An expression is any combination of symbols that can be evaluated to a number (or perhaps to some other data type). An equation has an equal sign, and an expression on both sides of the equal sign - it is a claim that the two expressions are equal.
Both have a value
An equation has the 'equals' sign ( = ) in it. An expression hasn't.
An equation consists of two expressions, one on either side of an equality symbol.
A proportion is generally multiplicative relationship between two measures of a quantity. An equation is a mathematical statement that relates two quantities. The quantities may contain a number of expressions, with each expression comprising a number of numerical constants, variables and functions.
equations have an = sign, inequalities do not
expressions don't have an equal sign and equations do
Both have a value
Yes. An equation has an "=" sign.
similarities and differences between ordinary fractions and rational expressions.
Algebraic expressions are the written relations of or between variables. For example, x2, 1/x, and x + y + z are all algebraic expressions. Algebraic equations are simply algebraic expressions that equate to something. For example, x2 = 4, 1/x = y, and x + y + z = 42 are all algebraic equations. In general, one differentiates algebraic expressions from exponential, trigonometric, hyperbolic, and logarithmic expressions by requiring algebraic expressions to be confined to polynomial expressions. I've added a link regarding polynomials below.
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An equation has the 'equals' sign ( = ) in it. An expression hasn't.
Linear equations are a tiny subset of functions. Linear equations are simple, continuous functions.
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An equation consists of two expressions, one on either side of an equality symbol.