Maths - Elements of an equation

An equation is a mathematical expression with an equals sign in it.

Other possible elements of an equation are:

These are explained below:


There are different types of numbers, for instance:

and these numbers may be coded in different ways:

Unless otherwise specified we usually assume that numbers are decimal.


Sometimes an equation contains a number but we don't yet know its value, or we may want to apply the equation to a range of values.

An example of the first is using x as the unknown, for example,

x + 1 = 3

An example of the second might be an equation of a line:

y = 2 * x + 3

In general we use:

x, y, z for unknowns.

a, b, c for values which are not yet specified.

Binary Operators

The operators:

take the two numbers on either side and replace it by a single number.


In the following plot the height is given by a+b, this gives a flat plane at 45° to both a and b:


how this graph was produced

Of course the plane is infinite in all directions but here we have only shown a section of the plane.


In the following plot the height is given by a*b, this gives a surface made up of straight lines along a or b directions (bi-linear). If we take a direction at 45° to both a and b then we get a parabola.


how this graph was produced

Unary operators

The operators:

apply to the number to the right. '-' inverts the number (subtracts from 0) '+' says the number to the right is positive (the default).


When we mix + and * then the answer we get depends on the order that we apply them.

For example

2 + 1 * 3

To clarify this we can put brackets around the operation to be applied first:

(2 + 1) * 3 = 9

2 + (1 * 3) = 5

If we don't specify which has precedence by using bracket then by default * and ÷ have precedence over + and -. So,

2 + 1 * 3 = 5


A function takes one number and uses it to generate another number. For example the function sin() takes an angle as input and returns the ratio of opposite and hypotenuse in a right angled triangle.

metadata block
see also:


Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

cover The MathML Handbook - for people interested in working with mathematics on the web.

Other Math Books

Terminology and Notation

Specific to this page here:


This site may have errors. Don't use for critical systems.

Copyright (c) 1998-2023 Martin John Baker - All rights reserved - privacy policy.