What is the benchmark of 19/20 and 27/28 using 1?

Question

We are using reasoning methods like finding the benchmark to come up with which on is greater, but we can't use common denominators. I'm struggling, HELP!

Answer 1

Shelby,

Are you trying to compare the two fractions? If the following isn't what you need, could you please clarify what the requirement is and what exactly you're allowed and not allowed (other than not allowed common deminators). But notice this:

 

19/20 = 1 - 1/20 and

 

27/28 = 1 - 1/28

 

Now 28>20 so 1/28 is smaller than 1/20

 

Thus 1-(1/28) is BIGGER than 1 - (1/20) since we get a bigger number if we subtracted a smaller amount.

 

Thus since 1-(1/28) > 1 - (1/20) we conclude that 27/28 > 19/20

 

If that's not what you're trying to prove or what you're allowed to use, please clarify these two issues and I'll try to respond again.

Answer 2

What is the question asking you?  A benchmark is a number used to give a close approximation to the answer of a question like" what is 19 divided by 20" or "what is 27 divided by 28."  We know that 20 divided by 20 is equal to 1.  Likewise, 28 divided by 28 is also 1.  So it is very easy to say that 19/20 is slightly less than 1.  The same can be said about 27/28.