There can be lots of ways to describe this. I like using money. For instance, a negative number means you "don't have" that much money, or you "owe" that much money. Subtraction would mean you "owe even more money" or "someone took even more money". So, if you start out with "owing 5 dollars". Then, you find out that one of your kids took 7 more dollars out of your wallet ("took out", "took away", subtraction), then you would be in the hole 12 dollars, or -12. So, the answer would be -12.
- 5 - (+7) = - 5 -7 = -12
When the terms are taken out of the bracket the signs multiply with each other, and the product of a negative and a positive sign is always negative,
i.e. -1 x + 1 = -1
in our case, we can also write the given equation as
- 5 + (-1)x(+1)x (7) = -5 +(-1)x(7) = -5 -7 = -12.
To solve this, it is helpful to know the properties of positive and negative numbers. If there are two positive numbers, the answer will be positive:
If there are two negative numbers, the answer will be negative because adding a negative to a negative results in a negative answer:
If there is one positive number and one negative number, the answer varies depending on the sign of the bigger number. If the bigger number has a negative sign, the answer will be negative. If it has no sign/positive sign, answer will be positive. But in both cases, you have to subtract. For example:
10+(-5)=5. In both cases, we subtract.
For your problem: -5- (+7), we can change the subtraction sign to a plus sign. When we do this, we are switching the signs of the 7 and the subtraction sign to get: -5+ -7. After changing this it is easy to solve since as I said earlier, adding two negative numbers will give a negative number so the answer is simple:
-5 + -7= -12. Hope this helped!
Thank you so much. Now we understand it. However do you know why the symbols get switched?? I am assuming they would always switch in a -# - (+#) situation.
As i can't reply directly up there, I'll reply here. The reason the signs switch is because we are distributing the sign in front of the parenthesis to the number inside. So let say your example:
the reason the the sign of the 7 changes is because you are distributing the - in front of (+7)
this - is being multiplied to the number inside and we know that a negative multiplied by a positive is a negative, therefore the sign becomes negative.
But let say the sign inside was a -
-5-(-7) the answer would have been -5 +7
this is because you are distributing the - and a - x - is a +
The simplest way to understand this is the number line
So, our starting point is -5 which is 5 units left of the zero.
Whenever we subtract postive nos. We move left of the number line, while wheneer we add positve nos., we move rigt of the no. line.
So 7 units left of -5 = total of 12 units left from the zero mark i.e. -12
Hope you understood it!! :)
let negatives be a bad person.
let positives be a good person.
Let's look at the four different situations for multiplying
1*1 = 1
if something good(+) happens to a good person(+) then it is good(+)
1*-1 = -1
if something good happens(+) happens to a bad person(-) then it is bad(-)
-1*-1 = 1
if something bad happens(-) happens to a bad person(-) then it is good(+)
-1*1 = -1
if something bad happens(-) to a good person(+) then it is bad(-)
now lets use this for the problem!
-5 - (+7) = ?
lets look at 7 first...lets rewrite this to see what we are doing
-5 + -1*(+7) = ?
here we see -1 being multiplied by 7... Using the rules above we know that if we multiply a negative number by a positive number we get a negative number! so now we know
-1*(+7) = -7
plug it back in!
-5 - 7 = ?
? = -12
It is a little tricky if you are just learning but i'm sure you will get the hang of it fast!