# Counting backwards through zero: Negative numbers

## In a nutshell

Just like it's possible to count backwards in ones to zero through the positive numbers, it's also possible to count backwards from zero through the negative numbers.

## Negative numbers

### Definition

Negative numbers are numbers below zero. They have a minus sign in front of them in order to show that they are negative.

Negative numbers count from zero in the opposite direction to positive numbers, as shown by this number line.

$\begin{array}{cccccccccccccc}&&&&&&&&&&\leftarrow\text{negative|positive}\rightarrow\\&&&&&&&&&&\text{increasing}\\&&&&&&&&&&\longrightarrow\\-5&&-4&&-3&&-2&&-1&&\bold0&&1&&2&&3&&4&&5&&6& \\|&&|&&|&&|&&|&&|&&|&&|&&|&&|&&|&&|\\ \hline\\&&&&&&&&&&\text{decreasing}\\&&&&&&&&&&\longleftarrow\\\end{array}$

Just like with positive numbers, negative numbers get bigger in this direction: ($\rightarrow$) and get smaller in this direction: ($\leftarrow$).

##### Example 1

$4$* is greater than *$2$*.*

*$\begin{array}{cccccccccccccc}&&&&&&&&&&\text{increasing}\\&&&&&&&&&&\rightarrow\\-5&&-4&&-3&&-2&&-1&&\bold0&&1&&\underline2&&3&&\underline4&&5&&6& \\|&&|&&|&&|&&|&&|&&|&&|&&|&&|&&|&&|\\ \hline\end{array}$*

*But *$-2$* is greater than *$-4$*.*

*$\begin{array}{cccccccccccccc}&&&&&&&&&&\text{increasing}\\&&&&&&&&&&\rightarrow\\-5&&\underline{-4}&&-3&&\underline{-2}&&-1&&\bold0&&1&&2&&3&&4&&5&&6& \\|&&|&&|&&|&&|&&|&&|&&|&&|&&|&&|&&|\\ \hline\end{array}$*

*Tip:** The closer a negative number is to zero, the larger it is!*

## Counting backwards through zero using negative numbers

Counting backwards through zero with negative numbers, using a number line, is exactly the same as just using positive numbers.

To count backwards, move down the number line in the decreasing direction.

##### Example 2

*Count backwards six from *$1$*.*

Find your starting point: $1$.

*Count down from one until you reach zero. *

*Then, continue down a further five, taking you through zero into the negative numbers, until you reach *$\underline{-5}$.

$\begin{array}{cccccccccccccc}&&&-1&&-1&&-1&&-1&&-1&&-1 \\& &&\curvearrowleft&&\curvearrowleft &&\curvearrowleft &&\curvearrowleft &&\curvearrowleft&&\curvearrowleft\\-6&&\underline{-5}&&-4&&-3&&-2&&-1&&\bold0&&\underline1&&2 \\|&&|&&|&&|&&|&&|&&|&&|&&| \\ \hline\end{array}$