Equations: meaning, definitions and examples

General usage for any mathematical expression that asserts the equality of two expressions. It can be used both in everyday language and academic settings.

• We need to solve these equations before moving on to the next chapter.
• His notebook was filled with equations and diagrams.

Used in academic and formal settings to refer to declarative sentences that are either true or false within the context of mathematics. It's often broader than just equations.

• The mathematical statement 'all even numbers are divisible by 2' is true.
• Every proof in this chapter starts with a mathematical statement.

Specific and systematic expressions used to represent mathematical principles, chemical mixtures, or scientific relationships. Common in both education and professional settings.

• We use the formula E=mc^2 to illustrate the relationship between energy and mass.
• Remember to apply the quadratic formula to find the roots of the equation.

Typically used in more formal or academic settings to specify that the equation belongs to the field of mathematics. Emphasizes the mathematical nature of the equation.

• A mathematical equation like x + y = z can represent a wide variety of problems.
• The lecturer wrote a complex mathematical equation on the board.

Equations are used to describe mathematical relationships between variables that are equal to each other, often found in math, physics, and engineering.

• The quadratic equation is used to find the roots of a polynomial
• Newton's second law is represented by the equation F = ma

Physical relationships describe how physical quantities are related to each other, often used in physics to explain natural phenomena.

• Ohm's Law describes the physical relationship between voltage, current, and resistance: V = IR
• Boyle's Law describes the relationship between the pressure and volume of a gas: P1V1 = P2V2

Formulas are used to provide a concise way of expressing information symbolically, such as mathematical, scientific, and technical information. Often, formulas relate variables in a standard format.

• The area of a circle is given by the formula A = πr²
• The quadratic formula is used to solve quadratic equations: x = (-b ± √(b²-4ac)) / 2a

Mathematical expressions are combinations of numbers, operators, and sometimes variables that represent a value. They do not necessarily imply equality like equations.

• 3x + 2 is a simple mathematical expression
• The expression 4(3 + 5) can be simplified to 4 * 8