6th Grade Math Flashcards: Use Variables In Real World Problems

What this deck covers

This deck focuses on Use Variables In Real World Problems, giving you a quick way to review the definitions, rules, and examples that matter most for 6th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

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

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

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

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

Flashcard 3: Which expression represents "$3$ times a number $k$"?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Answer: rac{m}{5}. "Divided by" means the number is in the numerator.

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

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

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

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

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

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

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

Answer: $st$. Distance equals speed multiplied by time.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Answer: 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.

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

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

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

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

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

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

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

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

Flashcard 47: What is a variable in an algebraic expression?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Flashcard 60: What is a variable in an expression?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Answer: $60h$. Each hour contains 60 minutes.

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

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

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

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

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

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

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

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