Adding with Negative Numbers
Question: What is the value of - 8 + 6 ?
Misconception
There are several possible misconceptions including
-8 + 6 = 2
and
-8 + 6 = -14
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Correct
The correct answer is -2 as this sum results from
adding positive 6 to negative 8, as can be seen from the
number line below.
Starting at negative 8 and adding 6 you get the answer
negative 2.
Hence -8 + 6 = -2
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Further Explanation
With mathematics, everything is logical; there is no
"guessing" and no "maybe", only logical
reasoning.
We associate the minus sign with opposite (as in give and take
).
For example,
- 8 means taking away 8, while ( + 6 ) means giving 6
So - 8 + 6 translates to
taking away 8 and giving back 6
which is equivalent to taking away only 2
But taking away 2 is what is meant by - 2 . That is why -8 + 6
= -2 .
You can argue in a similar way, or do the calculation on a
number line, to show that, for example,
6 - 8 = - 2 and - 6 - 8 = -14
Note that the order of giving/taking does not matter.
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