# 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 ##### byAbdullah Sam
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