Addition and Subtraction:

Subtracting From a Negative Number

If subtraction is taking an amount away from another amount, what does it mean to take an amount away from a negative amount?

Remember that subtraction is the same as addition but in the opposite direction. On the number line, subtraction is shown by moving to the left. If our starting number is already negative, then moving to the left makes our solution a larger negative number.

This concept is most familiar when it comes to temperature. If it is $-5$ degrees and the temperature gets 10 degrees colder, the temperature can be calculated as:
$-5-10=-5+(-10)=-15$
Another example is debt. If I am $1000 in debt and I spend another $500, I subtract 500 from $-1000$. This is shown as:
$-1000-500=-1000+(-500)=-1500$

If the starting number is negative and we subtract a number from it, we add the numbers together but the answer is a larger negative number.

Video Source (03:42 mins) | Transcript

Practice Problems

Evaluate the following expression:

$-2-3=?$
$-4-4=?$
$-5-2=?$
$-17-2=?$
$-10-15=?$
$-46-15=?$

Solutions

$-5$ (Written Solution)

For this solution observe the pattern:

$-2-0=-2$ (zero has no value, therefore the answer is $-2$)

$-2-1=-3$

$-2-2=-4$

${\color{Red} -2-3=-5}$

When we subtract a positive number from a negative number our answers are always negative. The above pattern shows how increasing the value of the positive number results in a decreasing solution. The answer becomes more negative.
$-8$ (Written Solution)

For this solution observe the pattern:

$-4-0=-4$ (zero has no value, therefore the answer is $-4$)

$-4-1=-5$

$-4-2=-6$

$-4-3=-7$

${\color{Red} -4-4=-8}$

This same problem could be re-written as $-4 + -4$; negative four plus negative four results in negative eight. It is the same idea as when we are adding positive numbers only we are going in the negative direction.
$-7$
$-19$ (Solution Video | Transcript)
$-25$
$-61$ (Solution Video | Transcript)