Question

Sam is going to multiply 3 digit whole number times a two digit whole number. He will make the greatest product he can make and the least product he can make. What is the difference between products?

Answer 1

Sam is going to multiply 3 digit whole number times a two digit whole number.

Let the numbers for getting the greatest product be,

3 digit whole number = 999        (after 999 we have 1000 - a 4 digit number)

2 digit whole number = 99           (after 99 we have 100 - a 3 digit number)

The product of these 2 is = 999 × 99 = 98901

Let the numbers for getting the least product be,

3 digit whole number = 100          (before 100 we have 99 - a 2 digit number)

2 digit whole number = 10             (before 10 we have 9 - a 1 digit number.)

The product of these 2 is = 100 × 10 = 1000

The difference between the greatest product  and least product is

98901 - 1000 = 97901