How not to change the signs inside the brackets?

All of us are taught to change signs when opening or closing brackets of the expression in brackets, if before the brackets minus sign. Let's look at this tedious process for half-dead examples.

11-(2+5-4) = 11-3 = 8

Before the expression in brackets is a minus sign, it means that the disclosure of the brackets need to change all the signs to the contrary all the numbers that are inside the parentheses. Consider the same example, but without the brackets.

11-(2+5-4) = 11-2-5+4 = 9-5+4 = 4+4 = 8

Now let's try to take a part of the expression in parentheses.

1+2+3+4 = 10

Naturally, you ask: "Where is the minus sign?!" Do not worry, now appear.

1+2-(-3-4) = 3-(-7) = 3+7 = 10

I put in front of the brackets and the minus sign to change the sign before the numbers inside the parentheses. In disclosing the brackets again I changed the sign, because before my braces a minus sign. In the end, the result remained unchanged.

Now a more complex example.

17-6+9 = 20
17-(6-9) = 17-(-3) = 17+3 = 20

As you can see, continuous headache turns out, when suddenly appears before the brackets the minus sign. How not to change the signs inside the brackets? Very simply - no need to put a minus in front of the brackets. Look how it's done.

17-6+9 = 17+(-6+9) = 17+(3) = 17+3 = 20

Now consider the last two examples under the microscope. In the first case I put the first parenthesis after the minus sign. I like a knife cut a negative number into two parts - a minus sign and a positive number. The minus sign was in front of the bracket, and a positive number - within the brackets. Look.

17-(6........

In fact, we are in parentheses conclude a positive number, which until then was negative. Changing the sign of the first number in parentheses passed on complete autopilot without our intervention. A sort of a machine circumcision minus sign in numbers. But with the other numbers that fall into these brackets are already having problems. Signs they need to be changed manually.

In the second case I put the opening bracket before the minus sign. In fact, I put in brackets a negative number with a minus sign. Here's how it looks initially.

17(-6.........

Now, between numbers 17 and bracket there is no sign that mathematics implies multiplication. But I do not have anything to multiply. To answer in the solution remained the same example, I set the bracket additional "plus" sign.

17+(-6.........

Now everything is correctly written. Before the parentheses appears the plus sign and signs before the numbers inside the brackets intact. No mathematical crime I did not commit, just competently get rid of extra action on the replacement characters inside the brackets. Why mathematics always do? They had not taught this. If it is not in the curriculum, and then teach you that no one will. Math enough to know, you need to also know how to use her.