# (ii)  What will be the sign of the product if we multiply together:                (a) 8 negative integers and 3 positive integers?                (b) 5 negative integers and 4 positive integers?                (c) (–1), twelve times?                (d) (–1), 2m times, m is a natural number?

We know,

If the number of negative integers in a product is even, then the product is a positive integer and if the number of negative integers in a product is odd, then the product is a negative integer

And, any number of positive integers will always give a positive integer.

So, the sign of the product will be decided by the number of negative integers.

(a) 8 negative integers and 3 positive integers: Even number of negative integers, hence product is positive.

(b) 5 negative integers and 4 positive integers: Odd number of negative integers, hence product is negative.

(c) (–1), twelve times: Even number of negative integers, hence product is positive.

(d) (–1), 2m times, m is a natural number: Even number of negative integers, hence product is positive.

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