If you multiply a non zero whole number by a fraction less then 1 is the product always less than the whole number? And why?

Answer 1

Yes!

Remember that a fraction less than one represents a division; e.g. R * (2/3) means divide 3 into 2*R.

That is not a really good reason; I will have to think about it some more and get back to you with a clear reason.

LATER -- here is the reason

A fraction less than one means the quotient of two positive integers n (the numerator) and d (the denominator) such that n < d

n < d

Now multiply by a positive integer N

Nn < Nd

Divide by d

N (n/d) < N

Sorry for the delay in getting you the full answer.

n < d