Number of Students Riding / Number of Buses Needed
240
320
400
500
  1. Write an expression that represents the number of buses needed, if the number of students riding is “x”
  1. The farm always has four times the number of chicks as hens. Determine the number of chicks, given the number of hens.

Number of Hens / Number of Chicks
20
40
50
60
  1. Write an expression that represents the number of chicks, given the number of hens.
  1. Each person running in the race will eat two hotdogs. Determine the number of hotdogs needed, given the amount of people running in the race.

Number of People Running / Number of Hotdogs needed
150
230
410
520
  1. Write an expression that represents the number of hotdogs needed, given the number of people running in the race.

Write an expression for each of the following situations.

  1. Bob weighs 17 pounds less than Jack. Jack weighs x pounds. Bob’s weight:
  1. Tiffany has 50 dollars more than Jessica. Jessica has x dollars. Tiffany’s money:
  1. Samantha has 12 times as many stickers than Mike. Mike has x stickers. Samantha’s sticker amount:
  1. The recipe calls for triple the amount of sugar than flour. There is f amount of flour in the recipe. Amount of sugar:
  1. Mark’s quiz grade is six more than double Ted’s quiz grade. Ted’s quiz grade is x. Mark’s quiz grade:
  1. Laura paid x dollars for her prom dress. Beth paid 16 dollars more than Laura. Beth’s prom gown price:
  1. David ran the 5k in x minutes. Harry ran the same race in half the time that David ran the race. Harry’s time:
  1. The beans grew k inches. The tomatoes grew triple the height of the beans, less 2 inches. Tomato height:

Create a scenario for the following expressions:

  1. 2(x + 3)
  2. x - 4

Evaluating Expressions

Classwork

  1. Evaluate the expression for the given value
  1. (2n + 1)2 for n = 3
  2. 2(n + 1)2 for n = 4
  3. 2n + 22 for n = 3
  4. 4x + 3x for x = 5
  5. 3(x – 3) for x = 7
  6. 8(x + 5)(x – 2) for x = 4
  7. 3x2 for x = 2
  8. 5x + 45 for x = 6
  9. 4x for x = 10

5

  1. 4y + x for x = 2 and y = 3
  2. x + 17 for x = 12 and y = 2

y

  1. 6x + 8y for x = 9 and y = ¼
  2. x + (2x – 8) for x = 10
  3. 5(3x) + 8y for x = 2 and y = 10

Homework

  1. Evaluate the expression for the given value
  2. (2n + 1)2 for n = 1
  3. 2(n + 1)2 for n = 3
  4. 2n + 22 for n = 5
  5. 4x + 3x for x = 6
  6. 3(x – 3) for x = 3
  7. 8(x + 5)(x – 2) for x = 6
  8. 3x2 for x = 8
  9. 5x + 45 for x = 3
  10. 4x for x = 15

5

  1. 4y + x for x = 12 and y = 13
  2. x + 17 for x = 2 and y = 2

y

  1. 6x + 8y for x = 8 and y = ¾
  2. x + (2x – 8) for x = 11
  3. 5(3x) + 8y for x = 12 and y = 5

Expressions Unit Review

Determine whether the given terms are like terms. Circle your response.

1.3x and -2xAre Like TermsAre Unlike Terms

2.5a and 5bAre Like TermsAre Unlike Terms

3.4y and 5xyAre Like TermsAre Unlike Terms

4.x2y and xy2Are Like TermsAre Unlike Terms

6.xy and –xyAre Like TermsAre Unlike Terms

7.Match the expression 3(-4 + 3) with an equivalent expression.

a.4(3) + 4(3)

b.3(-4) + 3(3)

c.4(3) - 4(3)

d.3(4) + 3(3)

8.Which algebraic expression represents the number of days in w weeks?

a.w – 7

b.

c.w + 7

d.7w

9.Which algebraic expression represents the number of hours in m minutes?

a.m – 60

b.

c.m + 60

d.60m

10.In the expression 3x + 5, the value of 3 is best described as:

a.the constant

b.the operation

c.the variable

d.the coefficient

11.In the expression 2x + 16, the value of 16 is best described as:

a.the coefficient

b.the variable

c.the operation

d.the constant

12.Evaluate the expression 2x, when x = 10

a.20

b.12

c.210

d.

15.A music store sells CDs for $15 and tapes for $3. Which expression could be used to find the dollar total of the sales for an hour if the store sold 8 CDs and 5 tapes?

a.(8 + 15) • (5 + 3)

b.(8 •15) + (5 • 3)

c.(8 • 3) + (5 •15)

d.(15 ÷8) + (5 ÷ 3)

17.Use the distributive property to rewrite the expression without parentheses:

7(x – 8)

  1. 7x – 8
  2. x – 56
  3. 7x + 56
  4. 7x – 56

18.What is the value of the expression x + y when x = 15 and y = 21?

a.6

b.30

c.36

d.42

19. Collect the like terms: 5x2 + 2x + x2 + 9x – 3

  1. 13x
  2. 13x2
  3. 17x – 3
  4. 6x2 + 11x – 3

20.Claire has had her driver’s license for three years. Bill has had his license for “b” fewer years than Claire. Which expression can be used to show the number of years Bill has had his driver’s license?

a.3 + b

b.b + 3

c.3 - b

d.b < 3

21.Which situation is best modeled by the expression 25 – x?

a.George places “x” more video games on a shelf with 25 games

b.Sarah has driven “x” miles of a 25 mile trip

c.Amelia paid $25 of an “x” dollar lunch she shared with Ariel

d.George has 25 boxes full of “x” baseball cards each

22. 15 + (11 – 9 )15 – 5 + 9

  1. =

23.Nine decreased by the quantity eight times a number “x”.

a.8x - 9

b.9 – 8x

c.9x - 8

d.8 – 9x

24.Four more than the quotient of 25 and y.

a. + 4

b. + 4

c.

d.

25.What is the coefficient of x in the expression 4y + 5 - x?

a.5

b.1

c.-1

d.0

26.A rectangle is 6 inches longer than it is wide. Write and simplify an expression for the perimeter of the rectangle in terms of the width w.

27.You and a friend worked in the school store last week. You worked 4 hours less than your friend. Let h be the number of hours your friend worked. Write an expression in simplest form that represents the total number of hours you both worked.

28.A trail mix contains peanuts, raisins, and M&Ms. In the mix, the amount of peanuts is three times the amount of M&Ms; and the amount of raisins is two times the amount of M&Ms. Let m represent the amount of M&Ms. Write and simplify an expression for the total number of pieces of food in the trail mix.

29. Simplify: 5 + 2(3x + 4) + x

30.Evaluate the expression (F – 32) when F = 41

31. At the video arcade, Jenny buys 25 tokens. She uses two tokens for each game she plays.

a)Write an expression for the number of tokens Jenny has left after playing ggames.

b)Find the number of tokens Jenny has left after playing 1, 4, 6, 10 and 12 games.

32.Bob wants to go to the movies with his friends. The movie theater charges $8 per ticket. Bob’s friends reserve $48.00 worth of tickets in advance. How many people in total can attend the movie?

a)Identify the variable

b)Identify the constant

c)Write an equation which includes the number of people attending the movie, the price of each ticket, and the total cost of the movie.

33.Write an expression that has four terms and simplifies to 16x+ 5.

a)Identify the like terms

b)Identify the coefficients

c)Identify the constant terms

34. Simplify the expression:

a)15 + 3 x 2 – 6 (Show all steps)

b) Add parentheses to the expression so that it simplifies to a different answer.

(Show all steps)

c) Explain why parts a and b have a different answer.

Answer Key

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1)

  1. constant: -3, coefficient: 5
  2. constant: 7, coefficient: 2
  3. constant: 2, coefficient: -4
  4. constant: 3, coefficient: 1

2)7x + 4

3)–x - 12

4)Multiple answers; ex: 6x + 1 = 5

5)Multiple answers; ex: -13x + 1 = 7

6)

  1. constant: -5, coefficient: 3
  2. constant: -1, coefficient: 2
  3. constant: 7, coefficient: -8
  4. constant: 2, coefficient: 1

7)17x + 3

8)–x - 1

9)Multiple answers; ex: 4x + 2 = 10

10)Multiple answers; ex: -12x + 2 = 15

11)27

12)42

13)37

14)79

15)27

16)65

17)56

18)1

19)3

20)48

21)3

22)2

23)

  1. 24
  2. 5 x (6-6) = 0

24)

  1. 18
  2. 9 ÷ (1 + 9) = 0.90

25)3(9) + (25 - 4) = $48

26)36 + 3(12) = $72

27)32

28)19

29)110

30)21

31)54

32)30

33)14

34)36

35)2

36)40

37)9

38)2

39)

  1. 7
  2. (3 + 12) ÷ 3 = 5

40)

  1. 10
  2. (22 – 6) x 2 = 32

41)75 + 11(25) = $350

42)3(22) + 4(8.5) - 20 = $80

43)

  1. x + 4
  2. 8x - 16
  3. 6x + 24
  4. x - 4
  5. 8x + 16

44)7(60 + 5) = 7(60) + 7(5) = 420 + 35 = 455

45)9(20 + 6) = 9(20) + 9(6) = 180 + 54 = 234

46)

  1. 5x + 20
  2. 7x - 84
  3. 3x - 42
  4. x - 2
  5. 5x - 10

47)6(16+24) = 6(40) = 240

48)2(9) + 2(4) + 2(3) = 2(9 + 4 + 3) = 2(16) = 32

49)

  1. Multiple Answers, ex: 6x
  2. Multiple Answers, ex: 26y
  3. Multiple Answers, ex: 3x2
  4. Multiple Answers, ex: 4xy
  5. Multiple Answers, ex: 5x

50)

  1. 15x
  2. 8x + 8y
  3. 20x2
  4. 7x + 16
  5. 14y
  6. 16x + 24
  7. 2x
  8. 10y + 10x
  9. 3x
  10. 6x2
  11. 6x + 3
  12. 3y
  13. 12y
  14. 7x + 12
  15. 7x + 15

51)

  1. Multiple Answers, ex: 7x
  2. Multiple Answers, ex: 3y
  3. Multiple Answers, ex: 8x2
  4. Multiple Answers, ex: 9xy
  5. Multiple Answers, ex: 3x

52)

  1. 35x + 3
  2. 4x + 7y
  3. 20x2 + 2x
  4. 7x + 19
  5. 14y - 5
  6. 16x + 66
  7. 2x + 6
  8. 10y + 10x + 9
  9. 9x
  10. 11x2
  11. 26x + 3y
  12. 3y + 10xy
  13. 12y + y2
  14. 12
  15. 7x + 15 - 7y

53)4x

54)x+6

55)9y

56)8-w

57)5+x

58)6-x

59)9(4x)

60)

61)

62)32-x

63)

64)7x-(y-4)

65)

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66)

Child Ticket Price / Adult Ticket Price
$5 / $8
$7 / $10
$10 / $13
$12 / $15

x + 3

67)

Number of Students Testing / Number of Classroom Needed
250 / 10
325 / 13
400 / 16
520 / 21

68)

69)

Jim’s Amount of Money / Mary’s Amount of Money
$50 / $25
$100 / $50
$175 / $87.50
$220 / $110

70)

71)

Number of People Running / Amount of Money Collected
150 / $3,000
230 / $4,600
410 / $8,200
520 / $10,400

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72)20x

73)x + 7

74)x - 6

75)x + 12

76)2f

77)2x + 1

78)x - 4

79)2x - 5

80)3k + 3

81)Multiple Answers

82)Multiple Answers

83)14x

84)

85)19+w

86)8-w

87)x-7

88)16 - y

89)9()

90)6x - 3

91)100/(x+2)

92)2-x

93)5(7-x)

94)

95)

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96)

Adult Ticket Price / Child Ticket Price
$10 / $7
$15 / $12
$20 / $17
$25 / $22

97)x-3

98)

Number of Students Riding / Number of Buses Needed
240 / 6
320 / 8
400 / 10
500 / 13

99)

100)

Number of Hens / Number of Chicks
20 / 80
40 / 160
50 / 200
60 / 240

101)4x

102)

Number of People Running / Number of Hotdogs needed
150 / 300
230 / 460
410 / 820
520 / 1040

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103)2x

104)x-17

105)x + 50

106)12x

107)3f

108)2x + 6

109)x+16

110)

111)3k - 2

112)Multiple Answers

113)Multiple Answers

114)

  1. 49
  2. 50
  3. 10
  4. 35
  5. 12
  6. 144
  7. 12
  8. 75
  9. 8
  10. 14
  11. 23
  12. 56
  13. 22
  14. 110

115)

  1. 9
  2. 32
  3. 14
  4. 42
  5. 0
  6. 352
  7. 192
  8. 60
  9. 12
  10. 64
  11. 18
  12. 54
  13. 25
  14. 220

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Expressions Unit Review Answer Key

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  1. Are Like Terms
  2. Are Unlike Terms
  3. Are Unlike Terms
  4. Are Like Terms
  5. Are Like Terms
  6. Are Like Terms
  7. b
  8. d
  9. b
  10. d
  11. d
  12. a
  13. b
  14. b
  15. b
  16. c
  17. d
  18. c
  19. d
  20. c
  21. b
  22. b
  23. b
  24. a
  25. c
  26. w+w+(w + 6)+(w+6)

4w + 12

  1. h + (h - 4)

2h – 4

  1. 3m + 2m + m

6m

  1. 5 + 6x + 8 + x

7x + 13

  1. 5

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  1. 25 - 2g
  2. 25 - 2(1) = 23 tokens left after 1 game

25 - 2(4) = 17 tokens left after 4 games

25 - 2(6) = 13 tokens left after 6 games

25 - 2(10) = 5 tokens left after 10 games

25 - 2(12) = 1 token left after 12 games

32.

  1. Variable: p = number of people
  2. Constant: 8 (dollars per ticket)
  3. 8p = 48

33.

  1. Answers will vary; for example 4(4x + 3) -7
  2. Like Terms: All terms that contain “x” are like terms; all numerical terms are like terms
  3. Coefficients: The numbers with “x” in the “x” terms
  4. Constants: The numbers in the numerical terms.

34.

  1. 15 + 3 x 2 – 6 = 15
  2. (15 + 3) x 2 – 6 = 30
  3. The parentheses cause you to do the addition prior to the multiplication.

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