Subtraction of directed numbers

[SilverSoldier]

Consider (+5)-(-7)
This is subtracting a value lesser than zero from a bigger value than zero. The answer has to be therefore lesser than the big number. But, the answer we get (+12) is bigger than the big number which should be impossible. What is the reason for this

 

[Steven G]

Consider (+5)-(-7)
This is subtracting a value lesser than zero from a bigger value than zero. The answer has to be therefore lesser than the big number. But, the answer we get (+12) is bigger than the big number which should be impossible. What is the reason for this

I think of it like this. The problem 5 - (-7) is NOT 5 - 7 (since -7 is not 7) so it must be 5+7.

Here are a few examples.
Also ignore the sign of the 2nd number to use my method.

10-(-8) is not 10-8 so it is 10+8.

12+(-2) is not 12 + 2 so it must be 12-2.

11 - 9 IS 11 - 9

15 - (-9) is not 15 - 9 so it must be 15 + 9

 

[SilverSoldier]

Thanks

I will try to understand. But (sorry if disturbing you people), if we put it another way, I have 5 plates with food (+5) and 7 plates without food (-7), to cancel the (-7), can't I break those plates?

 

[stapel]

I will try to understand. But (sorry if disturbing you people), if we put it another way, I have 5 plates with food (+5) and 7 plates without food (-7),....

"Without food" means "zero" ("nothing" or "empty"), not "negative".

You buy something for ten dollars, with a three-dollars-off coupon. The receipt is for "$10 + (-$3) = $7". Then you take the item back for a refund. They don't give you ten bucks back. Instead, the refund ticket reads "-($10 + (-$3)) = -$10 - (-$3) = -$10 + $3 = -$7; you get seven bucks back.

You have twelve (12) items. You sell seven of them to one guy, so you only have (12 + (-7) = 5) five left. But then the guy returns all seven (-(-7)). Do you then have five left? Do you then have -2 left? Or do you have 5 - (-7) = 5 + 7 = 12 left?

 

[Steven G]

I will try to understand. But (sorry if disturbing you people), if we put it another way, I have 5 plates with food (+5) and 7 plates without food (-7), to cancel the (-7), can't I break those plates?

Exactly! You say that you HAVE 5 plates with food and (HAVE) 7 plates w/o food. Since you HAVE then you add the two numbers, (5) + (-7). But what if I take away the 7 plates without food?
My usual example is just like a previous poster made earlier.
If I have $100 in my pocket and I also have a $70 in my other pocket then I really only have $30 in my pockets. But what if the person who sent me the $70 bill called me up and said forget about paying me. Isn't that like adding $70 to my pocket? And isn't it also like subtracting (taking away) the -$70 (which I owe)? So - (-70) is the same as +70