Rule of signs

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Identify positive or negative sign

The signs that accompany the numbers are very important, since they indicate whether the number is positive or negative. To identify if a number is positive, a cross is placed to the left of the number although many times a sign is not placed and it is understood that it is positive, on the other hand, to identify if a number is negative, a middle dash or line is placed to the left of the number.

3 ← Positive
+ 3 ← Positive
- 3 ← Negative

Note: For a positive number, to the left of the number we have no other number it is possible to leave unsigned.

On a number line you can see the difference between a positive signed number and a negative sign.

• -1
• 0
• 1

The zero is considered a neutral number, to the left of the zero of the previous line corresponds to the negative numbers to the least infinite (-inf) and to the right of the zero the positive numbers to the most infinite (+ inf) are considered

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Laws or rules of signs

The law or sign rule indicates the sign that prevails when operations of two equal or different signs are performed, and is applied differently for various mathematical operations:

Sign rule for addition and subtraction

• When two positive numbers are added, the result will have a positive sign. 3 + 5 = 8
• When two numbers are added or subtracted, one with a positive sign and the other with a negative sign, the result will have the sign of the largest number. 5 - 6 = - 1
• When two numbers are added or subtracted, one with a negative sign and the other with a positive sign, the result will have the sign of the largest number. - 7 + 4 = - 3
• When two negative numbers are subtracted, the result will have a negative sign. - 5 - 4 = - 9

Simplifying the above:

positive y positive = positive
positive + negative = largest number
negative + positive = largest number
negative y negative = negativo

Learn more about: “Sum” →

Learn more about: “Subtraction” →

Signs rule for multiplication and division

• When two positive numbers are multiplied or divided, the result will have a positive sign. (+) x (+) = +
  (+) ÷ (+) = +
• When two numbers are multiplied or divided, one with a positive sign and the other with a negative sign, the result will have a negative sign. (+) x (-) = -
  (+) ÷ (-) = -
• When two numbers are multiplied or divided, one with a negative sign and the other with a positive sign, the result will have a negative sign. (-) x (+) = -
  (-) ÷ (+) = -
• When two negative numbers are multiplied or divided, the result will have a positive sign. (-) x (-) = +
  (-) ÷ (-) = +

Learn more about: “Multiplication” →

Learn more about: “Division” →

Rule of signs for potentiation

• If the power exponent is even , the result will be a sign positive . (+)^par = +
  (-)^par = +
• If the power exponent is odd the result will keep the sign of the base number. (+)^impar = +
  (-)^impar = -

Learn more about: “Exponent” →