Verbal Expression
Pre-AlgebraA 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. It describes a math operation using everyday language.
Example
"The sum of a number and six" is a verbal expression for $n + 6$. "Three times a number" is a verbal expression for $3n$.
Key Insight
Every algebraic expression can be read aloud as a verbal expression. Practice writing both forms to strengthen your understanding of what the symbols mean.
Definition
A verbal expression uses words to describe mathematical operations. Converting between verbal and algebraic forms is a core skill in pre-algebra. Common operation keywords: sum/plus/increased by (addition), difference/minus/decreased by (subtraction), product/times (multiplication), quotient/divided by (division).
Example
The algebraic expression $(x + 4)/2 - 3$ can be verbalized as "four more than a number, divided by two, decreased by three."
Key Insight
Being able to read algebra aloud helps catch errors. If your verbal reading does not match the intended meaning, the expression is probably written incorrectly.
Definition
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: do symbols describe pre-existing mathematical objects, or do they constitute them? In applied mathematics, verbal problem descriptions must be carefully formalized before computation.
Example
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
The translation from verbal to symbolic is where most applied math problems begin. The skill scales from pre-algebra word problems all the way to modeling physical phenomena with differential equations.