Addition Expression

Write an expression for: "The sum of a number and 12"

Identify the operation: "Sum" means addition ($+$) = Operation: $+$

Identify the quantities: "A number" (unknown) and 12 = Variable and 12

Choose a variable: Let $n$ represent "a number" = $n$

Write the expression: Sum means add: $n + 12$ = $n + 12$

Answer: $n + 12$

Subtraction with 'Less Than'

Write an expression for: "7 less than a number"

Identify the operation: "Less than" means subtraction ($-$) = Operation: $-$

Watch the order!: "7 less than a number" means start with the number, then subtract 7 = Number first, then $-7$

Choose a variable: Let $x$ represent "a number" = $x$

Write the expression: Start with $x$, subtract 7: $x - 7$ = $x - 7$

Answer: $x - 7$ (not $7 - x$)

Multiplication Expression

Write an expression for: "Triple a number, then add 4"

Break into parts: Part 1: "Triple a number" | Part 2: "then add 4" = Two operations

Translate part 1: "Triple" means multiply by 3: $3x$ = $3x$

Translate part 2: "Add 4" means $+ 4$ = $+ 4$

Combine: Put together: $3x + 4$ = $3x + 4$

Answer: $3x + 4$

Division Expression

Write an expression for: "A number divided by 5, decreased by 2"

Identify operations: "Divided by" ($\div$) and "decreased by" ($-$) = Division, then subtraction

Translate the division: "A number divided by 5" = $\frac{n}{5}$ = $\frac{n}{5}$

Translate the subtraction: "Decreased by 2" means subtract 2 = $- 2$

Combine: $\frac{n}{5} - 2$ = $\frac{n}{5} - 2$

Answer: $\frac{n}{5} - 2$

Real-World Expression

A movie ticket costs 12 dollars. Write an expression for the total cost of $t$ tickets plus a 5 dollar popcorn.

Identify what varies: The number of tickets ($t$) can change = Variable: $t$

Cost of tickets: Each ticket is 12 dollars, so $t$ tickets cost $12 \times t$ = $12t$

Add the popcorn: Popcorn costs 5 dollars (fixed) = $+ 5$

Write final expression: Total cost = tickets + popcorn = $12t + 5$

Answer: $12t + 5$ dollars

Mistake: Writing "5 less than $x$" as $5 - x$ instead of $x - 5$

Why: "Less than" reverses the order! "5 less than $x$" means start with $x$ and take away 5.

Correct: "5 less than $x$" = $x - 5$. Think: "I have $x$ dollars and spend 5" leaves $x - 5$.

Mistake: Forgetting to use parentheses when needed

Why: "Twice the sum of $x$ and 3" needs parentheses to show you add first.

Correct: "Twice the sum of $x$ and 3" = $2(x + 3)$, not $2x + 3$

Mistake: Confusing "a number" with a specific number

Why: "A number" means an unknown value that should be a variable.

Correct: Always use a variable ($x$, $n$, $y$) when you see "a number," "some number," or "an unknown."

Shopping and Budgeting

Stores use expressions to calculate totals with discounts, tax, and multiple items.

If shirts cost 15 dollars each and you have a 10 dollar coupon, the cost for $s$ shirts is $15s - 10$.

Sports Statistics

Athletes and coaches use expressions to track performance and predict outcomes.

If a basketball player scores $p$ points per game, their total after $g$ games is $pg$.

Cooking and Recipes

Recipes are scaled using expressions when cooking for different numbers of people.

A recipe uses 2 cups of flour per person. For $p$ people, you need $2p$ cups.

Q: Does it matter what letter I use for a variable?

A: No! You can use any letter. However, some letters are traditional: $t$ for time, $d$ for distance, $n$ for "a number." Use whatever makes sense for the problem.

Q: Why is $2x$ written without a multiplication sign?

A: In algebra, we often skip the multiplication sign between a number and a variable. Writing $2x$ is the same as $2 \times x$. This makes expressions cleaner and easier to read.

Q: How do I know when to use parentheses?

A: Use parentheses when you need to do an operation on a group. "Twice the sum of $x$ and 5" needs parentheses: $2(x + 5)$. Without them, $2x + 5$ means "twice $x$, then add 5" - a different thing!