Answer: The required list is
[tex]\textup{Positive product}~~~~~~~~~~~~~~~~~~~~~~~~\textup{Negative product}\\\\\\(ii)~\left(-\dfrac{1}{3}\right)\times\left(-\dfrac{1}{3}\right)~~~~~~~~~~~~~~~~~~~~~~~~(i)~\left(-\dfrac{1}{3}\right)\times\left(\dfrac{1}{3}\right)\\\\\\(iv)~\left(\dfrac{1}{3}\right)\times\left(\dfrac{1}{3}\right)~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)~\left(\dfrac{1}{3}\right)\times\left(-\dfrac{1}{3}\right)[/tex]
Step-by-step explanation: We are given to match the following products with positive and negative.
We know the following rule :
(i) Product of positive and positive is POSITIVE.
(ii) Product of positive and negative is NEGATIVE.
(iii) Product of negative and positive is NEGATIVE.
(iv) Product of negative and negative is POSITIVE.
First product is
[tex]\left(-\dfrac{1}{3}\right)\times\left(\dfrac{1}{3}\right)=-\dfrac{1}{9}.[/tex]
So, this product is negative.
Second product is
[tex]\left(-\dfrac{1}{3}\right)\times\left(-\dfrac{1}{3}\right)=\dfrac{1}{9}.[/tex]
So, this product is positive.
Third product is
[tex]\left(\dfrac{1}{3}\right)\times\left(-\dfrac{1}{3}\right)=-\dfrac{1}{9}.[/tex]
So, this product is negative.
Fourth product is
[tex]\left(\dfrac{1}{3}\right)\times\left(\dfrac{1}{3}\right)=\dfrac{1}{9}.[/tex]
So, this product is positive.
Thus, the required list is
[tex]\textup{Positive product}~~~~~~~~~~~~~~~~~~~~~~~~\textup{Negative product}\\\\\\(ii)~\left(-\dfrac{1}{3}\right)\times\left(-\dfrac{1}{3}\right)~~~~~~~~~~~~~~~~~~~~~~~~(i)~\left(-\dfrac{1}{3}\right)\times\left(\dfrac{1}{3}\right)\\\\\\(iv)~\left(\dfrac{1}{3}\right)\times\left(\dfrac{1}{3}\right)~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)~\left(\dfrac{1}{3}\right)\times\left(-\dfrac{1}{3}\right)[/tex]
