Translate words into algebraic expressions

Verbal descriptions of quantities and relationships can be represented by algebraic expressions using variables, constants, coefficients, and operations; phrases such as “sum,” “difference,” “twice,” “quotient,” and “less than” must be interpreted carefully, including reversed order and grouping with parentheses when needed. The expressions represent the same quantity or relationship as the words in contexts involving whole numbers, decimals, and fractions, providing a foundation for writing and solving equations; formal polynomial manipulation and more generalized symbolic forms are beyond this scope.

Detailed Explanation: 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 $n$ .

Learn by doing: Translate words into algebraic expressions

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Algebraic Expression from Words - Multiplication and Addition or Subtraction

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