Why does a positive minus a negative equal a positive?

Question

I always wondered,
why is it when you do 10 - - 10 it equals positive 20.

But then when you put them in this order -10 - 10 = -20
It equals a negative.

Why does this rule work? It seems to not make sense.

Answer 1

It is a simply solution, look at your starting number.



On one you have 10, the other has -10



10 -(-10) = 10 + 10 = 20



- 10 - 10 = -20



Notice in the second one there is not 2 negative signs in front of the 10 so you just subtract it like normal. But in the first one there is 2 negative signs in front of the 10 so you add it instead.

Answer 2

I cannot tell the answer to you directly, but I can help you by imagining some scenarios involving numbers.



10--10 = 20



Draw a number line. Normally, if you are going to subtract numbers, you go to the left of the number line, approaching negative infinity. Now imagine a double negative. If in the process of subtraction, it is normal to go left, then a negative of a negative would be to turn the other way around. You have been moving to the left of the number line but since there is another negative, you will switch directions again, now to the right. So, instead of going to the left as a result of subtraction, you go to the right because you switched directions TWICE. Mark the point 10 and go to the left -10 times. Since -10 times is hard to imagine, what we can do is to switch signs again to go to the right.

10+10 = 20



Another situation is the concept of assets and liabilities. Asset has something to do with amount of property while liabilities are something you owe to other people. Having an asset is an advantage, meaning positive. Having liabilities is a disadvantage. A decrease in asset is a disadvantage. While a decrease in liabilities is an advantage, meaning POSITIVE. The last situation is an example of a double negative because you are talking about liabilities, which is negative in nature. Since the amount of debts is decreasing, it only means that you have an advantage because you have nothing to owe from others. If you have $10 asset, and someone owes you $10, he will pay you back with that amount you will have $20 dollars in your asset.



Well, these are just two cases. There are so much more to enumerate, just look at the surroundings and keep observing until you find the answer. Experience is the best teacher :-)



-10-10 = -20



Draw the number line. Since I said subtraction has something to do with going to the left of the number line, you can just imagine a point -10 and go ten to the left, which is -20.

Answer 3

Well because in the first problem the first ten is not negative and the 2 negative signs next to each other cancel out .... It's basically the expression "a negative plus a negative equals a positive"

Answer 4

always remember: - * - = + and - * + = - and +* + = + ( when signs get multiplied, ur 10--10 eg. is such type)



here 10 - - 10 , minus signs are getting multiplied. one is +10, and a -10 and a minus sign. -10 got multiplied with a minus sign = +. hence 10- -10 = 10+10 ( after multiplying the 2 signs which were together now you can solve it further like 10+10=20

another eg. of this case -10-(+10) first multiply the two signs together i.e. + and - sign then it will be: -10-10(coz +*- = -) now solve... calculation of no.s with different signs is like this:-



in the case of numbers its little different: say: 1) -no.+no.=subtraction of numbers with the sign of the greater no.. eg. -1+2= 1 ( sub. and sign of grtr no. i.e. 2)



2)+no.+no. = addition with +ve sign



3)and -no.-no. = addition with -ve sign( -10-10 = -20)





you have got confused between the cases of numbers and signs. your 2 egs have in one sign multiplicaton and then simple calculation as we do with the no.s.

Answer 5

a - b mean to take a + (-b), where -b is the additive inverse of b

If b is -10, the additive inverse of b is +10

so a - (-10) means a + 10.

This makes perfect sense.

Subtractions is the the addition of the the additive inverse.

The additive inverse of x is the number you need to add to x to get 0.

Answer 6

If x is positive number and y is a negative number then x>y therefore x-y>0 . We can also say that y