Terms

A term, in the context of mathematics, is a component of an expression. This includes fractions, ratios, proportions, and sequences, among many other mathematical objects.

Most typically, the terms of an expression are constants, coefficients, or variables. When they are part of an equation, the terms are all the objects in the equation, not including operation or equality symbols such as -, +, ×, ÷, =, ≤ etc.

Terms of a common fraction

The terms of a common fraction are the numerator and the denominator. The fraction bar is not considered a term.

In this case, the terms of the fraction are both integers. This doesn't have to be the case however, and the terms can be different expressions, types of numbers, etc.

Terms of a proportion

Proportions can be written in a number of ways. Most typically, they are written as an equality of fractions or ratios. The values in a proportion are the terms of the proportion, regardless whether they are integers, variables, or some other mathematical object. The figure below shows the various forms of a proportion; all the numbers in green are the terms of the proportion.

Terms of a sequence

Each object (usually separated by commas) in a pattern or sequence is referred to as a term (or element). The terminology nth term is commonly used to refer to a term in a specific position of a sequence. For example, the first term (n = 1) in the sequence below is 2. The 5th term (n = 5) is 32.

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,

Terms of an expression

In algebra, the terms of an equation are typically made up of coefficients and variables. All the objects in the equation, other than any operation or equality symbols are terms of the algebraic equation.

The x is a variable, the 2 is a coefficient (and also a constant), and the -1 and 23 are constants. All of these objects are considered terms.