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"
Do not worry about your difficulties in mathematics, I assure you that mine are greater
". Einstein, Albert (1879-1955)
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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.
Example:
| – 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.
Examples:
( + 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.
Examples:
( – 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.
Examples:
( + 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.
Examples:
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:
+ : + = +
+ : – = –
– : + = –
– : – = +
Example:
( – 12 ) : ( + 4 ) = – 3 .
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