Question

When you multiply 2/3 by a fraction less than one, how does the product compare to the factors? Explain

Answer 1

Hello from MrBillDoesMath!

Answer:

Not so simple. See discussion below

Discussion:

Consider these two examples:

0<= f < = 1, then             (2/3) * f < (2/3) * 1  = 2/3      

   so the product is less than either of the factors

f = -5, then (2/3)* (-5/1) =  -10/3

   so the product is actually larger than the factor -5 !

In other words, the general answer depends upon the sign as well as value of the fraction. The problem probably meant that multiplying a positive fraction by a number less than 1 and >= 0 makes the product smaller. But as your see from the above examples, a more fine grained analysis is required for a full answer.

Thank you,

MrB