For integers a and b, where 4 (less than) a (less than) 6 and 8 (less than) b (less than) 10, what is the greatest possible value of 3/(b-a)?

I know the answer but I need an explanation as to how I get the answer.
Answer: 3/2

Question

For integers a and b, where 4 (less than) a (less than) 6 and 8 (less than) b (less than) 10, what is the greatest possible value of 3/(b-a)?

I know the answer but I need an explanation as to how I get the answer.
Answer: 3/2

mathmath333 · Answer

can u form the equation from the words

anonymous · Answer

yes

anonymous · Answer

$$4\le a \le 6$$
$$8\le b \le 10$$

mathmath333 · Answer

it should be
$\large\tt \begin{align} \color{black}{
4<a<6\hspace{.33em}\~\
8<b<10\hspace{.33em}\~\
}\end{align}$

mathmath333 · Answer

$\Huge \leq $  is pronounced as "less than equal to"

anonymous · Answer

oh yes thats what i meant my fault

mathmath333 · Answer

ohk

mathmath333 · Answer

i mean

$\Large \dfrac{3}{b-a}_{max}$

anonymous · Answer

Alright yes thats what the question is asking for

anonymous · Answer

The answer its says is 3/2

anonymous · Answer

But I'm not sure how to get there exactly

mathmath333 · Answer

ohk thats easy

mathmath333 · Answer

for finding

$\Large \dfrac{3}{b-a}_{max}$

do u agree that 

$\large (b-a)$  should be minimum

anonymous · Answer

Hmm how is that so?

mathmath333 · Answer

well consider the fraction $\dfrac{8}{y}$ if u have y digits from 

${1~to~9}$ when will be $\  \dfrac{8}{y}$ will be maximim ,try to put each digit between 
1 and 9

anonymous · Answer

Okay i  think i got you now

mathmath333 · Answer

so which digit of $y$ will make $\dfrac{8}{y}$maximum

anonymous · Answer

Since it's between 1 and 9 well 2 cause itll give you 4 right?

mathmath333 · Answer

okay if $y$ was $1$ then ?

anonymous · Answer

8 would be the max

mathmath333 · Answer

so for making fraction maximum the denominator should be the least did u agree that ?

anonymous · Answer

Yes!

mathmath333 · Answer

so 

or finding

$\Large \dfrac{3}{b−a}_{max}$



$\Large (b−a)$  should be minimum, right ?

anonymous · Answer

Yes alright now i understand your poibt.

mathmath333 · Answer

ohk so now for making $\Large (b-a)$ minimum

do u think $\large b$ should be minimum and $\large a$ should be maximim

or 

do u think $\large a$ should be minimum and $\large b$ should be maximim

anonymous · Answer

b minimum and a maximum

mathmath333 · Answer

thats right !

anonymous · Answer

3/8-6 correct?

anonymous · Answer

3/2

mathmath333 · Answer

yes!  $\Huge \checkmark$

anonymous · Answer

Wow so this was a really simple equation hah XD Alright thank you so much!

mathmath333 · Answer

yw