Calculations with Negative Numbers
Question: What is the value that satisfies -4 + ? = -10 ?
There are several possible misconceptions including
? = 6
? = 14
? = - 14
The correct answer is - 6 as this satisfies the sum -4
+ (-6) = -10. It can be shown on a number line as given
Starting at negative 4 and adding negative 6 you get
the answer negative 10.
Hence -4 + (-6) = -10.
It is important to realise that there is no guessing, no
doubts but straightforward logic. Here we can associate the
meaning owning when the quantity is positive and owing if it
negative. Also, as before, we associate the minus sign with
In this example,
I start by owing 4 ( i.e. the '- 4 ' )
What is this '+?' that must have happened if I ended up 'owing
10' ? ( i.e. the ' - 10 ')
Another debt of 6 must have been added to my plight
We write 'adding a debt of 6' as ' + ( -6) '
So in - 4 + ? = - 10 the ? must be - 6
This is equivalent to the use of a number line as shown above;
it does not matter which way you argue as long as you get the