Question

Amy made the following conjecture: When any number is multiplied by itself, the product will be greater than this starting number.

For example: in 2x2=4, the product 4 is greater than the starting number 2.
Megan disagreed with Amy's conjecture, however,

`(1)/(2 ) * (1)/(2) = (1)/(4)`
and

`(1)/(4)`
is less than

`(1)/(2)`
how could Amy's conjecture be improved? Explain the change(s) you would make

Answer 1

Amy's conjecture can be improved by including a limit. Since any number greater than one multiplied by itself will be greater (for example, 2x2 = 4). But, any number less than one (excluding zero, but including negatives) will yield a smaller result.

Amy's conjecture should be

"When a number greater than 1 is multiplied by itself, the product will be greater than the starting number,"

Answer 2

Change the conjecture to: The product of a number and itself will be greater than the number if the number is greater than one.