May 21st
May 21st
Calculations with Negative Numbers
Question: What is the value that satisfies -4 + ? = -10 ?
Misconception
There are several possible misconceptions including
? = 6
and
? = 14
or even
? = - 14
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Correct
The correct answer is - 6 as this satisfies the sum -4
+ (-6) = -10. It can be shown on a number line as given
below.
Starting at negative 4 and adding negative 6 you get
the answer negative 10.
Hence -4 + (-6) = -10.
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Further Explanation
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
opposite.
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
logic correct!
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