Equation (noun, “Eek-WAY-shun”)
An equation is a statement in math that says two things are equal. All equations contain an equal sign (=). The set of numbers and/or variables on either side of that sign is called an expression. (Variables are unknown values typically written as letters).
The difference between an expression and an equation is sort of like the difference between a phrase and a sentence. A phrase contains a single idea that is incomplete by itself. A sentence makes a complete statement. Likewise, an expression conveys a single idea — such as “one plus two” (1+2) or “x minus y” (x–y). An equation represents a complete sentence, such as one plus two equals three (1+2=3). Or, x minus y equals z (x–y=z).
Formulas are a special type of equation. They express an important relationship between two or more variables. For instance, the formula A=πr2 shows how the area of a circle (A) is related to its radius (r). (The area equals the constant pi (π) times the radius squared.) Formulas are used to express many rules in geometry and laws of physics. One example is F=ma. That is, force (F) equals mass (m) times acceleration (a).
Equations are not the only kind of “complete sentences” in math. Inequalities also link up expressions to form complete ideas. An inequality says that one expression is bigger or smaller than another. For example, “x is greater than y” (x > y) or “y is less than z” (y < z). But inequalities don’t contain equal signs. So they aren’t equations.
In a sentence
The Drake equation relates the number of advanced alien civilizations that could exist in our galaxy to factors such as the number of stars with planets and the number of those planets that could host life.