Who out there has ever heard anyone talk about the rule of signs? Even before learning about it, many people are scared to death of this little rule! But you will see how simple it is to use it in calculations.
Whenever we need to perform a multiplication or division of positive and negative numbers, we must pay attention to the sign of the result. To calculate 2 ∙ 3or 4: 2,you shouldn't have any doubts, but what if the multiplication is (– 2) ∙ (– 3)and the division, (+ 4): (– 2), how will we do these calculations?
To perform multiplication and division of negative numbers, we must always resort to the rule of signs. This rule tells you what the sign of the result will be. To use it, you just need to remember two pieces of information:
1 – if the signs are EQUALS, the result will be POSITIVE.
2 – if the signs are MANY DIFFERENT, the result will be NEGATIVE.
Knowing the sign of the result, simply multiply or divide the numbers. Remember that if the result is positive, you don't need to put the + sign, if the number is unsigned, we can guarantee that it is positive. Let's see some examples:
(– 2) ∙ (– 3) → equal signs, the result is positive.
(– 2) ∙ (– 3) = 6
(+1) ∙ (– 5) → different signs, the result is negative.
(+ 1) ∙ (– 5) = – 5
(+ 3) ∙ (+ 4) → equal signs, the result is positive.
(+ 3) ∙ (+ 4) = 12
(– 7) ∙ (+ 2) → different signs, the result is negative.
(– 7) ∙ (+ 2) = – 14
(– 10): (– 2) → equal signs, the result is positive.
(– 10): (– 2) = 5
(– 5): (+1) → different signs, the result is negative.
(– 5): (+ 1) = – 5
(+ 9): (+ 3) → equal signs, the result is positive.
(+ 9): (+ 3) = 3
(+ 12): (– 4) → different signs, the result is negative.
(+ 12): (– 4) = – 3
But what if you multiply or divide several numbers at the same time? In this case, we can analyze the signs every two and do the calculation normally! Let's see an example of a multiplication of several positive and negative numbers:
(– 2) ∙ (– 1) ∙ (+ 3) ∙ (– 5) ∙ (+ 4)
Let's solve these multiplications by analyzing the numbers always in pairs:
(– 2) ∙ (– 1) ∙ (+ 3) ∙ (– 5) ∙ (+ 4)
We have a multiplication of equal signs, so the result is positive (+2):
(+ 2)∙ (+ 3) ∙ (– 5) ∙ (+ 4)
We have again a multiplication of numbers with the same sign, so the result is positive (+6):
(+ 6) ∙ (– 5) ∙ (+ 4)
Now the multiplication is between numbers of different signs, so the result of the multiplication is negative (– 30):
(– 30) ∙ (+ 4)
We only have a multiplication between numbers of different signs, which guarantees us a result negative: – 120.
By Amanda Gonçalves
Graduated in Mathematics
