Why does 1- -1=2?

Question

Double negatives make a positive in English and in Math. In English it makes sense, but in math it does not make that much sense. For me that concept has just been a rule and I do not comprehend its reasoning. If anything 1- -1 should equal -1 since you are subtracting twice because of the two subtraction signs.

Answer 1

Well, when you have 1--1=2, what you're really saying is

1-(0-1)=2

Now we know the associative property (I hope!), so we can expand that to

1 -0 +1 = 2

which simplifies to

1+1=2

Which I hope you agree with :)

Another way to think about a negative number is as a "debt", and the - operation as "losing" something. So you are "losing" a "debt". Is that not like gaining money? :)

Answer 2

Double negatives become a POSitive makes sense in math if you think it this way:

Every number has a sign in front of it, implicitly or explicitly. For a positive number, there is an implicit "+" sign, but we normally don't write it that way....until we take a course in algebra. For a negative number, well, the "-" sign has to be explicit for it to be understood as a negative number.

To illustrate, if we have an equation such as 8-3 = 5, in algebra, the 3 can be interpreted two ways. One as a negative number or 'negative 3' to take into account the negative sign in front of it, allowing us to directly subtract 3 from 8. This method is what we are most familiar with.

The 2nd way: the 3 could be regarded as a positive number or '+3', allowing the equation be rewritten as 8 - +3 = 5, thus showing that a "NEGative" sign in front of a "POSitive 3" = "NEGative 3".

If we had an equation 8 - -3, the answer would be 11, thus showing that a "NEGative" sign in front of a "NEGative 3" = "POSitive 3".

As someone else had replied earlier regarding a number line, for the first, you would step BACK 3 (NEGATIVE direction, toward zero and into negative number territory, if necessary) from 8 to get to 5, and for the second, you would step AHEAD 3 (POSITIVE direction, toward infinity) to get to 11.

In regard to your reasoning, two subtract signs do not mean subtracting twice, but rather they signal a change in the POSITIVE direction. Thus, the answer to your problem of 1- -1 is = 2.

In summary for the examples above, a NEG and a POS = NEG; a NEG and a NEG (double NEG's) = POS. Of course, a POS and POS = POS.

In algebra, you will come across multiplication and division of positive and negative numbers. The rule is still the same. For examples, (-8) x 9 = -72, (-8) x (-2) = 16; (-81) / 9 = -9, (-16 ) / (-2) = 8, etc. I like to use () to keep track of negative numbers in these type of operations.

In multiplication and division, however, you can have a string of negative numbers and/or positive numbers, such as (-8) x (-2) x (-3) = -48 and (-8) x (-6) / (3) = 16. In general, the rule is: Count the negative signs. If the count is odd, the answer is NEG, if the count is even, the answer is POS. This rule fits the paragraph above, where only two numbers are involved.

I hope this will help.

Answer 3

That's because order of operations and how things are defined in math. Two operators, like - -, are not defined to mean 'subtract the number twice.' The '-' sign is defined to mean subtraction, but in the situation you have, something is actually left out which might make things clearer, but which is usually understood implicitly.

What a minus sign is really telling you to do is to make the number in front of it the opposite of what it is.

For example, you can think of "1 - 1" as actually saying "1 - (+1)".
So, "1 - - 1" means "- (-1)" (which is what it actually should be written as... you need the parentheses). In the first example, you subtracted a full positive one. But in the second the negative indicates you do the opposite, so 'taking away' -1 means you're really adding +1.

You can also think of a negative sign as multiplying whatever is after it by -1. Thus, - (-4) is "-1 times -4" or -2 is "-1 times 2"

Answer 4

Imagine you are standing on the number line at 1. Normally, you face the positive direction, but since you are going to subtract *negative* 1 (or the opposite of 1) you turn around and face the other way. Now you take one step backwards (because it's subtraction.) Now you are standing at 2.

Answer 5

Think of a subtraction sign as "The opposite of" when you are confused. Thus 1 - - 1 could be read as 1 and "the opposite of" -1. It this case combine 1 and 1 to get two.

Otherwise just stick to the mechanics that it takes two negatives together to make the plus sign by rotating one on top of the other.

Answer 6

Imagine you are standing on the number line at 1. Normally, you face the positive direction, but since you are going to subtract *negative* 1 (or the opposite of 1) you turn around and face the other way. Now you take one step backwards (because it's subtraction.) Now you are standing at 2.
its all number line stuff.

Answer 7

I like mathsmarts answer, but here's another way of looking at it. If you have -1 dollar (you owe someone a dollar) and you then give that person you owe 1 dollar, you are "subtracting" a negative dollar from yourself so you are no longer at -1 dollar you are at 0 dollars. So you see, if you - -1 dollar you actually gain.

Answer 8

if you subtracted one from two you would get one but if you took the subtracted the subtacted one for the equation you would still have two 1-2=1 the 1--1=2
and deepak is wrong -1-1=-2

Answer 9

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Answer 10

8 - 5 = 3
You are at the 8th floor (8)
You go to the 5th floor (5)
Their distance is 3.

1- -1=2
You are at the first floor (+1)
You go to the first cellar (-1)
Their distance is 2.

When you see - -1 the first - is an action: subtract.
The second - shows a state.