The difference between an expression and an equation is that an expression is a mathematical phrase representing a single value whereas an equation is a mathematical sentence asserting equality between two quantities. Also, an equation is normally separated into left- and right-hand sides by an equal sign.
Expressions can be numeric or algebraic. A numerical expression consists of one or more numeric constants and operations. The numeric constant is a known quantity with an unchanging value. The operation is a mathematical procedure, such as addition, subtraction, multiplication or division. Numerical expressions have fixed values.
An algebraic expression has one or more variables in addition to the numeric constants or operations it may contain. Variables are symbols, usually letters, that substitute for unknown values. The value of algebraic expressions can change.
Expressions and equations are used to represent real-life problems by converting math-related situations expressed in words into mathematical language. The values that are known are expressed as numeric consonants. The values that are unknown or could change are written as variables. The relationships between them are represented using operations.
By accurately identifying the constants, variables and operations describing what one knows and wants to know in combination with how they are related, one can convert information into mathematical expressions and equations that can be used to solve problems efficiently.