Question

Is the quotient `4.5 -: .9` greater or less than `4.5`? Why?

Answer 1

`4.5/.9>4.5` because `4.5/.9` is equivalent to 5.

Explanation:

Is `4.5/.9>4.5` or is `4.5/.9<4.5`?

Let's think this way - we know that:

`4.5/1=4.5`

If we split 4.5 into two pieces, that's:

`4.5/2=2.25`

and if we split 4.5 into ten pieces, that's:

`4.5/10=.45`

So what are we saying when we have `4.5/.9`? It means that we don't have a complete piece - it's .1 short of a complete piece. So how big is a whole piece?

`4.5/.9=(4.5/1)/(9/10)=(4.5/1)(10/9)=45/9=5`

And so `4.5/.9>4.5` because `4.5/.9` is equivalent to 5.