Use Variables in Real-World Problems - 6th Grade Math
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Which expression represents the perimeter of a rectangle with length $L$ and width $W$?
Which expression represents the perimeter of a rectangle with length $L$ and width $W$?
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$2L + 2W$. Perimeter adds all four sides: $L+L+W+W$.
$2L + 2W$. Perimeter adds all four sides: $L+L+W+W$.
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Which expression represents “$7$ less than a number $n$”?
Which expression represents “$7$ less than a number $n$”?
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$n - 7$. "Less than" means subtraction, so subtract $7$ from $n$.
$n - 7$. "Less than" means subtraction, so subtract $7$ from $n$.
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What does a variable represent in an expression such as $x + 5$?
What does a variable represent in an expression such as $x + 5$?
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A number that can be unknown or can vary. Variables can stand for unknowns or change based on context.
A number that can be unknown or can vary. Variables can stand for unknowns or change based on context.
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Which expression represents your money after saving $\$5$ each week for $w$ weeks starting from $$12$?
Which expression represents your money after saving $\$5$ each week for $w$ weeks starting from $$12$?
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$12 + 5w$. Start with $\$12$, add $$5$ for each week.
$12 + 5w$. Start with $\$12$, add $$5$ for each week.
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Which expression represents the total cost for $n$ items at $\$4$ each plus a $$3$ fee?
Which expression represents the total cost for $n$ items at $\$4$ each plus a $$3$ fee?
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$4n + 3$. Multiply items by price, then add the fixed fee.
$4n + 3$. Multiply items by price, then add the fixed fee.
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Which expression represents the area of a rectangle with length $L$ and width $W$?
Which expression represents the area of a rectangle with length $L$ and width $W$?
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$LW$. Area of rectangle is length times width.
$LW$. Area of rectangle is length times width.
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Which expression represents “$7$ times a number $n$”?
Which expression represents “$7$ times a number $n$”?
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$7n$. "Times" indicates multiplication of $7$ and $n$.
$7n$. "Times" indicates multiplication of $7$ and $n$.
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Which expression represents “a number $n$ divided by $7$”?
Which expression represents “a number $n$ divided by $7$”?
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$\frac{n}{7}$. Place $n$ in the numerator when it's being divided.
$\frac{n}{7}$. Place $n$ in the numerator when it's being divided.
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Which expression represents “$7$ divided by a number $n$”?
Which expression represents “$7$ divided by a number $n$”?
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$\frac{7}{n}$. Place $7$ in the numerator when it's being divided.
$\frac{7}{n}$. Place $7$ in the numerator when it's being divided.
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Which expression represents “the difference of a number $x$ and $y$” (in that order)?
Which expression represents “the difference of a number $x$ and $y$” (in that order)?
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$x - y$. "Difference" means subtract the second from the first.
$x - y$. "Difference" means subtract the second from the first.
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Which expression represents “the sum of twice $x$ and $5$”?
Which expression represents “the sum of twice $x$ and $5$”?
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$2x + 5$. First double $x$, then add $5$ to that result.
$2x + 5$. First double $x$, then add $5$ to that result.
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What is the correct expression for “$3$ fewer than $x$”?
What is the correct expression for “$3$ fewer than $x$”?
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$x - 3$. "Fewer than" reverses order: subtract from $x$.
$x - 3$. "Fewer than" reverses order: subtract from $x$.
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What is the correct expression for “$3$ less than $x$”?
What is the correct expression for “$3$ less than $x$”?
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$x - 3$. "Less than" reverses order: subtract from $x$.
$x - 3$. "Less than" reverses order: subtract from $x$.
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Which expression represents “$3$ less than twice $x$”?
Which expression represents “$3$ less than twice $x$”?
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$2x - 3$. First double $x$, then subtract $3$ from that.
$2x - 3$. First double $x$, then subtract $3$ from that.
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Which expression represents “twice a number $x$ decreased by $3$”?
Which expression represents “twice a number $x$ decreased by $3$”?
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$2x - 3$. "Decreased by" means subtract from the doubled value.
$2x - 3$. "Decreased by" means subtract from the doubled value.
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What is the expression for your pay if you earn $\$15$ per hour for $h$ hours plus a $$20$ bonus?
What is the expression for your pay if you earn $\$15$ per hour for $h$ hours plus a $$20$ bonus?
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$15h + 20$. Total pay = hourly rate × hours worked + fixed bonus.
$15h + 20$. Total pay = hourly rate × hours worked + fixed bonus.
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Identify the set of values for $x$ if $x$ is a positive even integer.
Identify the set of values for $x$ if $x$ is a positive even integer.
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${2, 4, 6, 8, \dots}$. Positive even integers are 2, 4, 6, 8, and so on.
${2, 4, 6, 8, \dots}$. Positive even integers are 2, 4, 6, 8, and so on.
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Identify the set of values for $n$ if $n$ is a whole number less than $5$.
Identify the set of values for $n$ if $n$ is a whole number less than $5$.
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${0, 1, 2, 3, 4}$. Whole numbers less than 5 include 0 through 4.
${0, 1, 2, 3, 4}$. Whole numbers less than 5 include 0 through 4.
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What is the expression for the perimeter of a rectangle with length $l$ and width $w$?
What is the expression for the perimeter of a rectangle with length $l$ and width $w$?
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$2l + 2w$. Rectangle perimeter: add all 4 sides (2 lengths + 2 widths).
$2l + 2w$. Rectangle perimeter: add all 4 sides (2 lengths + 2 widths).
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What is the expression for “$4$ more than the product of $3$ and $y$”?
What is the expression for “$4$ more than the product of $3$ and $y$”?
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$3y + 4$. Multiply first, then add: $(3 \times y) + 4$.
$3y + 4$. Multiply first, then add: $(3 \times y) + 4$.
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What is the expression for “$7$ more than a number $n$”?
What is the expression for “$7$ more than a number $n$”?
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$n + 7$. "More than" means addition in algebraic expressions.
$n + 7$. "More than" means addition in algebraic expressions.
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What is the expression for “twice the sum of $x$ and $4$”?
What is the expression for “twice the sum of $x$ and $4$”?
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$2(x + 4)$. "Twice" means multiply by 2; parentheses show order.
$2(x + 4)$. "Twice" means multiply by 2; parentheses show order.
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What is the expression for “the difference of $a$ and $b$” (in that order)?
What is the expression for “the difference of $a$ and $b$” (in that order)?
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$a - b$. "Difference" means subtract the second from the first.
$a - b$. "Difference" means subtract the second from the first.
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What is the expression for “the sum of $p$ and $q$”?
What is the expression for “the sum of $p$ and $q$”?
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$p + q$. "Sum" means to add the two variables together.
$p + q$. "Sum" means to add the two variables together.
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What is the expression for the perimeter of a square with side length $s$?
What is the expression for the perimeter of a square with side length $s$?
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$4s$. A square has 4 equal sides, so perimeter is $4 \times s$.
$4s$. A square has 4 equal sides, so perimeter is $4 \times s$.
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