Translate verbal phrases into algebraic expressions

Verbal descriptions of quantities and relationships are interpreted as algebraic expressions by identifying variables, constants, coefficients, and operation words such as sum, difference, product, quotient, and squared; the symbolic form must preserve operation order and grouping, as in “five less than twice $n$ ” becoming $2n-5$ , not $5-2n$ . The scope is limited to straightforward one- or two-variable phrases with whole-number or rational values, including recognition of equivalent expressions and the distinction between an expression and an equation, providing a foundation for simplifying, evaluating, and solving algebraic relationships.

Detailed Explanation: Translate verbal phrases into algebraic expressions

Words can describe numbers and operations. To translate a phrase into an algebraic expression:

Choose a letter for the unknown number.
Identify the operation words.
Write the operations in the correct order.
Check that the expression matches the words.

Worked example

Translate “five less than twice $n$ ” into an algebraic expression.

Step 1: Identify the variable.
The unknown number is represented by $n$ .

Step 2: Translate “twice $n$ .”
“Twice” means multiply by $2$ :

2n

Step 3: Translate “five less than.”
“Five less than” means subtract $5$ from the amount that comes before it:

2n-5

So, “five less than twice $n$ ” is

\boxed{2n-5}

Be careful: it is not $(5-2n)$ . The phrase “five less than twice $n$ ” starts with $(2n)$ , then takes away $5$ .

An expression such as $(2n-5)$ does not have an equals sign. An equation would include one, such as $(2n-5=9)$ .

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Algebraic Expression from Words - Multiplication and Addition or Subtraction

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