Use Variables in Real-World Problems - 6th Grade Math

1. What is the expression for "the sum of $2x$ and $4$"?

   $2x + 4$. This is direct addition of two terms.

2. What is the algebraic expression for "the sum of $m$ and $12$"?

   $m + 12$. "Sum" means addition of the two values.

3. Which expression represents "$3$ times a number $k$"?

   $3k$. "Times" indicates multiplication of the variable.

4. Identify the set of values for $x$ if $x$ is a positive even integer.

   $\{2, 4, 6, 8, \dots\}$. Positive even integers are 2, 4, 6, 8, and so on.

5. What is the expression for the number of cents in $d$ dollars?

   $100d$. Each dollar contains $100$ cents.

6. Which expression represents the perimeter of a rectangle with length $L$ and width $W$?

   $2L + 2W$. Perimeter adds all four sides: $L+L+W+W$.

7. Which expression represents "a number $n$ divided by $7$"?

   $\frac{n}{7}$. Place $n$ in the numerator when it's being divided.

8. What is the expression for the perimeter of a square with side length $s$?

   $4s$. A square has 4 equal sides, so perimeter is $4 \times s$.

9. What is the algebraic expression for "$7$ more than a number $x$"?

   $x + 7$. "More than" means addition, so add $7$ to $x$.

10. What is the algebraic expression for "$9$ less than a number $n$"?

    $n - 9$. "Less than" means subtract from the number, so $n$ minus $9$.

11. Which expression represents "the sum of a number $x$ and $y$"?

    $x + y$. "Sum" means addition of the two variables.

12. Which expression represents total cost for $n$ items at $4 each?

    $4n$. Multiply quantity by unit price for total cost.

13. Identify the correct expression for "$3$ times the quantity $x + 2$": which is correct, $3x+2$ or $3(x+2)$?

    $3(x + 2)$. Parentheses show multiplication applies to the entire sum.

14. Which expression represents "the sum of twice $x$ and $5$"?

    $2x + 5$. First double $x$, then add $5$ to that result.

15. What does it mean when a variable is restricted to a specified set, such as $n \in \{1,2,3,4\}$?

    $n$ can only take values from $\{1,2,3,4\}$. The variable is limited to only those specific values in the set.

16. Identify the set of possible values if $d$ is the number of days in a week.

    $d = 7$. A week always has exactly $7$ days.

17. Identify the set of values for $n$ if $n$ is a whole number less than $5$.

    $\{0, 1, 2, 3, 4\}$. Whole numbers less than 5 include 0 through 4.

18. What is the expression for your pay if you earn $15 per hour for $h$ hours plus a $20 bonus?

    $15h + 20$. Total pay = hourly rate × hours worked + fixed bonus.

19. What is the algebraic expression for "$5$ times a number $t$"?

    $5t$. "Times" indicates multiplication of the variable by $5$.

20. What is the expression for the total cost of $k$ tickets at $12 each?

    $12k$. Total cost equals price per ticket times number of tickets.

21. Which expression represents "the difference of $20$ and $y$"?

    $20-y$. "Difference" means subtract the second from the first.

22. What is the expression for the perimeter of a rectangle with length $l$ and width $w$?

    $2l + 2w$. Rectangle perimeter: add all 4 sides (2 lengths + 2 widths).

23. Which expression represents "$7$ more than a number $n$"?

    $n + 7$. "More than" means addition, so add $7$ to $n$.

24. Identify the correct expression for "$5$ less than a number $n$": which is correct, $5-n$ or $n-5$?

    $n - 5$. "$5$ less than $n$" means subtract $5$ from $n$.

25. Which expression represents the area of a rectangle with length $L$ and width $W$?

    $LW$. Area of rectangle is length times width.

26. What is the expression for "the sum of $p$ and $q$"?

    $p + q$. "Sum" means to add the two variables together.

27. What is the expression for "a number $m$ divided by $5$"?

    $\frac{m}{5}$. "Divided by" means the number is in the numerator.

28. What restriction should be stated if $n$ represents the number of students?

    $n$ is a whole number, $n\ge 0$. Students must be counted as whole, non-negative numbers.

29. What expression represents the perimeter of a rectangle with length $l$ and width $w$?

    $2l + 2w$. Perimeter is the sum of all four sides: $l+l+w+w$.

30. What is the algebraic expression for "a number $p$ divided by $4$"?

    $\frac{p}{4}$. "Divided by" means the variable is in the numerator.

31. What expression represents the distance traveled at speed $s$ for time $t$ hours?

    $st$. Distance equals speed multiplied by time.

32. What restriction should be stated if $t$ represents time in minutes?

    $t\ge 0$. Time cannot be negative in real-world contexts.

33. What does it mean if a variable can represent any number in a specified set?

    Its value can be any number allowed by the given restrictions. Variables can take multiple values within defined constraints.

34. What is the algebraic expression for "the quotient of $k$ and $8$, increased by $2$"?

    $\frac{k}{8} + 2$. First divide $k$ by $8$, then add $2$ to the quotient.

35. What is the expression for "twice the sum of $x$ and $4$"?

    $2(x + 4)$. "Twice" means multiply by 2; parentheses show order.

36. Find and correct the expression error: "$3+n$" for "$3$ times a number $n$".

    Correct expression: $3n$. Addition $(+)$ was incorrectly used instead of multiplication.

37. What does it mean if a variable can represent any number in a set?

    The value can be any number that fits the stated restrictions. Variables can represent multiple values within defined constraints.

38. What is the algebraic expression for "$4$ less than the product of $6$ and $y$"?

    $6y - 4$. First multiply $6$ and $y$, then subtract $4$ from the product.

39. Which expression represents "a number $p$ divided by $4$"?

    $\frac{p}{4}$. "Divided by" means the variable is in the numerator.

40. Identify the expression for "$9$ decreased by $t$".

    $9-t$. "Decreased by" means subtract from the first number.

41. What does a variable represent in an expression such as $x + 5$?

    A number that can be unknown or can vary. Variables can stand for unknowns or change based on context.

42. What is a variable in an expression, and what can it represent?

    A letter that represents an unknown number or a set of possible numbers. Variables are symbols used in algebra to represent values that can change.

43. Identify the expression for "$t$ decreased by $9$".

    $t-9$. Start with $t$ and subtract $9$ from it.

44. Which expression represents "$7$ less than a number $n$"?

    $n - 7$. "Less than" means subtraction, so subtract $7$ from $n$.

45. What is the expression for "$9$ less than a number $x$"?

    $x - 9$. "Less than" means subtract from the original number.

46. Which expression represents "the difference of a number $x$ and $y$" (in that order)?

    $x - y$. "Difference" means subtract the second from the first.

47. What is a variable in an algebraic expression?

    A symbol, usually a letter, that represents a number. Variables stand in for numerical values in expressions.

48. Which expression represents your money after saving $5 each week for $w$ weeks starting from $12?

    $12 + 5w$. Start with $12, add $5 for each week.

49. Which expression represents "$7$ times a number $n$"?

    $7n$. "Times" indicates multiplication of $7$ and $n$.

50. Which expression represents the total cost for $n$ items at $4 each plus a $3 fee?

    $4n + 3$. Multiply items by price, then add the fixed fee.

51. Which expression represents the number of cents in $d$ dollars?

    $100d$. Each dollar contains $100$ cents.

52. Which expression represents "$5$ more than a number $n$"?

    $n+5$. "More than" indicates addition to the variable.

53. Which expression represents "$7$ less than a number $x$"?

    $x-7$. "Less than" means subtract from the variable.

54. What expression represents the total cost for $n$ notebooks at $3 each?

    $3n$. Multiply price per notebook by number of notebooks.

55. What is the algebraic expression for "the difference of $a$ and $3$"?

    $a - 3$. "Difference" means subtract the second value from the first.

56. What is the expression for "the difference of $a$ and $b$" (in that order)?

    $a - b$. "Difference" means subtract the second from the first.

57. What expression represents your age $a$ years from now if you are $x$ years old now?

    $x + a$. Add years to current age to find future age.

58. Which expression represents total cost for $n$ items at $4 each plus $7 shipping?

    $4n+7$. Add fixed shipping cost to the variable product cost.

59. What is the algebraic expression for "twice the sum of $x$ and $3$"?

    $2(x + 3)$. First add $x$ and $3$, then multiply the sum by $2$.

60. What is a variable in an expression?

    A letter or symbol that represents a number. Variables stand in for numerical values in algebraic expressions.

61. Which expression represents "twice a number $x$ decreased by $3$"?

    $2x - 3$. "Decreased by" means subtract from the doubled value.

62. Which expression matches "$5$ less than twice a number $n$": $2n - 5$ or $2(n - 5)$?

    $2n - 5$. First double $n$, then subtract 5 from the result.

63. Which expression represents "twice the sum of $x$ and $5$"?

    $2(x + 5)$. "Twice" means multiply the entire sum by $2$.

64. Which expression represents "$3$ less than twice $x$"?

    $2x - 3$. First double $x$, then subtract $3$ from that.

65. Which expression represents "the sum of $m$ and $12$"?

    $m+12$. "Sum" means add the two values together.

66. What expression represents the total cost for $n$ items at $5 each plus a $2 fee?

    $5n + 2$. Total equals item cost times quantity plus fixed fee.

67. What does it mean if a variable represents an unknown number?

    Its value is not given and must be found. Unknown variables require solving to determine their specific value.

68. What is the expression for "$3$ times a number $t$"?

    $3t$. "Times" indicates multiplication in algebraic expressions.

69. What is the algebraic expression for "$3$ more than twice a number $x$"?

    $2x + 3$. First multiply $x$ by $2$, then add $3$ to the result.

70. What is the correct expression for "$3$ less than $x$"?

    $x - 3$. "Less than" reverses order: subtract from $x$.

71. What is the expression for the number of minutes in $h$ hours?

    $60h$. Each hour contains 60 minutes.

72. Which expression represents "$7$ divided by a number $n$"?

    $\frac{7}{n}$. Place $7$ in the numerator when it's being divided.

73. What is the expression for "$7$ more than a number $n$"?

    $n + 7$. "More than" means addition in algebraic expressions.

74. What is the correct expression for "$3$ fewer than $x$"?

    $x - 3$. "Fewer than" reverses order: subtract from $x$.

75. What is the expression for "$4$ more than the product of $3$ and $y$"?

    $3y + 4$. Multiply first, then add: $(3 \times y) + 4$.

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