# Operations with negative and positive numbers * Absolute value (modulus) of a number. Addition.* Subtraction. Multiplication. Division. Rules of signs at multiplication and division. *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 insideof which the number is written.
E x a m p l e s :
| 5 | = 5, | 7 | = 7, | 0 | = 0. **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 :
( + 8 ) ( + 5 ) = ( + 8 ) + ( 5 ) = 3; ( + 8 ) ( 5 ) = ( + 8 ) + ( + 5 ) = 13; ( 8 ) ( 5 ) = ( 8 ) + ( + 5 ) = 3; ( 8 ) ( + 5 ) = ( 8 ) + ( 5 ) = 13.*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 absolutevalue 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 :
( 12 ) : ( + 4 ) = 3 .Back |