Law of Signs In Mathematics

The law of signs or the rule of signs are indications that allow us to determine the sign of a final result when operations are performed with integers. Generally speaking, positive numbers may or may not have the “+” sign.

Law of signs in addition

When performing addition operations with integers, the following rules are followed:

  • if the two numbers are positive (greater than zero): they add up and keep their “+” sign.
  • If the two numbers are negative (less than zero): they are added and the “-” sign remains.
  • If a number greater than zero and a number less than zero are added: they are subtracted and the sign of the number with the greatest absolute value is left.

Examples of sign law in addition

When we have two numbers greater than zero, that is, with a “+” sign:

 

When we have two numbers less than zero, that is, negative numbers with a “-” sign:

 

When we have numbers with different signs:

 

Law of signs in subtraction

When you perform subtraction operations on whole numbers, the subtraction sign changes the sign of the number that follows it:

 

 

Law of signs in multiplication

When we multiply whole numbers, the result is equal to the multiplication of the figures with the sign as shown in the table:

Multiplication +
+ +
+

That is to say:

  • If two numbers with a “+” sign are multiplied, the result will have a “+” sign;
  • If two numbers with sign “-” are multiplied, the result will have the sign “+”; and
  • If a number with a “+” sign and another with a “-” sign are multiplied, the result will have a “-” sign.

Examples of the law of signs in multiplication

Multiplication -10 -5 5 10 twenty
-10 100 fifty -fifty -100 -200
-5 fifty 25 -25 -fifty -100
5 -fifty -25 25 fifty 100
10 -100 -fifty fifty 100 200
twenty -200 -100 100 200 400

Law of signs in division

When we divide two whole numbers, the result is equal to the division of the figures with the sign as shown in the table:

Division +
+ +
+

That is to say:

  • If two numbers with a “+” sign are divided, the result will have a “+” sign;
  • if two numbers with sign “-” are divided, the result will have the sign “+”; and
  • If you divide a number with a “+” sign and another with a “-” sign, the result will have a “-” sign.

Examples of law of signs in division

Division -10 -5 5 10 twenty
-10 1 2 -2 -1 -1/2
-5 1/2 1 -1 -1/2 -1/4
5 -1/2 -1 1 1/2 1/4
10 -1 -2 2 1 1/2
twenty -2 -4 4 2 1

 

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