What will be the sign of the product if we multiply together
(i) 8 negative integers and 1 positive integer?
(ii) 21 negative integers and 3 positive integers?
(iii) 199 negative integers and 10 positive integers?

Negative numbers, when multiplied even number of times, give a positive number. However, when multiplied odd number of times, they give a negative number. Therefore, we have:
(i) (negative) $8$ times × (positive) $1$ time = positive × positive = positive integer
(ii) (negative) $21$ times × (positive) $3$ times = negative ×positive = negative integer
(iii) (negative) $199$ times × (positive) $10$ times = negative × positive = negative integer