Question

Q.6)
What will be the sign of the product, if we
multiply together:
8 negative integers and 1 positive integer?
ii. 21 negative integers and 3 positive integers?
i.​

Answer 1

Answer:

The answer is negative. Odd numbers of negative integers when multiplied yield negative integer only. Consider an integer -x = (-1)*x. Let -y be another integer.

Then product of -x * -y = (-1)^2* xy = xy

similarly - x* -y* -z = (-1)^3* xyz = -xyz

-x*-y*-z*-s = (-1)^4* xyzs = xyzs

proceeding same way, you will observe that multiple of odd negative numbers are resulting in negative digit while multiples of even negative numbers will result in positive digits. A digit when multiplied by positive numbers, the sign of the resultant digit wont change. Hence the answer should be a positive.

Answer 2

Answer:

i. It will be positive. Ex- (-2)⁸×3=256×3=768

ii. It will be negative Ex- -(1)²¹×9=-9

Hope it'll help you.....