Skill: Translate words into algebraic expressions

Words can be translated into algebra by matching each phrase with an operation.

• sum means add: $a+b$
• difference means subtract: $a-b$
• twice a number means multiply by $2$: $2n$
• less than reverses the order: “$4$ less than $2n$” means $2n-4$

Example

Write an expression for:

The sum of a number $n$ and $4$ less than twice the number.

Step 1: Identify the variable.

The number is represented by $n$.

Step 2: Translate “twice the number.”

Twice $n$ is:

$$2n$$

Step 3: Translate “$4$ less than twice the number.”

Because “less than” reverses the order, this is:

$$2n-4$$

It is not $4-2n$.

Step 4: Translate “the sum of a number and...”

Add $n$ to the expression $2n-4$:

$$n+(2n-4)$$

So, the algebraic expression is:

$$\boxed{n+(2n-4)}$$

The parentheses show that $4$ is subtracted from twice the number before it is added to $n$.