Verbal Expression
A verbal expression is a mathematical relationship described in words rather than symbols, such as "five more than twice a number."
Definition
A verbal expression is a math idea written in plain words instead of numbers and symbols, describing a math operation using everyday language. Common operation keywords include sum/plus/increased by (addition), difference/minus/decreased by (subtraction), product/times (multiplication), and quotient/divided by (division), and converting between verbal and algebraic forms is a core pre-algebra skill. Verbal expressions correspond to informal semantic descriptions of formal syntactic objects (algebraic terms); in the philosophy of mathematics, the relationship between symbolic and verbal representations raises questions about mathematical Platonism, whether symbols describe pre-existing mathematical objects or constitute them, and in applied mathematics verbal problem descriptions must be carefully formalized before computation.
Example
"The sum of a number and six" is a verbal expression for $n + 6$, and "three times a number" is a verbal expression for $3n$. The algebraic expression $(x + 4)/2 - 3$ can be verbalized as "four more than a number, divided by two, decreased by three." The verbal description "the rate of change of population with respect to time is proportional to the current population" formalizes as the differential equation $dP/dt = kP$, whose solution is $P(t) = P_0e^{kt}$.
Key Insight
Every algebraic expression can be read aloud as a verbal expression, and practicing both directions strengthens understanding of what the symbols mean; if your verbal reading does not match the intended meaning, the expression is probably written incorrectly. The translation from verbal to symbolic is where most applied math problems begin, a skill that scales from pre-algebra word problems all the way to modeling physical phenomena with differential equations.