Question

How would you order the number from least to greatest: `\frac{\sqrt{6}}{2}, \frac{61}{50}, \sqrt{1.5}, \frac{16}{13}`?

Answer 1

I assume we may not use a calculator, otherwise it's quite simple.

Let's look at the first: this can be written as:
`root 2 6/root 2 4=root 2 (6/4)=root 2 1.5` is the same as number three.

number two: `61/50=1+11/50=1+22/100=1.22`

number four: `16/13=1+3/13`

These numbers are all close together (I did check with a calculator) so I think this one cannot be solved without a calculator.

The correct order is:
`61/50=1.22` then

`root 2 6/2` and `root 2 1.5` (both`=1.2247...`) then

`16/13=1.2307...`

I'm sorry I can't do this by reasoning alone, but I hope this helps.

Answer 2

I don't think my answer was correct.