# Subtraction

In mathematics, **subtraction** is one of the four basic arithmetic operations. It is usually denoted by an infix minus sign.

The traditional names for the terms of the subtraction

*c*−*b*=*a*

**difference**(

*a*),

**minuend**(c) and

**subtrahend**(b).

## Basic subtraction

Imagine a straight line of length*b*painted on the ground with the left end labeled

*a*and the right end labeled

*c*.

Starting from position *a*, it takes you *b* steps to the right to reach position *c*. This movement to the right, called **addition**, can be stated as:

*a*+*b*=*c*

*c*, it takes you

*b*steps to the left to get back to

*a*. This movement to the left, called

**subtraction**, can be stated as:

*c*−*b*=*a*

From position 3, it takes no steps to the left to stay at position 3, so

- 3 − 0 = 3

- 3 − 1 = 2

- 3 − 2 = 1

For subtraction of natural numbers, the line would have every natural number (0, 1, 2, 3, 4, ...) on it.

Using the natural number line, from position 3, it takes you 3 steps to the left to get to position 0, so

- 3 − 3 = 0

Using the integer number line (…, −3, −2, −1, 0, 1, 2, 3, …), from position 3, it takes you 4 steps to the left to get to position −1, so

- 3 − 4 = −1

## See also