Question

How do you reorder these numbers from least to greatest: `2/5, 0, -3/2, -9/8, 8/7`?

Answer 1

`-3/2," "-9/8," "0," "2/5," "8/7`

Explanation:

Another method of comparing these numbers is to convert them to fractions which have a common denominator. IN this way you will avoid working with recurring decimals.
Note that some of the fractions are negative.

The LCM is `280`

`2/5 = 112/280`

`0 =0/280`

`-3/2 =( -420)/280" "larr` the smallest

`-9/8 = (-315)/280`

`8/7 = 320/280" "larr` the greatest

Now you compare the numerators.

Remember to use the numbers in their original form.

Answer 2

The order from least to greatest is `{-3/2,-9/8,0,2/5,8/7}`

Explanation:

I am just adding another answer as first of all, I feel taking GCD and then comparing is a bit complicated and secondly what one does if some irrational numbers such as `sqrt3` or `pi` etc. are included.

Hence, in my view it is better to convert all given numbers to decimal numbers say up to `4` or `5` or more places of decimals for a better result.

Now `2/5=0.400000`

`0=0.000000`,

`-3/2=-1.500000`

`-9/8=-1.125000`

`8/7=1.142857`

Comparing them we find that the order from least to greatest is

`{-3/2,-9/8,0,2/5,8/7}`