What is the product of the greatest negative integer and the smallest positive integer?
(a) 2
(b) – 2
(c) – 1
(d) 1

Hint: Integers are numbers that can be written without a fractional part. The greatest negative integer is the number one less than 0 and the smallest positive integer is the number one greater than 0. Use this to find their product.

Complete step-by-step answer:
Integers include whole numbers and negative whole numbers. It can be positive, negative or zero. The numbers that can be simplified to non-fractional numbers is an integer. Examples are 1, 0, - 2, etc.
There are an infinite number of integers. The numbers with the negative sign are called the negative integers and the number without a sign or with a positive sign are called positive integers. The number 0 is neither positive nor negative.
The smallest positive integer is the first positive integer. The first positive integer is one greater than 0 and the number is 1.
The greatest negative integer is the first negative integer from zero. The first negative integer from zero is one less than 0 and the number is – 1.
Now, we need to find the product of the number 1 and – 1. We know that 1 is the multiplicative identity and any number multiplied with 1 will give the same number. Hence, we have:
\[1 \times - 1 = - 1\]
Hence, the correct answer is option (c).

Note: We may think that 0 is the first positive integer but it is wrong. The number 0 is neither positive nor negative and it divides the positive integers and negative integers.