Translate verbal statements into algebraic expressions

Verbal descriptions of quantities and relationships are interpreted as algebraic expressions by identifying variables, constants, coefficients, and operations, including sums, differences, products, quotients, and repeated quantities. Translation preserves the intended order and grouping—especially for phrases such as “less than,” “divided by,” and “the sum of”—and includes expressions involving integers, fractions, decimals, and one or more variables, but not advanced symbolic generalizations or function notation.

Detailed Explanation: 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 $2$ .

Translate “five times a number $n$ .”

5n

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

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

5n-7

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 $3-n$ .

Learn by doing: Translate verbal statements into algebraic expressions

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Algebraic Equation from Sentence (Length vs Width) - Multiplication and Addition or Subtraction (Two Variables)

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Translate verbal statements into algebraic expressions

Detailed Explanation: Translate verbal statements into algebraic expressions

Learn by doing: Translate verbal statements into algebraic expressions

Practice with unlimited practice problems

Practice:

Algebraic Equation from Sentence (Length vs Width) - Multiplication and Addition or Subtraction (Two Variables)