What’s nine tenths divided by two fifths?

Set up the problem as a complex fraction( one fraction divided by a second fraction)

`( 9/10)/(2/5)`

To simplify the complex fraction multiply both the top and the bottom fractions by the inverse of the bottom fraction. ( multiplication property of equality )

`( 9/10 xx 5/2)/(2/5 xx 5/2)`

The bottom fraction disappears

`2/5 xx 5/2 = 1` This leaves

`9/10 xx 5/2` This gives

`45/20` dividing both sides by 5 gives

`9/4` which is an improper fraction. As a mixed number is

`2 1/4`

`9/10:2/5`

There is a simple rule that says:

`a:(b/c)=axxc/b`

So, we can apply it:

`9/10:2/5=9/10xx5/2=9/(2*cancel(5))xxcancel(5)/2=9/4`

We can write this expression as:

`9/10 -: 2/5 => (9/10)/(2/5)`

We can now use this rule for dividing fractions to evaluate the expression:

`(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))`

`(color(red)(9)/color(blue)(10))/(color(green)(2)/color(purple)(5)) =>(color(red)(9) xx color(purple)(5))/(color(blue)(10) xx color(green)(2)) =>(color(red)(9) xx color(blue)(cancel(color(purple)(5))))/(color(purple)(cancel(color(blue)(10)))2 xx color(green)(2)) => 9/4`

If necessary, we can convert this into mixed number:

`9/4 => (8 + 1)/4 = 8/4 + 1/4 = 2 + 1/4 = 2 1/4`