Operations with negative and positive numbers

Absolute value (modulus): for a negative number  this is a positive number, received by changing the sign “ – “  by  “ + ”; for a positive number and zero this is the number itself.  The designation of an absolute value (modulus) of a number is the two straight brackets inside of which the number is written.
E x a m p l e s : 

Addition:

1)  at addition of two numbers of the same sign their absolute values are added and before the sum their common sign      is written.      E x a m p l e s : ( + 6 ) + ( + 5 ) =   11 ; ( – 6 ) + ( – 5 ) = – 11 ; 2)  at addition of two numbers with different signs their absolute values are subtracted (the smaller from the greater)      and a sign of a number, having a greater absolute value is chosen.      E x a m p l e s : ( – 6 ) + ( + 9 ) =    3 ; ( – 6 ) + ( + 3 ) = – 3 .

Subtraction:  it is possible to change subtraction of  two numbers by addition, thereat a minuend saves its sign, and a subtrahend is taken with the back sign.
E x a m p l e s :

Multiplication: at multiplication of two numbers their absolute values are multiplied, and a product has the sign “ + ”, if signs of factors are the same, and  “ – “, if the signs are different. The next scheme ( a rule of signs at multiplication) is useful:

At multiplication of some factors ( two and more ) a product has the sign “ + ”, if a number of negative factors is even, and the sign “ – “,  if this number is odd.
E x a m p l e :

Division: at division of  two numbers the first absolute value is divided by the second and a quotient has the sign “ + ”, if signs of dividend and divisor  are the same, and “ – “, if they are different. The same rule of signs as at multiplication acts:

E x a m p l e : 

Back