# How do you evaluate 4-6?

Dec 20, 2016

$4 - 6 = - 2$

#### Explanation:

$4 - 6$ is the same as $- \left(6 - 4\right)$

$- \left(6 - 4\right) = - \left(2\right) = - 2$

Dec 20, 2016

$\textcolor{b l u e}{4} \textcolor{red}{- 6} = \textcolor{red}{- 2}$

#### Explanation:

This is the type of question which you would not have been able to answer when your number line started from 0.

However as soon as you work with integers you realise that there are as many negative numbers on the left of 0 as there are positive numbers on the right of 0.

What does $4 - 6$ mean?

Start at 4 on the number line and count 6 places to the left. After a count of 4 you will be on 0.
No problem, keep going and you will end up 2 spaces to the left of 0, which is $- 2$

You can also work this out using the fact additive inverses add to 0.
$+ 1 - 1 = 0$

$\textcolor{b l u e}{4} \textcolor{red}{- 6}$ can be written as

$\textcolor{b l u e}{+ 1 + 1 + 1 + 1} \textcolor{red}{- 1 - 1 - 1 - 1 - 1 - 1} \text{ } \leftarrow$ re-arrange

$= \left(+ 1 - 1\right) + \left(+ 1 - 1\right) + \left(+ 1 - 1\right) + \left(+ 1 - 1\right) - 1 - 1$

$= 0 + 0 + 0 + 0 - 1 - 1 = - 2$

There are two more negatives than positives, so the answer will be negative.