Skill: Translate verbal statements into algebraic expressions

Start by identifying the quantities and the operation words.

• A number you do not know can be represented by a variable, such as $n$.
• A number multiplied by a variable is written with a coefficient: “five times a number” becomes $5n$.
• Words such as “difference” mean subtraction.
• Words such as “quotient” mean division.
• “The difference between … and …” keeps the order shown.

Example: Translate this verbal statement into an algebraic expression:

The quotient of the difference between five times a number $n$ and $7$, and $2$.

1. Translate “five times a number $n$.”

$$5n$$

2. Translate “the difference between five times a number $n$ and $7$.”

   Since “difference between $5n$ and $7$” means subtract $7$ from $5n$:

$$5n-7$$

3. Translate “the quotient of [that expression] and $2$.”

   The entire difference is divided by $2$, so use parentheses:

$$\boxed{\frac{5n-7}{2}}$$

Parentheses or a fraction bar show that both $5n$ and $7$ are included in the division. Also remember that phrases like “$3$ less than $n$” mean $n-3$, not $3-n$.