Question

How do you simplify `\frac{\frac{8}{5}}{4}`?

Answer 1

See below.

Explanation:

There are a few ways to tackle this:

If we look at this as being just like any other fraction, then the same rules will apply:

`(8/5)/4` we can multiply top and bottom without changing the relationship so, using `8/5 -: 4`

Multiply top and bottom by `5`:

`((cancel(5)(8))/(cancel(5)))/(5(4))` = `8/((5)(4)` = `8/20` = `color(blue)(2/5)`

Alternatively:

`8/5 -: 4` is equal to `8/5 xx` the reciprocal of `4`. The reciprocal of a number can be found by putting `1` over the number. So:

Reciprocal of `4` is `1/4`

So we have:

`8/5 xx 1/4 = (8xx1)/(5 xx 4)= 8/20=color(blue)(2/5)`

There are even more ways to achieve this, but you can just use the one you find easiest.

Answer 2

`(8/5)/4=color(red)(2/5)`

Explanation:

In general `color(blue)a/color(magenta)b=color(blue)axxcolor(magenta)(1/b)`

In this case we have
`color(white)("XXX")color(blue)a=color(blue)(8/5)` and `color(magenta)b=color(magenta)4`

So
`color(white)("XXX")(color(blue)(8/5))/color(magenta)4=color(blue)(8/5) xx color(magenta)(1/4)`

`color(white)("XXXXX")=(cancel(8)^2)/5xx1/cancel(4)`

`color(white)("XXXXX")=2/5`